id	sid	tid	token	lemma	pos
randomwalker-info-585	1	1	On	on	IN
randomwalker-info-585	1	2	the	the	DT
randomwalker-info-585	1	3	Instability	Instability	NNP
randomwalker-info-585	1	4	of	of	IN
randomwalker-info-585	1	5	Bitcoin	Bitcoin	NNP
randomwalker-info-585	1	6	Without	without	IN
randomwalker-info-585	1	7	the	the	DT
randomwalker-info-585	1	8	Block	Block	NNP
randomwalker-info-585	1	9	Reward	Reward	NNP
randomwalker-info-585	1	10	Miles	Miles	NNP
randomwalker-info-585	1	11	Carlsten	Carlsten	NNP
randomwalker-info-585	1	12	carlsten@cs.princeton.edu	carlsten@cs.princeton.edu	IN
randomwalker-info-585	1	13	Harry	Harry	NNP
randomwalker-info-585	1	14	Kalodner	Kalodner	NNP
randomwalker-info-585	1	15	kalodner@cs.princeton.edu	kalodner@cs.princeton.edu	NNP
randomwalker-info-585	1	16	S.	S.	NNP
randomwalker-info-585	1	17	Matthew	Matthew	NNP
randomwalker-info-585	1	18	Weinberg	Weinberg	NNP
randomwalker-info-585	1	19	smweinberg@princeton.edu	smweinberg@princeton.edu	-LRB-
randomwalker-info-585	1	20	Arvind	Arvind	NNP
randomwalker-info-585	1	21	Narayanan	Narayanan	NNP
randomwalker-info-585	1	22	arvindn@cs.princeton.edu	arvindn@cs.princeton.edu	IN
randomwalker-info-585	1	23	ABSTRACT	ABSTRACT	NNP
randomwalker-info-585	1	24	Bitcoin	Bitcoin	NNP
randomwalker-info-585	1	25	provides	provide	VBZ
randomwalker-info-585	1	26	two	two	CD
randomwalker-info-585	1	27	incentives	incentive	NNS
randomwalker-info-585	1	28	for	for	IN
randomwalker-info-585	1	29	miners	miner	NNS
randomwalker-info-585	1	30	:	:	:
randomwalker-info-585	1	31	block	block	NN
randomwalker-info-585	1	32	rewards	reward	NNS
randomwalker-info-585	1	33	and	and	CC
randomwalker-info-585	1	34	transaction	transaction	NN
randomwalker-info-585	1	35	fees	fee	NNS
randomwalker-info-585	1	36	.	.	.
randomwalker-info-585	2	1	The	the	DT
randomwalker-info-585	2	2	former	former	JJ
randomwalker-info-585	2	3	accounts	account	NNS
randomwalker-info-585	2	4	for	for	IN
randomwalker-info-585	2	5	the	the	DT
randomwalker-info-585	2	6	vast	vast	JJ
randomwalker-info-585	2	7	ma-	ma-	JJ
randomwalker-info-585	2	8	jority	jority	NN
randomwalker-info-585	2	9	of	of	IN
randomwalker-info-585	2	10	miner	miner	NN
randomwalker-info-585	2	11	revenues	revenue	NNS
randomwalker-info-585	2	12	at	at	IN
randomwalker-info-585	2	13	the	the	DT
randomwalker-info-585	2	14	beginning	beginning	NN
randomwalker-info-585	2	15	of	of	IN
randomwalker-info-585	2	16	the	the	DT
randomwalker-info-585	2	17	system	system	NN
randomwalker-info-585	2	18	,	,	,
randomwalker-info-585	2	19	but	but	CC
randomwalker-info-585	2	20	it	-PRON-	PRP
randomwalker-info-585	2	21	is	be	VBZ
randomwalker-info-585	2	22	expected	expect	VBN
randomwalker-info-585	2	23	to	to	TO
randomwalker-info-585	2	24	transition	transition	VB
randomwalker-info-585	2	25	to	to	IN
randomwalker-info-585	2	26	the	the	DT
randomwalker-info-585	2	27	latter	latter	JJ
randomwalker-info-585	2	28	as	as	IN
randomwalker-info-585	2	29	the	the	DT
randomwalker-info-585	2	30	block	block	NN
randomwalker-info-585	2	31	rewards	reward	NNS
randomwalker-info-585	2	32	dwindle	dwindle	VBP
randomwalker-info-585	2	33	.	.	.
randomwalker-info-585	3	1	There	there	EX
randomwalker-info-585	3	2	has	have	VBZ
randomwalker-info-585	3	3	been	be	VBN
randomwalker-info-585	3	4	an	an	DT
randomwalker-info-585	3	5	implicit	implicit	JJ
randomwalker-info-585	3	6	belief	belief	NN
randomwalker-info-585	3	7	that	that	IN
randomwalker-info-585	3	8	whether	whether	IN
randomwalker-info-585	3	9	miners	miner	NNS
randomwalker-info-585	3	10	are	be	VBP
randomwalker-info-585	3	11	paid	pay	VBN
randomwalker-info-585	3	12	by	by	IN
randomwalker-info-585	3	13	block	block	NN
randomwalker-info-585	3	14	rewards	reward	NNS
randomwalker-info-585	3	15	or	or	CC
randomwalker-info-585	3	16	transaction	transaction	NN
randomwalker-info-585	3	17	fees	fee	NNS
randomwalker-info-585	3	18	does	do	VBZ
randomwalker-info-585	3	19	not	not	RB
randomwalker-info-585	3	20	affect	affect	VB
randomwalker-info-585	3	21	the	the	DT
randomwalker-info-585	3	22	security	security	NN
randomwalker-info-585	3	23	of	of	IN
randomwalker-info-585	3	24	the	the	DT
randomwalker-info-585	3	25	block	block	NN
randomwalker-info-585	3	26	chain	chain	NN
randomwalker-info-585	3	27	.	.	.
randomwalker-info-585	4	1	We	-PRON-	PRP
randomwalker-info-585	4	2	show	show	VBP
randomwalker-info-585	4	3	that	that	IN
randomwalker-info-585	4	4	this	this	DT
randomwalker-info-585	4	5	is	be	VBZ
randomwalker-info-585	4	6	not	not	RB
randomwalker-info-585	4	7	the	the	DT
randomwalker-info-585	4	8	case	case	NN
randomwalker-info-585	4	9	.	.	.
randomwalker-info-585	5	1	Our	-PRON-	PRP$
randomwalker-info-585	5	2	key	key	JJ
randomwalker-info-585	5	3	insight	insight	NN
randomwalker-info-585	5	4	is	be	VBZ
randomwalker-info-585	5	5	that	that	IN
randomwalker-info-585	5	6	with	with	IN
randomwalker-info-585	5	7	only	only	JJ
randomwalker-info-585	5	8	transaction	transaction	NN
randomwalker-info-585	5	9	fees	fee	NNS
randomwalker-info-585	5	10	,	,	,
randomwalker-info-585	5	11	the	the	DT
randomwalker-info-585	5	12	variance	variance	NN
randomwalker-info-585	5	13	of	of	IN
randomwalker-info-585	5	14	the	the	DT
randomwalker-info-585	5	15	block	block	NN
randomwalker-info-585	5	16	reward	reward	NN
randomwalker-info-585	5	17	is	be	VBZ
randomwalker-info-585	5	18	very	very	RB
randomwalker-info-585	5	19	high	high	JJ
randomwalker-info-585	5	20	due	due	JJ
randomwalker-info-585	5	21	to	to	IN
randomwalker-info-585	5	22	the	the	DT
randomwalker-info-585	5	23	exponentially	exponentially	RB
randomwalker-info-585	5	24	distributed	distribute	VBN
randomwalker-info-585	5	25	block	block	NN
randomwalker-info-585	5	26	arrival	arrival	NN
randomwalker-info-585	5	27	time	time	NN
randomwalker-info-585	5	28	,	,	,
randomwalker-info-585	5	29	and	and	CC
randomwalker-info-585	5	30	it	-PRON-	PRP
randomwalker-info-585	5	31	becomes	become	VBZ
randomwalker-info-585	5	32	attractive	attractive	JJ
randomwalker-info-585	5	33	to	to	TO
randomwalker-info-585	5	34	fork	fork	VB
randomwalker-info-585	5	35	a	a	DT
randomwalker-info-585	5	36	“	"	``
randomwalker-info-585	5	37	wealthy	wealthy	JJ
randomwalker-info-585	5	38	”	"	''
randomwalker-info-585	5	39	block	block	NN
randomwalker-info-585	5	40	to	to	TO
randomwalker-info-585	5	41	“	"	``
randomwalker-info-585	5	42	steal	steal	VB
randomwalker-info-585	5	43	”	"	''
randomwalker-info-585	5	44	the	the	DT
randomwalker-info-585	5	45	rewards	reward	NNS
randomwalker-info-585	5	46	therein	therein	RB
randomwalker-info-585	5	47	.	.	.
randomwalker-info-585	6	1	We	-PRON-	PRP
randomwalker-info-585	6	2	show	show	VBP
randomwalker-info-585	6	3	that	that	IN
randomwalker-info-585	6	4	this	this	DT
randomwalker-info-585	6	5	results	result	VBZ
randomwalker-info-585	6	6	in	in	IN
randomwalker-info-585	6	7	an	an	DT
randomwalker-info-585	6	8	equilibrium	equilibrium	NN
randomwalker-info-585	6	9	with	with	IN
randomwalker-info-585	6	10	undesirable	undesirable	JJ
randomwalker-info-585	6	11	properties	property	NNS
randomwalker-info-585	6	12	for	for	IN
randomwalker-info-585	6	13	Bitcoin	Bitcoin	NNP
randomwalker-info-585	6	14	’s	’s	POS
randomwalker-info-585	6	15	security	security	NN
randomwalker-info-585	6	16	and	and	CC
randomwalker-info-585	6	17	performance	performance	NN
randomwalker-info-585	6	18	,	,	,
randomwalker-info-585	6	19	and	and	CC
randomwalker-info-585	6	20	even	even	RB
randomwalker-info-585	6	21	non	non	JJ
randomwalker-info-585	6	22	-	-	JJ
randomwalker-info-585	6	23	equilibria	equilibria	JJ
randomwalker-info-585	6	24	in	in	IN
randomwalker-info-585	6	25	some	some	DT
randomwalker-info-585	6	26	circumstances	circumstance	NNS
randomwalker-info-585	6	27	.	.	.
randomwalker-info-585	7	1	We	-PRON-	PRP
randomwalker-info-585	7	2	also	also	RB
randomwalker-info-585	7	3	revisit	revisit	VBP
randomwalker-info-585	7	4	selfish	selfish	JJ
randomwalker-info-585	7	5	mining	mining	NN
randomwalker-info-585	7	6	and	and	CC
randomwalker-info-585	7	7	show	show	VBP
randomwalker-info-585	7	8	that	that	IN
randomwalker-info-585	7	9	it	-PRON-	PRP
randomwalker-info-585	7	10	can	can	MD
randomwalker-info-585	7	11	be	be	VB
randomwalker-info-585	7	12	made	make	VBN
randomwalker-info-585	7	13	profitable	profitable	JJ
randomwalker-info-585	7	14	for	for	IN
randomwalker-info-585	7	15	a	a	DT
randomwalker-info-585	7	16	miner	miner	NN
randomwalker-info-585	7	17	with	with	IN
randomwalker-info-585	7	18	an	an	DT
randomwalker-info-585	7	19	arbitrarily	arbitrarily	RB
randomwalker-info-585	7	20	low	low	JJ
randomwalker-info-585	7	21	hash	hash	NN
randomwalker-info-585	7	22	power	power	NN
randomwalker-info-585	7	23	share	share	NN
randomwalker-info-585	7	24	,	,	,
randomwalker-info-585	7	25	and	and	CC
randomwalker-info-585	7	26	who	who	WP
randomwalker-info-585	7	27	is	be	VBZ
randomwalker-info-585	7	28	arbitrarily	arbitrarily	RB
randomwalker-info-585	7	29	poorly	poorly	RB
randomwalker-info-585	7	30	connected	connect	VBN
randomwalker-info-585	7	31	within	within	IN
randomwalker-info-585	7	32	the	the	DT
randomwalker-info-585	7	33	network	network	NN
randomwalker-info-585	7	34	.	.	.
randomwalker-info-585	8	1	Our	-PRON-	PRP$
randomwalker-info-585	8	2	results	result	NNS
randomwalker-info-585	8	3	are	be	VBP
randomwalker-info-585	8	4	derived	derive	VBN
randomwalker-info-585	8	5	from	from	IN
randomwalker-info-585	8	6	theoretical	theoretical	JJ
randomwalker-info-585	8	7	analysis	analysis	NN
randomwalker-info-585	8	8	and	and	CC
randomwalker-info-585	8	9	confirmed	confirm	VBN
randomwalker-info-585	8	10	by	by	IN
randomwalker-info-585	8	11	a	a	DT
randomwalker-info-585	8	12	new	new	JJ
randomwalker-info-585	8	13	Bitcoin	Bitcoin	NNP
randomwalker-info-585	8	14	mining	mining	NN
randomwalker-info-585	8	15	simulator	simulator	NN
randomwalker-info-585	8	16	that	that	WDT
randomwalker-info-585	8	17	may	may	MD
randomwalker-info-585	8	18	be	be	VB
randomwalker-info-585	8	19	of	of	IN
randomwalker-info-585	8	20	independent	independent	JJ
randomwalker-info-585	8	21	interest	interest	NN
randomwalker-info-585	8	22	.	.	.
randomwalker-info-585	9	1	We	-PRON-	PRP
randomwalker-info-585	9	2	discuss	discuss	VBP
randomwalker-info-585	9	3	the	the	DT
randomwalker-info-585	9	4	troubling	troubling	JJ
randomwalker-info-585	9	5	implications	implication	NNS
randomwalker-info-585	9	6	of	of	IN
randomwalker-info-585	9	7	our	-PRON-	PRP$
randomwalker-info-585	9	8	results	result	NNS
randomwalker-info-585	9	9	for	for	IN
randomwalker-info-585	9	10	Bitcoin	Bitcoin	NNP
randomwalker-info-585	9	11	’s	’s	POS
randomwalker-info-585	9	12	future	future	JJ
randomwalker-info-585	9	13	security	security	NN
randomwalker-info-585	9	14	and	and	CC
randomwalker-info-585	9	15	draw	draw	VB
randomwalker-info-585	9	16	lessons	lesson	NNS
randomwalker-info-585	9	17	for	for	IN
randomwalker-info-585	9	18	the	the	DT
randomwalker-info-585	9	19	design	design	NN
randomwalker-info-585	9	20	of	of	IN
randomwalker-info-585	9	21	new	new	JJ
randomwalker-info-585	9	22	cryptocurrencies	cryptocurrencie	NNS
randomwalker-info-585	9	23	.	.	.
randomwalker-info-585	10	1	1	1	LS
randomwalker-info-585	10	2	.	.	.
randomwalker-info-585	11	1	INTRODUCTION	introduction	VB
randomwalker-info-585	11	2	The	the	DT
randomwalker-info-585	11	3	security	security	NN
randomwalker-info-585	11	4	of	of	IN
randomwalker-info-585	11	5	Bitcoin	Bitcoin	NNP
randomwalker-info-585	11	6	’s	’s	POS
randomwalker-info-585	11	7	consensus	consensus	NN
randomwalker-info-585	11	8	protocol	protocol	NN
randomwalker-info-585	11	9	relies	rely	VBZ
randomwalker-info-585	11	10	on	on	IN
randomwalker-info-585	11	11	min-	min-	NNP
randomwalker-info-585	11	12	ers	ers	NNP
randomwalker-info-585	11	13	behaving	behave	VBG
randomwalker-info-585	11	14	correctly	correctly	RB
randomwalker-info-585	11	15	.	.	.
randomwalker-info-585	12	1	They	-PRON-	PRP
randomwalker-info-585	12	2	are	be	VBP
randomwalker-info-585	12	3	incentivized	incentivize	VBN
randomwalker-info-585	12	4	to	to	TO
randomwalker-info-585	12	5	do	do	VB
randomwalker-info-585	12	6	so	so	RB
randomwalker-info-585	12	7	via	via	IN
randomwalker-info-585	12	8	mining	mining	NN
randomwalker-info-585	12	9	revenues	revenue	NNS
randomwalker-info-585	12	10	under	under	IN
randomwalker-info-585	12	11	the	the	DT
randomwalker-info-585	12	12	assumption	assumption	NN
randomwalker-info-585	12	13	that	that	IN
randomwalker-info-585	12	14	they	-PRON-	PRP
randomwalker-info-585	12	15	are	be	VBP
randomwalker-info-585	12	16	ratio-	ratio-	VBG
randomwalker-info-585	12	17	nal	nal	NNP
randomwalker-info-585	12	18	entities	entity	NNS
randomwalker-info-585	12	19	.	.	.
randomwalker-info-585	13	1	Any	any	DT
randomwalker-info-585	13	2	deviant	deviant	NN
randomwalker-info-585	13	3	miner	miner	NN
randomwalker-info-585	13	4	behavior	behavior	NN
randomwalker-info-585	13	5	that	that	WDT
randomwalker-info-585	13	6	outperforms	outperform	VBZ
randomwalker-info-585	13	7	the	the	DT
randomwalker-info-585	13	8	default	default	NN
randomwalker-info-585	13	9	is	be	VBZ
randomwalker-info-585	13	10	thus	thus	RB
randomwalker-info-585	13	11	a	a	DT
randomwalker-info-585	13	12	serious	serious	JJ
randomwalker-info-585	13	13	threat	threat	NN
randomwalker-info-585	13	14	to	to	IN
randomwalker-info-585	13	15	the	the	DT
randomwalker-info-585	13	16	security	security	NN
randomwalker-info-585	13	17	of	of	IN
randomwalker-info-585	13	18	Bitcoin	Bitcoin	NNP
randomwalker-info-585	13	19	.	.	.
randomwalker-info-585	14	1	Miners	miner	NNS
randomwalker-info-585	14	2	receive	receive	VBP
randomwalker-info-585	14	3	two	two	CD
randomwalker-info-585	14	4	types	type	NNS
randomwalker-info-585	14	5	of	of	IN
randomwalker-info-585	14	6	revenue	revenue	NN
randomwalker-info-585	14	7	:	:	:
randomwalker-info-585	14	8	block	block	NN
randomwalker-info-585	14	9	rewards	reward	NNS
randomwalker-info-585	14	10	and	and	CC
randomwalker-info-585	14	11	transaction	transaction	NN
randomwalker-info-585	14	12	fees	fee	NNS
randomwalker-info-585	14	13	.	.	.
randomwalker-info-585	15	1	The	the	DT
randomwalker-info-585	15	2	former	former	JJ
randomwalker-info-585	15	3	account	account	NN
randomwalker-info-585	15	4	for	for	IN
randomwalker-info-585	15	5	the	the	DT
randomwalker-info-585	15	6	vast	vast	JJ
randomwalker-info-585	15	7	majority	majority	NN
randomwalker-info-585	15	8	of	of	IN
randomwalker-info-585	15	9	miner	miner	NN
randomwalker-info-585	15	10	revenues	revenue	NNS
randomwalker-info-585	15	11	at	at	IN
randomwalker-info-585	15	12	the	the	DT
randomwalker-info-585	15	13	beginning	beginning	NN
randomwalker-info-585	15	14	of	of	IN
randomwalker-info-585	15	15	the	the	DT
randomwalker-info-585	15	16	system	system	NN
randomwalker-info-585	15	17	,	,	,
randomwalker-info-585	15	18	but	but	CC
randomwalker-info-585	15	19	it	-PRON-	PRP
randomwalker-info-585	15	20	is	be	VBZ
randomwalker-info-585	15	21	expected	expect	VBN
randomwalker-info-585	15	22	to	to	TO
randomwalker-info-585	15	23	transition	transition	VB
randomwalker-info-585	15	24	to	to	IN
randomwalker-info-585	15	25	the	the	DT
randomwalker-info-585	15	26	latter	latter	JJ
randomwalker-info-585	15	27	as	as	IN
randomwalker-info-585	15	28	the	the	DT
randomwalker-info-585	15	29	block	block	NN
randomwalker-info-585	15	30	rewards	reward	NNS
randomwalker-info-585	15	31	dwindle	dwindle	NN
randomwalker-info-585	15	32	(	(	-LRB-
randomwalker-info-585	15	33	specifically	specifically	RB
randomwalker-info-585	15	34	,	,	,
randomwalker-info-585	15	35	they	-PRON-	PRP
randomwalker-info-585	15	36	halve	halve	VBP
randomwalker-info-585	15	37	every	every	DT
randomwalker-info-585	15	38	four	four	CD
randomwalker-info-585	15	39	years	year	NNS
randomwalker-info-585	15	40	)	)	-RRB-
randomwalker-info-585	15	41	.	.	.
randomwalker-info-585	16	1	There	there	EX
randomwalker-info-585	16	2	has	have	VBZ
randomwalker-info-585	16	3	been	be	VBN
randomwalker-info-585	16	4	an	an	DT
randomwalker-info-585	16	5	unexamined	unexamined	JJ
randomwalker-info-585	16	6	belief	belief	NN
randomwalker-info-585	16	7	that	that	IN
randomwalker-info-585	16	8	in	in	IN
randomwalker-info-585	16	9	terms	term	NNS
randomwalker-info-585	16	10	of	of	IN
randomwalker-info-585	16	11	the	the	DT
randomwalker-info-585	16	12	security	security	NN
randomwalker-info-585	16	13	of	of	IN
randomwalker-info-585	16	14	the	the	DT
randomwalker-info-585	16	15	block	block	NN
randomwalker-info-585	16	16	chain	chain	NN
randomwalker-info-585	16	17	(	(	-LRB-
randomwalker-info-585	16	18	including	include	VBG
randomwalker-info-585	16	19	incentives	incentive	NNS
randomwalker-info-585	16	20	of	of	IN
randomwalker-info-585	16	21	the	the	DT
randomwalker-info-585	16	22	mining	mining	NN
randomwalker-info-585	16	23	game	game	NN
randomwalker-info-585	16	24	)	)	-RRB-
randomwalker-info-585	16	25	,	,	,
randomwalker-info-585	16	26	it	-PRON-	PRP
randomwalker-info-585	16	27	is	be	VBZ
randomwalker-info-585	16	28	immaterial	immaterial	JJ
randomwalker-info-585	16	29	whether	whether	IN
randomwalker-info-585	16	30	miners	miner	NNS
randomwalker-info-585	16	31	receive	receive	VB
randomwalker-info-585	16	32	(	(	-LRB-
randomwalker-info-585	16	33	say	say	VBP
randomwalker-info-585	16	34	)	)	-RRB-
randomwalker-info-585	16	35	25	25	CD
randomwalker-info-585	16	36	bitcoins	bitcoin	NNS
randomwalker-info-585	16	37	in	in	IN
randomwalker-info-585	16	38	each	each	DT
randomwalker-info-585	16	39	block	block	NN
randomwalker-info-585	16	40	as	as	IN
randomwalker-info-585	16	41	a	a	DT
randomwalker-info-585	16	42	block	block	NN
randomwalker-info-585	16	43	reward	reward	NN
randomwalker-info-585	16	44	or	or	CC
randomwalker-info-585	16	45	25	25	CD
randomwalker-info-585	16	46	bitcoins	bitcoin	NNS
randomwalker-info-585	16	47	in	in	IN
randomwalker-info-585	16	48	expectation	expectation	NN
randomwalker-info-585	16	49	as	as	IN
randomwalker-info-585	16	50	transaction	transaction	NN
randomwalker-info-585	16	51	fees	fee	NNS
randomwalker-info-585	16	52	.	.	.
randomwalker-info-585	17	1	Illustrative	illustrative	JJ
randomwalker-info-585	17	2	example	example	NN
randomwalker-info-585	17	3	(	(	-LRB-
randomwalker-info-585	17	4	Figure	figure	NN
randomwalker-info-585	17	5	1	1	CD
randomwalker-info-585	17	6	)	)	-RRB-
randomwalker-info-585	17	7	.	.	.
randomwalker-info-585	18	1	Imagine	imagine	VB
randomwalker-info-585	18	2	a	a	DT
randomwalker-info-585	18	3	popula-	popula-	NN
randomwalker-info-585	18	4	This	this	DT
randomwalker-info-585	18	5	is	be	VBZ
randomwalker-info-585	18	6	an	an	DT
randomwalker-info-585	18	7	extended	extended	JJ
randomwalker-info-585	18	8	version	version	NN
randomwalker-info-585	18	9	of	of	IN
randomwalker-info-585	18	10	our	-PRON-	PRP$
randomwalker-info-585	18	11	paper	paper	NN
randomwalker-info-585	18	12	that	that	WDT
randomwalker-info-585	18	13	appeared	appear	VBD
randomwalker-info-585	18	14	at	at	IN
randomwalker-info-585	18	15	ACM	ACM	NNP
randomwalker-info-585	18	16	CCS	CCS	NNP
randomwalker-info-585	18	17	2016	2016	CD
randomwalker-info-585	18	18	.	.	.
randomwalker-info-585	19	1	Some	some	DT
randomwalker-info-585	19	2	of	of	IN
randomwalker-info-585	19	3	the	the	DT
randomwalker-info-585	19	4	figures	figure	NNS
randomwalker-info-585	19	5	have	have	VBP
randomwalker-info-585	19	6	been	be	VBN
randomwalker-info-585	19	7	updated	update	VBN
randomwalker-info-585	19	8	with	with	IN
randomwalker-info-585	19	9	more	more	RBR
randomwalker-info-585	19	10	accurate	accurate	JJ
randomwalker-info-585	19	11	versions	version	NNS
randomwalker-info-585	19	12	due	due	JJ
randomwalker-info-585	19	13	to	to	IN
randomwalker-info-585	19	14	improvements	improvement	NNS
randomwalker-info-585	19	15	to	to	IN
randomwalker-info-585	19	16	our	-PRON-	PRP$
randomwalker-info-585	19	17	simulator	simulator	NN
randomwalker-info-585	19	18	.	.	.
randomwalker-info-585	20	1	Figure	figure	NN
randomwalker-info-585	20	2	1	1	CD
randomwalker-info-585	20	3	:	:	:
randomwalker-info-585	20	4	One	one	CD
randomwalker-info-585	20	5	possible	possible	JJ
randomwalker-info-585	20	6	state	state	NN
randomwalker-info-585	20	7	of	of	IN
randomwalker-info-585	20	8	the	the	DT
randomwalker-info-585	20	9	block	block	NN
randomwalker-info-585	20	10	chain	chain	NN
randomwalker-info-585	20	11	and	and	CC
randomwalker-info-585	20	12	two	two	CD
randomwalker-info-585	20	13	possible	possible	JJ
randomwalker-info-585	20	14	actions	action	NNS
randomwalker-info-585	20	15	a	a	DT
randomwalker-info-585	20	16	miner	miner	NN
randomwalker-info-585	20	17	could	could	MD
randomwalker-info-585	20	18	take	take	VB
randomwalker-info-585	20	19	.	.	.
randomwalker-info-585	21	1	tion	tion	NN
randomwalker-info-585	21	2	of	of	IN
randomwalker-info-585	21	3	rational	rational	JJ
randomwalker-info-585	21	4	,	,	,
randomwalker-info-585	21	5	self	self	NN
randomwalker-info-585	21	6	-	-	HYPH
randomwalker-info-585	21	7	interested	interested	JJ
randomwalker-info-585	21	8	miners	miner	NNS
randomwalker-info-585	21	9	.	.	.
randomwalker-info-585	22	1	Consider	consider	VB
randomwalker-info-585	22	2	a	a	DT
randomwalker-info-585	22	3	block	block	NN
randomwalker-info-585	22	4	chain	chain	NN
randomwalker-info-585	22	5	with	with	IN
randomwalker-info-585	22	6	blocks	block	NNS
randomwalker-info-585	22	7	of	of	IN
randomwalker-info-585	22	8	exponentially	exponentially	RB
randomwalker-info-585	22	9	distributed	distribute	VBN
randomwalker-info-585	22	10	rewards	reward	NNS
randomwalker-info-585	22	11	,	,	,
randomwalker-info-585	22	12	as	as	IN
randomwalker-info-585	22	13	we	-PRON-	PRP
randomwalker-info-585	22	14	expect	expect	VBP
randomwalker-info-585	22	15	when	when	WRB
randomwalker-info-585	22	16	the	the	DT
randomwalker-info-585	22	17	fixed	fix	VBN
randomwalker-info-585	22	18	block	block	NN
randomwalker-info-585	22	19	reward	reward	NN
randomwalker-info-585	22	20	runs	run	VBZ
randomwalker-info-585	22	21	out	out	RP
randomwalker-info-585	22	22	.	.	.
randomwalker-info-585	23	1	A	a	DT
randomwalker-info-585	23	2	miner	miner	NN
randomwalker-info-585	23	3	has	have	VBZ
randomwalker-info-585	23	4	numerous	numerous	JJ
randomwalker-info-585	23	5	options	option	NNS
randomwalker-info-585	23	6	to	to	TO
randomwalker-info-585	23	7	consider	consider	VB
randomwalker-info-585	23	8	when	when	WRB
randomwalker-info-585	23	9	mining	mining	NN
randomwalker-info-585	23	10	,	,	,
randomwalker-info-585	23	11	but	but	CC
randomwalker-info-585	23	12	let	let	VB
randomwalker-info-585	23	13	’s	-PRON-	PRP
randomwalker-info-585	23	14	fo-	fo-	DT
randomwalker-info-585	23	15	cus	cus	VB
randomwalker-info-585	23	16	on	on	IN
randomwalker-info-585	23	17	just	just	RB
randomwalker-info-585	23	18	two	two	CD
randomwalker-info-585	23	19	possibilities	possibility	NNS
randomwalker-info-585	23	20	.	.	.
randomwalker-info-585	24	1	She	-PRON-	PRP
randomwalker-info-585	24	2	could	could	MD
randomwalker-info-585	24	3	extend	extend	VB
randomwalker-info-585	24	4	the	the	DT
randomwalker-info-585	24	5	longest	long	JJS
randomwalker-info-585	24	6	chain	chain	NN
randomwalker-info-585	24	7	(	(	-LRB-
randomwalker-info-585	24	8	Option	Option	NNP
randomwalker-info-585	24	9	One	one	CD
randomwalker-info-585	24	10	)	)	-RRB-
randomwalker-info-585	24	11	,	,	,
randomwalker-info-585	24	12	obtaining	obtain	VBG
randomwalker-info-585	24	13	a	a	DT
randomwalker-info-585	24	14	reward	reward	NN
randomwalker-info-585	24	15	of	of	IN
randomwalker-info-585	24	16	5	5	CD
randomwalker-info-585	24	17	and	and	CC
randomwalker-info-585	24	18	leaving	leave	VBG
randomwalker-info-585	24	19	a	a	DT
randomwalker-info-585	24	20	reward	reward	NN
randomwalker-info-585	24	21	of	of	IN
randomwalker-info-585	24	22	0	0	CD
randomwalker-info-585	24	23	for	for	IN
randomwalker-info-585	24	24	the	the	DT
randomwalker-info-585	24	25	next	next	JJ
randomwalker-info-585	24	26	miner	miner	NN
randomwalker-info-585	24	27	(	(	-LRB-
randomwalker-info-585	24	28	at	at	IN
randomwalker-info-585	24	29	least	least	JJS
randomwalker-info-585	24	30	until	until	IN
randomwalker-info-585	24	31	more	more	JJR
randomwalker-info-585	24	32	transac-	transac-	NN
randomwalker-info-585	24	33	tions	tion	NNS
randomwalker-info-585	24	34	arrive	arrive	VBP
randomwalker-info-585	24	35	)	)	-RRB-
randomwalker-info-585	24	36	.	.	.
randomwalker-info-585	25	1	Alternatively	alternatively	RB
randomwalker-info-585	25	2	,	,	,
randomwalker-info-585	25	3	she	-PRON-	PRP
randomwalker-info-585	25	4	could	could	MD
randomwalker-info-585	25	5	fork	fork	VB
randomwalker-info-585	25	6	it	-PRON-	PRP
randomwalker-info-585	25	7	(	(	-LRB-
randomwalker-info-585	25	8	Option	Option	NNP
randomwalker-info-585	25	9	Two	two	CD
randomwalker-info-585	25	10	)	)	-RRB-
randomwalker-info-585	25	11	,	,	,
randomwalker-info-585	25	12	obtaining	obtain	VBG
randomwalker-info-585	25	13	reward	reward	NN
randomwalker-info-585	25	14	of	of	IN
randomwalker-info-585	25	15	55	55	CD
randomwalker-info-585	25	16	while	while	IN
randomwalker-info-585	25	17	leaving	leave	VBG
randomwalker-info-585	25	18	a	a	DT
randomwalker-info-585	25	19	reward	reward	NN
randomwalker-info-585	25	20	of	of	IN
randomwalker-info-585	25	21	50	50	CD
randomwalker-info-585	25	22	Bitcoin	Bitcoin	NNP
randomwalker-info-585	25	23	unclaimed	unclaimed	JJ
randomwalker-info-585	25	24	.	.	.
randomwalker-info-585	26	1	The	the	DT
randomwalker-info-585	26	2	Bitcoin	Bitcoin	NNP
randomwalker-info-585	26	3	protocol	protocol	NN
randomwalker-info-585	26	4	dictates	dictate	VBZ
randomwalker-info-585	26	5	Option	Option	NNP
randomwalker-info-585	26	6	One	one	CD
randomwalker-info-585	26	7	,	,	,
randomwalker-info-585	26	8	but	but	CC
randomwalker-info-585	26	9	a	a	DT
randomwalker-info-585	26	10	quick	quick	JJ
randomwalker-info-585	26	11	reasoning	reasoning	NN
randomwalker-info-585	26	12	suggests	suggest	VBZ
randomwalker-info-585	26	13	that	that	IN
randomwalker-info-585	26	14	Option	Option	NNP
randomwalker-info-585	26	15	Two	two	CD
randomwalker-info-585	26	16	is	be	VBZ
randomwalker-info-585	26	17	better	well	JJR
randomwalker-info-585	26	18	.	.	.
randomwalker-info-585	27	1	To	to	TO
randomwalker-info-585	27	2	reason	reason	VB
randomwalker-info-585	27	3	about	about	IN
randomwalker-info-585	27	4	this	this	DT
randomwalker-info-585	27	5	correctly	correctly	RB
randomwalker-info-585	27	6	,	,	,
randomwalker-info-585	27	7	we	-PRON-	PRP
randomwalker-info-585	27	8	must	must	MD
randomwalker-info-585	27	9	consider	consider	VB
randomwalker-info-585	27	10	which	which	WDT
randomwalker-info-585	27	11	strategies	strategy	NNS
randomwalker-info-585	27	12	the	the	DT
randomwalker-info-585	27	13	other	other	JJ
randomwalker-info-585	27	14	miners	miner	NNS
randomwalker-info-585	27	15	are	be	VBP
randomwalker-info-585	27	16	using	use	VBG
randomwalker-info-585	27	17	.	.	.
randomwalker-info-585	28	1	For	for	IN
randomwalker-info-585	28	2	instance	instance	NN
randomwalker-info-585	28	3	,	,	,
randomwalker-info-585	28	4	if	if	IN
randomwalker-info-585	28	5	all	all	DT
randomwalker-info-585	28	6	other	other	JJ
randomwalker-info-585	28	7	miners	miner	NNS
randomwalker-info-585	28	8	follow	follow	VBP
randomwalker-info-585	28	9	the	the	DT
randomwalker-info-585	28	10	heuristic	heuristic	NN
randomwalker-info-585	28	11	of	of	IN
randomwalker-info-585	28	12	mining	mining	NN
randomwalker-info-585	28	13	on	on	IN
randomwalker-info-585	28	14	the	the	DT
randomwalker-info-585	28	15	block	block	NN
randomwalker-info-585	28	16	they	-PRON-	PRP
randomwalker-info-585	28	17	heard	hear	VBD
randomwalker-info-585	28	18	about	about	IN
randomwalker-info-585	28	19	first	first	RB
randomwalker-info-585	28	20	in	in	IN
randomwalker-info-585	28	21	the	the	DT
randomwalker-info-585	28	22	case	case	NN
randomwalker-info-585	28	23	of	of	IN
randomwalker-info-585	28	24	a	a	DT
randomwalker-info-585	28	25	1-block	1-block	CD
randomwalker-info-585	28	26	fork	fork	NN
randomwalker-info-585	28	27	(	(	-LRB-
randomwalker-info-585	28	28	and	and	CC
randomwalker-info-585	28	29	if	if	IN
randomwalker-info-585	28	30	there	there	EX
randomwalker-info-585	28	31	is	be	VBZ
randomwalker-info-585	28	32	no	no	DT
randomwalker-info-585	28	33	latency	latency	NN
randomwalker-info-585	28	34	in	in	IN
randomwalker-info-585	28	35	the	the	DT
randomwalker-info-585	28	36	network	network	NN
randomwalker-info-585	28	37	)	)	-RRB-
randomwalker-info-585	28	38	,	,	,
randomwalker-info-585	28	39	then	then	RB
randomwalker-info-585	28	40	forking	forking	NN
randomwalker-info-585	28	41	is	be	VBZ
randomwalker-info-585	28	42	ineffective	ineffective	JJ
randomwalker-info-585	28	43	,	,	,
randomwalker-info-585	28	44	and	and	CC
randomwalker-info-585	28	45	Option	option	NN
randomwalker-info-585	28	46	One	one	CD
randomwalker-info-585	28	47	is	be	VBZ
randomwalker-info-585	28	48	clearly	clearly	RB
randomwalker-info-585	28	49	superior	superior	JJ
randomwalker-info-585	28	50	.	.	.
randomwalker-info-585	29	1	On	on	IN
randomwalker-info-585	29	2	the	the	DT
randomwalker-info-585	29	3	other	other	JJ
randomwalker-info-585	29	4	hand	hand	NN
randomwalker-info-585	29	5	,	,	,
randomwalker-info-585	29	6	since	since	IN
randomwalker-info-585	29	7	other	other	JJ
randomwalker-info-585	29	8	miners	miner	NNS
randomwalker-info-585	29	9	are	be	VBP
randomwalker-info-585	29	10	rational	rational	JJ
randomwalker-info-585	29	11	,	,	,
randomwalker-info-585	29	12	perhaps	perhaps	RB
randomwalker-info-585	29	13	they	-PRON-	PRP
randomwalker-info-585	29	14	will	will	MD
randomwalker-info-585	29	15	choose	choose	VB
randomwalker-info-585	29	16	to	to	TO
randomwalker-info-585	29	17	build	build	VB
randomwalker-info-585	29	18	on	on	IN
randomwalker-info-585	29	19	the	the	DT
randomwalker-info-585	29	20	fork	fork	NN
randomwalker-info-585	29	21	instead	instead	RB
randomwalker-info-585	29	22	of	of	IN
randomwalker-info-585	29	23	the	the	DT
randomwalker-info-585	29	24	older	old	JJR
randomwalker-info-585	29	25	block	block	NN
randomwalker-info-585	29	26	,	,	,
randomwalker-info-585	29	27	in	in	IN
randomwalker-info-585	29	28	which	which	WDT
randomwalker-info-585	29	29	case	case	NN
randomwalker-info-585	29	30	Option	option	NN
randomwalker-info-585	29	31	Two	two	CD
randomwalker-info-585	29	32	would	would	MD
randomwalker-info-585	29	33	yield	yield	VB
randomwalker-info-585	29	34	more	more	JJR
randomwalker-info-585	29	35	rewards	reward	NNS
randomwalker-info-585	29	36	.	.	.
randomwalker-info-585	30	1	Examples	example	NNS
randomwalker-info-585	30	2	like	like	IN
randomwalker-info-585	30	3	these	these	DT
randomwalker-info-585	30	4	reveal	reveal	VBP
randomwalker-info-585	30	5	novel	novel	JJ
randomwalker-info-585	30	6	incentive	incentive	NN
randomwalker-info-585	30	7	issues	issue	NNS
randomwalker-info-585	30	8	that	that	WDT
randomwalker-info-585	30	9	sim-	sim-	VBP
randomwalker-info-585	30	10	ply	ply	UH
randomwalker-info-585	30	11	do	do	VBP
randomwalker-info-585	30	12	n’t	not	RB
randomwalker-info-585	30	13	arise	arise	VB
randomwalker-info-585	30	14	when	when	WRB
randomwalker-info-585	30	15	block	block	NN
randomwalker-info-585	30	16	rewards	reward	NNS
randomwalker-info-585	30	17	are	be	VBP
randomwalker-info-585	30	18	fixed	fix	VBN
randomwalker-info-585	30	19	.	.	.
randomwalker-info-585	31	1	The	the	DT
randomwalker-info-585	31	2	goal	goal	NN
randomwalker-info-585	31	3	of	of	IN
randomwalker-info-585	31	4	this	this	DT
randomwalker-info-585	31	5	paper	paper	NN
randomwalker-info-585	31	6	is	be	VBZ
randomwalker-info-585	31	7	to	to	TO
randomwalker-info-585	31	8	understand	understand	VB
randomwalker-info-585	31	9	the	the	DT
randomwalker-info-585	31	10	potential	potential	JJ
randomwalker-info-585	31	11	impact	impact	NN
randomwalker-info-585	31	12	on	on	IN
randomwalker-info-585	31	13	Bitcoin	Bitcoin	NNP
randomwalker-info-585	31	14	’s	’s	POS
randomwalker-info-585	31	15	sta-	sta-	NN
randomwalker-info-585	31	16	bility	bility	NN
randomwalker-info-585	31	17	by	by	IN
randomwalker-info-585	31	18	investigating	investigate	VBG
randomwalker-info-585	31	19	the	the	DT
randomwalker-info-585	31	20	mining	mining	NN
randomwalker-info-585	31	21	game	game	NN
randomwalker-info-585	31	22	in	in	IN
randomwalker-info-585	31	23	the	the	DT
randomwalker-info-585	31	24	regime	regime	NN
randomwalker-info-585	31	25	where	where	WRB
randomwalker-info-585	31	26	the	the	DT
randomwalker-info-585	31	27	block	block	NN
randomwalker-info-585	31	28	reward	reward	NN
randomwalker-info-585	31	29	has	have	VBZ
randomwalker-info-585	31	30	dwindled	dwindle	VBN
randomwalker-info-585	31	31	to	to	IN
randomwalker-info-585	31	32	a	a	DT
randomwalker-info-585	31	33	negligible	negligible	JJ
randomwalker-info-585	31	34	amount	amount	NN
randomwalker-info-585	31	35	,	,	,
randomwalker-info-585	31	36	and	and	CC
randomwalker-info-585	31	37	transaction	transaction	NN
randomwalker-info-585	31	38	fees	fee	NNS
randomwalker-info-585	31	39	dominate	dominate	VBP
randomwalker-info-585	31	40	mining	mining	NN
randomwalker-info-585	31	41	rewards	reward	NNS
randomwalker-info-585	31	42	.	.	.
randomwalker-info-585	32	1	We	-PRON-	PRP
randomwalker-info-585	32	2	find	find	VBP
randomwalker-info-585	32	3	new	new	JJ
randomwalker-info-585	32	4	and	and	CC
randomwalker-info-585	32	5	surprising	surprising	JJ
randomwalker-info-585	32	6	incentive	incentive	NN
randomwalker-info-585	32	7	issues	issue	NNS
randomwalker-info-585	32	8	in	in	IN
randomwalker-info-585	32	9	a	a	DT
randomwalker-info-585	32	10	transaction	transaction	NN
randomwalker-info-585	32	11	-	-	HYPH
randomwalker-info-585	32	12	fee	fee	NN
randomwalker-info-585	32	13	regime	regime	NN
randomwalker-info-585	32	14	,	,	,
randomwalker-info-585	32	15	even	even	RB
randomwalker-info-585	32	16	assuming	assume	VBG
randomwalker-info-585	32	17	that	that	IN
randomwalker-info-585	32	18	transactions	transaction	NNS
randomwalker-info-585	32	19	(	(	-LRB-
randomwalker-info-585	32	20	and	and	CC
randomwalker-info-585	32	21	associated	associate	VBN
randomwalker-info-585	32	22	fees	fee	NNS
randomwalker-info-585	32	23	)	)	-RRB-
randomwalker-info-585	32	24	arrive	arrive	VBP
randomwalker-info-585	32	25	at	at	IN
randomwalker-info-585	32	26	a	a	DT
randomwalker-info-585	32	27	steady	steady	JJ
randomwalker-info-585	32	28	rate	rate	NN
randomwalker-info-585	32	29	.	.	.
randomwalker-info-585	33	1	To	to	TO
randomwalker-info-585	33	2	be	be	VB
randomwalker-info-585	33	3	clear	clear	JJ
randomwalker-info-585	33	4	:	:	:
randomwalker-info-585	33	5	the	the	DT
randomwalker-info-585	33	6	incentive	incentive	NN
randomwalker-info-585	33	7	issues	issue	NNS
randomwalker-info-585	33	8	we	-PRON-	PRP
randomwalker-info-585	33	9	uncover	uncover	VBP
randomwalker-info-585	33	10	arise	arise	VBP
randomwalker-info-585	33	11	not	not	RB
randomwalker-info-585	33	12	because	because	IN
randomwalker-info-585	33	13	transaction	transaction	NN
randomwalker-info-585	33	14	fees	fee	NNS
randomwalker-info-585	33	15	may	may	MD
randomwalker-info-585	33	16	arrive	arrive	VB
randomwalker-info-585	33	17	erratically	erratically	RB
randomwalker-info-585	33	18	,	,	,
randomwalker-info-585	33	19	but	but	CC
randomwalker-info-585	33	20	because	because	IN
randomwalker-info-585	33	21	the	the	DT
randomwalker-info-585	33	22	time	time	NN
randomwalker-info-585	33	23	-	-	HYPH
randomwalker-info-585	33	24	varying	vary	VBG
randomwalker-info-585	33	25	nature	nature	NN
randomwalker-info-585	33	26	of	of	IN
randomwalker-info-585	33	27	transaction	transaction	NN
randomwalker-info-585	33	28	fees	fee	NNS
randomwalker-info-585	33	29	allows	allow	VBZ
randomwalker-info-585	33	30	for	for	IN
randomwalker-info-585	33	31	a	a	DT
randomwalker-info-585	33	32	richer	rich	JJR
randomwalker-info-585	33	33	set	set	NN
randomwalker-info-585	33	34	of	of	IN
randomwalker-info-585	33	35	strategic	strategic	JJ
randomwalker-info-585	33	36	deviations	deviation	NNS
randomwalker-info-585	33	37	that	that	WDT
randomwalker-info-585	33	38	do	do	VBP
randomwalker-info-585	33	39	n’t	not	RB
randomwalker-info-585	33	40	arise	arise	VB
randomwalker-info-585	33	41	in	in	IN
randomwalker-info-585	33	42	the	the	DT
randomwalker-info-585	33	43	block	block	NN
randomwalker-info-585	33	44	-	-	HYPH
randomwalker-info-585	33	45	reward	reward	NN
randomwalker-info-585	33	46	model	model	NN
randomwalker-info-585	33	47	.	.	.
randomwalker-info-585	34	1	At	at	IN
randomwalker-info-585	34	2	a	a	DT
randomwalker-info-585	34	3	high	high	JJ
randomwalker-info-585	34	4	level	level	NN
randomwalker-info-585	34	5	,	,	,
randomwalker-info-585	34	6	there	there	EX
randomwalker-info-585	34	7	is	be	VBZ
randomwalker-info-585	34	8	an	an	DT
randomwalker-info-585	34	9	analogy	analogy	NN
randomwalker-info-585	34	10	with	with	IN
randomwalker-info-585	34	11	pool	pool	NN
randomwalker-info-585	34	12	hopping	hopping	NN
randomwalker-info-585	34	13	[	[	-LRB-
randomwalker-info-585	34	14	22	22	CD
randomwalker-info-585	34	15	]	]	-RRB-
randomwalker-info-585	34	16	.	.	.
randomwalker-info-585	35	1	With	with	IN
randomwalker-info-585	35	2	certain	certain	JJ
randomwalker-info-585	35	3	mining	mining	NN
randomwalker-info-585	35	4	pool	pool	NN
randomwalker-info-585	35	5	reward	reward	NN
randomwalker-info-585	35	6	schemes	scheme	NNS
randomwalker-info-585	35	7	,	,	,
randomwalker-info-585	35	8	the	the	DT
randomwalker-info-585	35	9	miner	miner	NN
randomwalker-info-585	35	10	’s	’s	,
randomwalker-info-585	35	11	ex-	ex-	XX
randomwalker-info-585	35	12	pected	pecte	VBD
randomwalker-info-585	35	13	reward	reward	NN
randomwalker-info-585	35	14	for	for	IN
randomwalker-info-585	35	15	participation	participation	NN
randomwalker-info-585	35	16	varies	varie	NNS
randomwalker-info-585	35	17	over	over	IN
randomwalker-info-585	35	18	time	time	NN
randomwalker-info-585	35	19	,	,	,
randomwalker-info-585	35	20	depend-	depend-	NNP
randomwalker-info-585	35	21	ing	ing	NNP
randomwalker-info-585	35	22	on	on	IN
randomwalker-info-585	35	23	how	how	WRB
randomwalker-info-585	35	24	many	many	JJ
randomwalker-info-585	35	25	shares	share	NNS
randomwalker-info-585	35	26	have	have	VBP
randomwalker-info-585	35	27	been	be	VBN
randomwalker-info-585	35	28	contributed	contribute	VBN
randomwalker-info-585	35	29	since	since	IN
randomwalker-info-585	35	30	the	the	DT
randomwalker-info-585	35	31	pool	pool	NN
randomwalker-info-585	35	32	found	find	VBD
randomwalker-info-585	35	33	its	-PRON-	PRP$
randomwalker-info-585	35	34	last	last	JJ
randomwalker-info-585	35	35	block	block	NN
randomwalker-info-585	35	36	.	.	.
randomwalker-info-585	36	1	The	the	DT
randomwalker-info-585	36	2	concern	concern	NN
randomwalker-info-585	36	3	is	be	VBZ
randomwalker-info-585	36	4	that	that	IN
randomwalker-info-585	36	5	miners	miner	NNS
randomwalker-info-585	36	6	would	would	MD
randomwalker-info-585	36	7	respond	respond	VB
randomwalker-info-585	36	8	by	by	IN
randomwalker-info-585	36	9	“	"	``
randomwalker-info-585	36	10	hopping	hopping	NN
randomwalker-info-585	36	11	”	"	''
randomwalker-info-585	36	12	in	in	IN
randomwalker-info-585	36	13	real	real	JJ
randomwalker-info-585	36	14	time	time	NN
randomwalker-info-585	36	15	to	to	IN
randomwalker-info-585	36	16	the	the	DT
randomwalker-info-585	36	17	pool	pool	NN
randomwalker-info-585	36	18	that	that	WDT
randomwalker-info-585	36	19	max-	max-	NN
randomwalker-info-585	36	20	imizes	imize	VBZ
randomwalker-info-585	36	21	their	-PRON-	PRP$
randomwalker-info-585	36	22	expected	expect	VBN
randomwalker-info-585	36	23	rewards	reward	NNS
randomwalker-info-585	36	24	.	.	.
randomwalker-info-585	37	1	For	for	IN
randomwalker-info-585	37	2	another	another	DT
randomwalker-info-585	37	3	illustration	illustration	NN
randomwalker-info-585	37	4	of	of	IN
randomwalker-info-585	37	5	this	this	DT
randomwalker-info-585	37	6	theme	theme	NN
randomwalker-info-585	37	7	,	,	,
randomwalker-info-585	37	8	consider	consider	VB
randomwalker-info-585	37	9	a	a	DT
randomwalker-info-585	37	10	future	future	NN
randomwalker-info-585	37	11	where	where	WRB
randomwalker-info-585	37	12	there	there	EX
randomwalker-info-585	37	13	are	be	VBP
randomwalker-info-585	37	14	multiple	multiple	JJ
randomwalker-info-585	37	15	cryp-	cryp-	JJ
randomwalker-info-585	37	16	tocurrencies	tocurrencie	NNS
randomwalker-info-585	37	17	with	with	IN
randomwalker-info-585	37	18	time	time	NN
randomwalker-info-585	37	19	-	-	HYPH
randomwalker-info-585	37	20	varying	vary	VBG
randomwalker-info-585	37	21	rewards	reward	NNS
randomwalker-info-585	37	22	which	which	WDT
randomwalker-info-585	37	23	can	can	MD
randomwalker-info-585	37	24	be	be	VB
randomwalker-info-585	37	25	mined	mine	VBN
randomwalker-info-585	37	26	by	by	IN
randomwalker-info-585	37	27	the	the	DT
randomwalker-info-585	37	28	same	same	JJ
randomwalker-info-585	37	29	hardware	hardware	NN
randomwalker-info-585	37	30	.	.	.
randomwalker-info-585	38	1	Perhaps	perhaps	RB
randomwalker-info-585	38	2	this	this	DT
randomwalker-info-585	38	3	will	will	MD
randomwalker-info-585	38	4	give	give	VB
randomwalker-info-585	38	5	rise	rise	NN
randomwalker-info-585	38	6	to	to	IN
randomwalker-info-585	38	7	coin-	coin-	NN
randomwalker-info-585	38	8	hopping	hopping	NN
randomwalker-info-585	38	9	,	,	,
randomwalker-info-585	38	10	i.e.	i.e.	FW
randomwalker-info-585	38	11	,	,	,
randomwalker-info-585	38	12	miners	miner	NNS
randomwalker-info-585	38	13	hopping	hop	VBG
randomwalker-info-585	38	14	to	to	IN
randomwalker-info-585	38	15	the	the	DT
randomwalker-info-585	38	16	cryptocurrency	cryptocurrency	NN
randomwalker-info-585	38	17	with	with	IN
randomwalker-info-585	38	18	the	the	DT
randomwalker-info-585	38	19	largest	large	JJS
randomwalker-info-585	38	20	transaction	transaction	NN
randomwalker-info-585	38	21	fee	fee	NN
randomwalker-info-585	38	22	pool	pool	NN
randomwalker-info-585	38	23	.	.	.
randomwalker-info-585	39	1	Contribution	contribution	NN
randomwalker-info-585	39	2	1	1	CD
randomwalker-info-585	39	3	:	:	:
randomwalker-info-585	39	4	A	a	DT
randomwalker-info-585	39	5	mining	mining	NN
randomwalker-info-585	39	6	strategy	strategy	NN
randomwalker-info-585	39	7	simulator	simulator	NN
randomwalker-info-585	39	8	.	.	.
randomwalker-info-585	40	1	While	while	IN
randomwalker-info-585	40	2	we	-PRON-	PRP
randomwalker-info-585	40	3	establish	establish	VBP
randomwalker-info-585	40	4	a	a	DT
randomwalker-info-585	40	5	number	number	NN
randomwalker-info-585	40	6	of	of	IN
randomwalker-info-585	40	7	theoretical	theoretical	JJ
randomwalker-info-585	40	8	results	result	NNS
randomwalker-info-585	40	9	in	in	IN
randomwalker-info-585	40	10	Sections	section	NNS
randomwalker-info-585	40	11	5	5	CD
randomwalker-info-585	40	12	and	and	CC
randomwalker-info-585	40	13	6	6	CD
randomwalker-info-585	40	14	,	,	,
randomwalker-info-585	40	15	the	the	DT
randomwalker-info-585	40	16	variety	variety	NN
randomwalker-info-585	40	17	of	of	IN
randomwalker-info-585	40	18	possible	possible	JJ
randomwalker-info-585	40	19	parameters	parameter	NNS
randomwalker-info-585	40	20	and	and	CC
randomwalker-info-585	40	21	assumptions	assumption	NNS
randomwalker-info-585	40	22	makes	make	VBZ
randomwalker-info-585	40	23	it	-PRON-	PRP
randomwalker-info-585	40	24	completely	completely	RB
randomwalker-info-585	40	25	infeasible	infeasible	JJ
randomwalker-info-585	40	26	to	to	TO
randomwalker-info-585	40	27	pose	pose	VB
randomwalker-info-585	40	28	a	a	DT
randomwalker-info-585	40	29	perfectly	perfectly	RB
randomwalker-info-585	40	30	accurate	accurate	JJ
randomwalker-info-585	40	31	Game	Game	NNP
randomwalker-info-585	40	32	-	-	HYPH
randomwalker-info-585	40	33	Theoretic	theoretic	JJ
randomwalker-info-585	40	34	model	model	NN
randomwalker-info-585	40	35	of	of	IN
randomwalker-info-585	40	36	Bitcoin	Bitcoin	NNP
randomwalker-info-585	40	37	that	that	WDT
randomwalker-info-585	40	38	is	be	VBZ
randomwalker-info-585	40	39	also	also	RB
randomwalker-info-585	40	40	tractable	tractable	JJ
randomwalker-info-585	40	41	.	.	.
randomwalker-info-585	41	1	To	to	TO
randomwalker-info-585	41	2	fill	fill	VB
randomwalker-info-585	41	3	the	the	DT
randomwalker-info-585	41	4	gaps	gap	NNS
randomwalker-info-585	41	5	and	and	CC
randomwalker-info-585	41	6	to	to	TO
randomwalker-info-585	41	7	confirm	confirm	VB
randomwalker-info-585	41	8	our	-PRON-	PRP$
randomwalker-info-585	41	9	theoretical	theoretical	JJ
randomwalker-info-585	41	10	results	result	NNS
randomwalker-info-585	41	11	,	,	,
randomwalker-info-585	41	12	we	-PRON-	PRP
randomwalker-info-585	41	13	’ve	have	VB
randomwalker-info-585	41	14	built	build	VBN
randomwalker-info-585	41	15	a	a	DT
randomwalker-info-585	41	16	mining	mining	NN
randomwalker-info-585	41	17	strategy	strategy	NN
randomwalker-info-585	41	18	simulator	simulator	NN
randomwalker-info-585	41	19	.	.	.
randomwalker-info-585	42	1	Theoretical	theoretical	JJ
randomwalker-info-585	42	2	results	result	NNS
randomwalker-info-585	42	3	in	in	IN
randomwalker-info-585	42	4	simple	simple	JJ
randomwalker-info-585	42	5	yet	yet	CC
randomwalker-info-585	42	6	principled	principle	VBN
randomwalker-info-585	42	7	models	model	NNS
randomwalker-info-585	42	8	provide	provide	VB
randomwalker-info-585	42	9	good	good	JJ
randomwalker-info-585	42	10	intuition	intuition	NN
randomwalker-info-585	42	11	to	to	TO
randomwalker-info-585	42	12	guide	guide	VB
randomwalker-info-585	42	13	practice	practice	NN
randomwalker-info-585	42	14	,	,	,
randomwalker-info-585	42	15	and	and	CC
randomwalker-info-585	42	16	simulations	simulation	NNS
randomwalker-info-585	42	17	of	of	IN
randomwalker-info-585	42	18	more	more	JJR
randomwalker-info-585	42	19	complex	complex	JJ
randomwalker-info-585	42	20	scenarios	scenario	NNS
randomwalker-info-585	42	21	confirm	confirm	VBP
randomwalker-info-585	42	22	that	that	IN
randomwalker-info-585	42	23	these	these	DT
randomwalker-info-585	42	24	results	result	NNS
randomwalker-info-585	42	25	have	have	VBP
randomwalker-info-585	42	26	applicability	applicability	NN
randomwalker-info-585	42	27	to	to	IN
randomwalker-info-585	42	28	more	more	RBR
randomwalker-info-585	42	29	realistic	realistic	JJ
randomwalker-info-585	42	30	models	model	NNS
randomwalker-info-585	42	31	where	where	WRB
randomwalker-info-585	42	32	mathematical	mathematical	JJ
randomwalker-info-585	42	33	proofs	proof	NNS
randomwalker-info-585	42	34	are	be	VBP
randomwalker-info-585	42	35	intractable	intractable	JJ
randomwalker-info-585	42	36	.	.	.
randomwalker-info-585	43	1	Miners	miner	NNS
randomwalker-info-585	43	2	in	in	IN
randomwalker-info-585	43	3	our	-PRON-	PRP$
randomwalker-info-585	43	4	simulation	simulation	NN
randomwalker-info-585	43	5	learn	learn	VBP
randomwalker-info-585	43	6	over	over	IN
randomwalker-info-585	43	7	time	time	NN
randomwalker-info-585	43	8	which	which	WDT
randomwalker-info-585	43	9	strate-	strate-	VBZ
randomwalker-info-585	43	10	gies	gy	NNS
randomwalker-info-585	43	11	are	be	VBP
randomwalker-info-585	43	12	successful	successful	JJ
randomwalker-info-585	43	13	using	use	VBG
randomwalker-info-585	43	14	no	no	DT
randomwalker-info-585	43	15	-	-	HYPH
randomwalker-info-585	43	16	regret	regret	NN
randomwalker-info-585	43	17	learning	learning	NN
randomwalker-info-585	43	18	algorithms	algorithm	NNS
randomwalker-info-585	43	19	that	that	WDT
randomwalker-info-585	43	20	iteratively	iteratively	RB
randomwalker-info-585	43	21	update	update	VBP
randomwalker-info-585	43	22	a	a	DT
randomwalker-info-585	43	23	probability	probability	NN
randomwalker-info-585	43	24	distribution	distribution	NN
randomwalker-info-585	43	25	over	over	IN
randomwalker-info-585	43	26	strategies	strategy	NNS
randomwalker-info-585	43	27	(	(	-LRB-
randomwalker-info-585	43	28	Section	section	NN
randomwalker-info-585	43	29	4.2	4.2	CD
randomwalker-info-585	43	30	)	)	-RRB-
randomwalker-info-585	43	31	.	.	.
randomwalker-info-585	44	1	Our	-PRON-	PRP$
randomwalker-info-585	44	2	simulator	simulator	NN
randomwalker-info-585	44	3	is	be	VBZ
randomwalker-info-585	44	4	versatile	versatile	JJ
randomwalker-info-585	44	5	and	and	CC
randomwalker-info-585	44	6	allows	allow	VBZ
randomwalker-info-585	44	7	model-	model-	NNP
randomwalker-info-585	44	8	ing	e	VBG
randomwalker-info-585	44	9	different	different	JJ
randomwalker-info-585	44	10	numbers	number	NNS
randomwalker-info-585	44	11	of	of	IN
randomwalker-info-585	44	12	miners	miner	NNS
randomwalker-info-585	44	13	,	,	,
randomwalker-info-585	44	14	hash	hash	NN
randomwalker-info-585	44	15	power	power	NN
randomwalker-info-585	44	16	distributions	distribution	NNS
randomwalker-info-585	44	17	,	,	,
randomwalker-info-585	44	18	network	network	NN
randomwalker-info-585	44	19	latencies	latency	NNS
randomwalker-info-585	44	20	,	,	,
randomwalker-info-585	44	21	and	and	CC
randomwalker-info-585	44	22	reward	reward	NN
randomwalker-info-585	44	23	schemes	scheme	NNS
randomwalker-info-585	44	24	.	.	.
randomwalker-info-585	45	1	We	-PRON-	PRP
randomwalker-info-585	45	2	show	show	VBP
randomwalker-info-585	45	3	how	how	WRB
randomwalker-info-585	45	4	it	-PRON-	PRP
randomwalker-info-585	45	5	allows	allow	VBZ
randomwalker-info-585	45	6	researchers	researcher	NNS
randomwalker-info-585	45	7	to	to	TO
randomwalker-info-585	45	8	quickly	quickly	RB
randomwalker-info-585	45	9	prototype	prototype	VB
randomwalker-info-585	45	10	and	and	CC
randomwalker-info-585	45	11	study	study	VB
randomwalker-info-585	45	12	new	new	JJ
randomwalker-info-585	45	13	set-	set-	JJ
randomwalker-info-585	45	14	tings	ting	NNS
randomwalker-info-585	45	15	within	within	IN
randomwalker-info-585	45	16	this	this	DT
randomwalker-info-585	45	17	parameter	parameter	NN
randomwalker-info-585	45	18	space	space	NN
randomwalker-info-585	45	19	.	.	.
randomwalker-info-585	46	1	The	the	DT
randomwalker-info-585	46	2	simulator	simulator	NN
randomwalker-info-585	46	3	does	do	VBZ
randomwalker-info-585	46	4	have	have	VB
randomwalker-info-585	46	5	limitations	limitation	NNS
randomwalker-info-585	46	6	:	:	:
randomwalker-info-585	46	7	it	-PRON-	PRP
randomwalker-info-585	46	8	can	can	MD
randomwalker-info-585	46	9	not	not	RB
randomwalker-info-585	46	10	model	model	VB
randomwalker-info-585	46	11	mining	mining	NN
randomwalker-info-585	46	12	pools	pool	NNS
randomwalker-info-585	46	13	or	or	CC
randomwalker-info-585	46	14	a	a	DT
randomwalker-info-585	46	15	non	non	JJ
randomwalker-info-585	46	16	-	-	JJ
randomwalker-info-585	46	17	constant	constant	JJ
randomwalker-info-585	46	18	arrival	arrival	NN
randomwalker-info-585	46	19	rate	rate	NN
randomwalker-info-585	46	20	of	of	IN
randomwalker-info-585	46	21	transactions	transaction	NNS
randomwalker-info-585	46	22	.	.	.
randomwalker-info-585	47	1	We	-PRON-	PRP
randomwalker-info-585	47	2	have	have	VBP
randomwalker-info-585	47	3	made	make	VBN
randomwalker-info-585	47	4	the	the	DT
randomwalker-info-585	47	5	simulator	simulator	NN
randomwalker-info-585	47	6	open	open	JJ
randomwalker-info-585	47	7	source.1	source.1	NN
randomwalker-info-585	47	8	In	in	IN
randomwalker-info-585	47	9	addition	addition	NN
randomwalker-info-585	47	10	to	to	IN
randomwalker-info-585	47	11	the	the	DT
randomwalker-info-585	47	12	versatility	versatility	NN
randomwalker-info-585	47	13	of	of	IN
randomwalker-info-585	47	14	settings	setting	NNS
randomwalker-info-585	47	15	,	,	,
randomwalker-info-585	47	16	our	-PRON-	PRP$
randomwalker-info-585	47	17	simulator	simulator	NN
randomwalker-info-585	47	18	allows	allow	VBZ
randomwalker-info-585	47	19	exploring	explore	VBG
randomwalker-info-585	47	20	a	a	DT
randomwalker-info-585	47	21	large	large	JJ
randomwalker-info-585	47	22	space	space	NN
randomwalker-info-585	47	23	of	of	IN
randomwalker-info-585	47	24	mining	mining	NN
randomwalker-info-585	47	25	strategies	strategy	NNS
randomwalker-info-585	47	26	,	,	,
randomwalker-info-585	47	27	defined	define	VBN
randomwalker-info-585	47	28	by	by	IN
randomwalker-info-585	47	29	the	the	DT
randomwalker-info-585	47	30	miner	miner	NN
randomwalker-info-585	47	31	’s	’s	POS
randomwalker-info-585	47	32	responses	response	NNS
randomwalker-info-585	47	33	to	to	IN
randomwalker-info-585	47	34	three	three	CD
randomwalker-info-585	47	35	questions	question	NNS
randomwalker-info-585	47	36	:	:	:
randomwalker-info-585	47	37	which	which	WDT
randomwalker-info-585	47	38	block	block	NN
randomwalker-info-585	47	39	to	to	TO
randomwalker-info-585	47	40	extend	extend	VB
randomwalker-info-585	47	41	,	,	,
randomwalker-info-585	47	42	how	how	WRB
randomwalker-info-585	47	43	much	much	JJ
randomwalker-info-585	47	44	of	of	IN
randomwalker-info-585	47	45	the	the	DT
randomwalker-info-585	47	46	outstanding	outstanding	JJ
randomwalker-info-585	47	47	transactions	transaction	NNS
randomwalker-info-585	47	48	to	to	TO
randomwalker-info-585	47	49	include	include	VB
randomwalker-info-585	47	50	in	in	IN
randomwalker-info-585	47	51	the	the	DT
randomwalker-info-585	47	52	block	block	NN
randomwalker-info-585	47	53	,	,	,
randomwalker-info-585	47	54	and	and	CC
randomwalker-info-585	47	55	when	when	WRB
randomwalker-info-585	47	56	to	to	TO
randomwalker-info-585	47	57	publish	publish	VB
randomwalker-info-585	47	58	found	find	VBN
randomwalker-info-585	47	59	blocks	block	NNS
randomwalker-info-585	47	60	.	.	.
randomwalker-info-585	48	1	We	-PRON-	PRP
randomwalker-info-585	48	2	define	define	VBP
randomwalker-info-585	48	3	a	a	DT
randomwalker-info-585	48	4	formal	formal	JJ
randomwalker-info-585	48	5	language	language	NN
randomwalker-info-585	48	6	to	to	TO
randomwalker-info-585	48	7	compactly	compactly	RB
randomwalker-info-585	48	8	express	express	VB
randomwalker-info-585	48	9	any	any	DT
randomwalker-info-585	48	10	strategy	strategy	NN
randomwalker-info-585	48	11	in	in	IN
randomwalker-info-585	48	12	this	this	DT
randomwalker-info-585	48	13	space	space	NN
randomwalker-info-585	48	14	(	(	-LRB-
randomwalker-info-585	48	15	Section	section	NN
randomwalker-info-585	48	16	4	4	CD
randomwalker-info-585	48	17	)	)	-RRB-
randomwalker-info-585	48	18	.	.	.
randomwalker-info-585	49	1	Contribution	contribution	NN
randomwalker-info-585	49	2	2	2	CD
randomwalker-info-585	49	3	:	:	:
randomwalker-info-585	49	4	Undercutting	undercut	VBG
randomwalker-info-585	49	5	attacks	attack	NNS
randomwalker-info-585	49	6	.	.	.
randomwalker-info-585	50	1	The	the	DT
randomwalker-info-585	50	2	focus	focus	NN
randomwalker-info-585	50	3	of	of	IN
randomwalker-info-585	50	4	this	this	DT
randomwalker-info-585	50	5	paper	paper	NN
randomwalker-info-585	50	6	is	be	VBZ
randomwalker-info-585	50	7	on	on	IN
randomwalker-info-585	50	8	analyzing	analyze	VBG
randomwalker-info-585	50	9	deviant	deviant	NN
randomwalker-info-585	50	10	mining	mining	NN
randomwalker-info-585	50	11	strategies	strategy	NNS
randomwalker-info-585	50	12	in	in	IN
randomwalker-info-585	50	13	the	the	DT
randomwalker-info-585	50	14	transaction	transaction	NN
randomwalker-info-585	50	15	-	-	HYPH
randomwalker-info-585	50	16	fee	fee	NN
randomwalker-info-585	50	17	regime	regime	NN
randomwalker-info-585	50	18	that	that	WDT
randomwalker-info-585	50	19	can	can	MD
randomwalker-info-585	50	20	harm	harm	VB
randomwalker-info-585	50	21	Bitcoin	Bitcoin	NNP
randomwalker-info-585	50	22	’s	’s	POS
randomwalker-info-585	50	23	security	security	NN
randomwalker-info-585	50	24	.	.	.
randomwalker-info-585	51	1	We	-PRON-	PRP
randomwalker-info-585	51	2	begin	begin	VBP
randomwalker-info-585	51	3	with	with	IN
randomwalker-info-585	51	4	the	the	DT
randomwalker-info-585	51	5	observation	observation	NN
randomwalker-info-585	51	6	that	that	IN
randomwalker-info-585	51	7	if	if	IN
randomwalker-info-585	51	8	there	there	EX
randomwalker-info-585	51	9	is	be	VBZ
randomwalker-info-585	51	10	a	a	DT
randomwalker-info-585	51	11	1-block	1-block	CD
randomwalker-info-585	51	12	fork	fork	NN
randomwalker-info-585	51	13	,	,	,
randomwalker-info-585	51	14	it	-PRON-	PRP
randomwalker-info-585	51	15	is	be	VBZ
randomwalker-info-585	51	16	more	more	RBR
randomwalker-info-585	51	17	profitable	profitable	JJ
randomwalker-info-585	51	18	for	for	IN
randomwalker-info-585	51	19	the	the	DT
randomwalker-info-585	51	20	next	next	JJ
randomwalker-info-585	51	21	miner	miner	NN
randomwalker-info-585	51	22	to	to	TO
randomwalker-info-585	51	23	break	break	VB
randomwalker-info-585	51	24	the	the	DT
randomwalker-info-585	51	25	tie	tie	NN
randomwalker-info-585	51	26	by	by	IN
randomwalker-info-585	51	27	extending	extend	VBG
randomwalker-info-585	51	28	the	the	DT
randomwalker-info-585	51	29	block	block	NN
randomwalker-info-585	51	30	that	that	WDT
randomwalker-info-585	51	31	leaves	leave	VBZ
randomwalker-info-585	51	32	the	the	DT
randomwalker-info-585	51	33	most	most	RBS
randomwalker-info-585	51	34	available	available	JJ
randomwalker-info-585	51	35	transaction	transaction	NN
randomwalker-info-585	51	36	fees	fee	NNS
randomwalker-info-585	51	37	rather	rather	RB
randomwalker-info-585	51	38	than	than	IN
randomwalker-info-585	51	39	the	the	DT
randomwalker-info-585	51	40	oldest	oldest	RBS
randomwalker-info-585	51	41	-	-	HYPH
randomwalker-info-585	51	42	seen	see	VBN
randomwalker-info-585	51	43	block	block	NN
randomwalker-info-585	51	44	.	.	.
randomwalker-info-585	52	1	We	-PRON-	PRP
randomwalker-info-585	52	2	call	call	VBP
randomwalker-info-585	52	3	this	this	DT
randomwalker-info-585	52	4	strategy	strategy	NN
randomwalker-info-585	52	5	PettyCompliant	PettyCompliant	NNP
randomwalker-info-585	52	6	.	.	.
randomwalker-info-585	53	1	Once	once	IN
randomwalker-info-585	53	2	any	any	DT
randomwalker-info-585	53	3	non	non	JJ
randomwalker-info-585	53	4	-	-	JJ
randomwalker-info-585	53	5	zero	zero	JJ
randomwalker-info-585	53	6	fraction	fraction	NN
randomwalker-info-585	53	7	of	of	IN
randomwalker-info-585	53	8	miners	miner	NNS
randomwalker-info-585	53	9	is	be	VBZ
randomwalker-info-585	53	10	PettyCompli-	PettyCompli-	NNP
randomwalker-info-585	53	11	ant	ant	NNP
randomwalker-info-585	53	12	,	,	,
randomwalker-info-585	53	13	it	-PRON-	PRP
randomwalker-info-585	53	14	enables	enable	VBZ
randomwalker-info-585	53	15	various	various	JJ
randomwalker-info-585	53	16	strategies	strategy	NNS
randomwalker-info-585	53	17	that	that	WDT
randomwalker-info-585	53	18	are	be	VBP
randomwalker-info-585	53	19	more	more	RBR
randomwalker-info-585	53	20	aggressive	aggressive	JJ
randomwalker-info-585	53	21	and	and	CC
randomwalker-info-585	53	22	harmful	harmful	JJ
randomwalker-info-585	53	23	to	to	IN
randomwalker-info-585	53	24	Bitcoin	Bitcoin	NNP
randomwalker-info-585	53	25	consensus	consensus	NN
randomwalker-info-585	53	26	.	.	.
randomwalker-info-585	54	1	We	-PRON-	PRP
randomwalker-info-585	54	2	call	call	VBP
randomwalker-info-585	54	3	this	this	DT
randomwalker-info-585	54	4	the	the	DT
randomwalker-info-585	54	5	undercut-	undercut-	JJ
randomwalker-info-585	54	6	ting	ting	NNP
randomwalker-info-585	54	7	attack	attack	NN
randomwalker-info-585	54	8	,	,	,
randomwalker-info-585	54	9	where	where	WRB
randomwalker-info-585	54	10	miners	miner	NNS
randomwalker-info-585	54	11	will	will	MD
randomwalker-info-585	54	12	actively	actively	RB
randomwalker-info-585	54	13	fork	fork	VB
randomwalker-info-585	54	14	the	the	DT
randomwalker-info-585	54	15	head	head	NN
randomwalker-info-585	54	16	of	of	IN
randomwalker-info-585	54	17	the	the	DT
randomwalker-info-585	54	18	chain	chain	NN
randomwalker-info-585	54	19	and	and	CC
randomwalker-info-585	54	20	leave	leave	VB
randomwalker-info-585	54	21	transactions	transaction	NNS
randomwalker-info-585	54	22	unclaimed	unclaime	VBN
randomwalker-info-585	54	23	in	in	IN
randomwalker-info-585	54	24	the	the	DT
randomwalker-info-585	54	25	hope	hope	NN
randomwalker-info-585	54	26	of	of	IN
randomwalker-info-585	54	27	incen-	incen-	NN
randomwalker-info-585	54	28	tivizing	tivize	VBG
randomwalker-info-585	54	29	PettyCompliant	PettyCompliant	NNP
randomwalker-info-585	54	30	miners	miner	NNS
randomwalker-info-585	54	31	to	to	TO
randomwalker-info-585	54	32	build	build	VB
randomwalker-info-585	54	33	on	on	IN
randomwalker-info-585	54	34	their	-PRON-	PRP$
randomwalker-info-585	54	35	block	block	NN
randomwalker-info-585	54	36	.	.	.
randomwalker-info-585	55	1	In	in	IN
randomwalker-info-585	55	2	some	some	DT
randomwalker-info-585	55	3	scenarios	scenario	NNS
randomwalker-info-585	55	4	,	,	,
randomwalker-info-585	55	5	our	-PRON-	PRP$
randomwalker-info-585	55	6	simulation	simulation	NN
randomwalker-info-585	55	7	reveals	reveal	VBZ
randomwalker-info-585	55	8	a	a	DT
randomwalker-info-585	55	9	non	non	JJ
randomwalker-info-585	55	10	-	-	JJ
randomwalker-info-585	55	11	equilibrium	equilibrium	JJ
randomwalker-info-585	55	12	with	with	IN
randomwalker-info-585	55	13	increasingly	increasingly	RB
randomwalker-info-585	55	14	aggressive	aggressive	JJ
randomwalker-info-585	55	15	undercutting	undercutting	NN
randomwalker-info-585	55	16	.	.	.
randomwalker-info-585	56	1	But	but	CC
randomwalker-info-585	56	2	with	with	IN
randomwalker-info-585	56	3	an	an	DT
randomwalker-info-585	56	4	ex-	ex-	JJ
randomwalker-info-585	56	5	panded	panded	JJ
randomwalker-info-585	56	6	strategy	strategy	NN
randomwalker-info-585	56	7	space	space	NN
randomwalker-info-585	56	8	,	,	,
randomwalker-info-585	56	9	and	and	CC
randomwalker-info-585	56	10	suitable	suitable	JJ
randomwalker-info-585	56	11	assumptions	assumption	NNS
randomwalker-info-585	56	12	,	,	,
randomwalker-info-585	56	13	we	-PRON-	PRP
randomwalker-info-585	56	14	are	be	VBP
randomwalker-info-585	56	15	able	able	JJ
randomwalker-info-585	56	16	to	to	TO
randomwalker-info-585	56	17	prove	prove	VB
randomwalker-info-585	56	18	that	that	IN
randomwalker-info-585	56	19	an	an	DT
randomwalker-info-585	56	20	equilibrium	equilibrium	NN
randomwalker-info-585	56	21	exists	exist	VBZ
randomwalker-info-585	56	22	.	.	.
randomwalker-info-585	57	1	However	however	RB
randomwalker-info-585	57	2	,	,	,
randomwalker-info-585	57	3	it	-PRON-	PRP
randomwalker-info-585	57	4	is	be	VBZ
randomwalker-info-585	57	5	one	one	CD
randomwalker-info-585	57	6	where	where	WRB
randomwalker-info-585	57	7	miners	miner	NNS
randomwalker-info-585	57	8	include	include	VBP
randomwalker-info-585	57	9	only	only	RB
randomwalker-info-585	57	10	a	a	DT
randomwalker-info-585	57	11	fraction	fraction	NN
randomwalker-info-585	57	12	of	of	IN
randomwalker-info-585	57	13	available	available	JJ
randomwalker-info-585	57	14	transactions	transaction	NNS
randomwalker-info-585	57	15	1https://github.com/citp/mining	1https://github.com/citp/mine	VBG
randomwalker-info-585	57	16	simulator	simulator	NN
randomwalker-info-585	57	17	into	into	IN
randomwalker-info-585	57	18	their	-PRON-	PRP$
randomwalker-info-585	57	19	blocks	block	NNS
randomwalker-info-585	57	20	.	.	.
randomwalker-info-585	58	1	This	this	DT
randomwalker-info-585	58	2	results	result	VBZ
randomwalker-info-585	58	3	in	in	IN
randomwalker-info-585	58	4	a	a	DT
randomwalker-info-585	58	5	backlog	backlog	NN
randomwalker-info-585	58	6	of	of	IN
randomwalker-info-585	58	7	transactions	transaction	NNS
randomwalker-info-585	58	8	whose	whose	WP$
randomwalker-info-585	58	9	size	size	NN
randomwalker-info-585	58	10	grows	grow	VBZ
randomwalker-info-585	58	11	indefinitely	indefinitely	RB
randomwalker-info-585	58	12	with	with	IN
randomwalker-info-585	58	13	time	time	NN
randomwalker-info-585	58	14	.	.	.
randomwalker-info-585	59	1	We	-PRON-	PRP
randomwalker-info-585	59	2	confirm	confirm	VBP
randomwalker-info-585	59	3	this	this	DT
randomwalker-info-585	59	4	result	result	NN
randomwalker-info-585	59	5	using	use	VBG
randomwalker-info-585	59	6	simulation	simulation	NN
randomwalker-info-585	59	7	.	.	.
randomwalker-info-585	60	1	Accurately	accurately	RB
randomwalker-info-585	60	2	predicting	predict	VBG
randomwalker-info-585	60	3	the	the	DT
randomwalker-info-585	60	4	steady	steady	JJ
randomwalker-info-585	60	5	-	-	HYPH
randomwalker-info-585	60	6	state	state	NN
randomwalker-info-585	60	7	mining	mining	NN
randomwalker-info-585	60	8	behavior	behavior	NN
randomwalker-info-585	60	9	requires	require	VBZ
randomwalker-info-585	60	10	modeling	model	VBG
randomwalker-info-585	60	11	a	a	DT
randomwalker-info-585	60	12	vast	vast	JJ
randomwalker-info-585	60	13	number	number	NN
randomwalker-info-585	60	14	of	of	IN
randomwalker-info-585	60	15	variables	variable	NNS
randomwalker-info-585	60	16	such	such	JJ
randomwalker-info-585	60	17	as	as	IN
randomwalker-info-585	60	18	miners	miner	NNS
randomwalker-info-585	60	19	’	’	POS
randomwalker-info-585	60	20	cost	cost	NN
randomwalker-info-585	60	21	structure	structure	NN
randomwalker-info-585	60	22	,	,	,
randomwalker-info-585	60	23	and	and	CC
randomwalker-info-585	60	24	is	be	VBZ
randomwalker-info-585	60	25	not	not	RB
randomwalker-info-585	60	26	the	the	DT
randomwalker-info-585	60	27	goal	goal	NN
randomwalker-info-585	60	28	of	of	IN
randomwalker-info-585	60	29	our	-PRON-	PRP$
randomwalker-info-585	60	30	work	work	NN
randomwalker-info-585	60	31	.	.	.
randomwalker-info-585	61	1	Instead	instead	RB
randomwalker-info-585	61	2	,	,	,
randomwalker-info-585	61	3	our	-PRON-	PRP$
randomwalker-info-585	61	4	results	result	NNS
randomwalker-info-585	61	5	can	can	MD
randomwalker-info-585	61	6	be	be	VB
randomwalker-info-585	61	7	seen	see	VBN
randomwalker-info-585	61	8	as	as	IN
randomwalker-info-585	61	9	an	an	DT
randomwalker-info-585	61	10	informal	informal	JJ
randomwalker-info-585	61	11	“	"	``
randomwalker-info-585	61	12	lower	low	JJR
randomwalker-info-585	61	13	bound	bound	NN
randomwalker-info-585	61	14	”	"	''
randomwalker-info-585	61	15	on	on	IN
randomwalker-info-585	61	16	the	the	DT
randomwalker-info-585	61	17	departures	departure	NNS
randomwalker-info-585	61	18	from	from	IN
randomwalker-info-585	61	19	compliant	compliant	JJ
randomwalker-info-585	61	20	behavior	behavior	NN
randomwalker-info-585	61	21	that	that	WDT
randomwalker-info-585	61	22	are	be	VBP
randomwalker-info-585	61	23	likely	likely	JJ
randomwalker-info-585	61	24	in	in	IN
randomwalker-info-585	61	25	a	a	DT
randomwalker-info-585	61	26	transaction	transaction	NN
randomwalker-info-585	61	27	-	-	HYPH
randomwalker-info-585	61	28	fee	fee	NN
randomwalker-info-585	61	29	regime	regime	NN
randomwalker-info-585	61	30	.	.	.
randomwalker-info-585	62	1	We	-PRON-	PRP
randomwalker-info-585	62	2	can	can	MD
randomwalker-info-585	62	3	realistically	realistically	RB
randomwalker-info-585	62	4	predict	predict	VB
randomwalker-info-585	62	5	that	that	IN
randomwalker-info-585	62	6	PettyCompliant	PettyCompliant	NNP
randomwalker-info-585	62	7	miners	miner	NNS
randomwalker-info-585	62	8	will	will	MD
randomwalker-info-585	62	9	arise	arise	VB
randomwalker-info-585	62	10	,	,	,
randomwalker-info-585	62	11	and	and	CC
randomwalker-info-585	62	12	that	that	IN
randomwalker-info-585	62	13	the	the	DT
randomwalker-info-585	62	14	existence	existence	NN
randomwalker-info-585	62	15	of	of	IN
randomwalker-info-585	62	16	such	such	JJ
randomwalker-info-585	62	17	miners	miner	NNS
randomwalker-info-585	62	18	opens	open	VBZ
randomwalker-info-585	62	19	the	the	DT
randomwalker-info-585	62	20	field	field	NN
randomwalker-info-585	62	21	for	for	IN
randomwalker-info-585	62	22	various	various	JJ
randomwalker-info-585	62	23	more	more	RBR
randomwalker-info-585	62	24	aggressive	aggressive	JJ
randomwalker-info-585	62	25	strategies	strategy	NNS
randomwalker-info-585	62	26	(	(	-LRB-
randomwalker-info-585	62	27	Section	section	NN
randomwalker-info-585	62	28	5	5	CD
randomwalker-info-585	62	29	)	)	-RRB-
randomwalker-info-585	62	30	.	.	.
randomwalker-info-585	63	1	Contribution	contribution	NN
randomwalker-info-585	63	2	3	3	CD
randomwalker-info-585	63	3	:	:	:
randomwalker-info-585	63	4	Revisiting	revisit	VBG
randomwalker-info-585	63	5	selfish	selfish	JJ
randomwalker-info-585	63	6	mining	mining	NN
randomwalker-info-585	63	7	.	.	.
randomwalker-info-585	64	1	We	-PRON-	PRP
randomwalker-info-585	64	2	re-	re-	RB
randomwalker-info-585	64	3	visit	visit	VBP
randomwalker-info-585	64	4	the	the	DT
randomwalker-info-585	64	5	selfish	selfish	JJ
randomwalker-info-585	64	6	mining	mining	NN
randomwalker-info-585	64	7	strategy	strategy	NN
randomwalker-info-585	64	8	of	of	IN
randomwalker-info-585	64	9	Eyal	Eyal	NNP
randomwalker-info-585	64	10	and	and	CC
randomwalker-info-585	64	11	Sirer	Sirer	NNP
randomwalker-info-585	64	12	[	[	-LRB-
randomwalker-info-585	64	13	9	9	CD
randomwalker-info-585	64	14	]	]	-RRB-
randomwalker-info-585	64	15	and	and	CC
randomwalker-info-585	64	16	show	show	VBP
randomwalker-info-585	64	17	that	that	IN
randomwalker-info-585	64	18	,	,	,
randomwalker-info-585	64	19	contrary	contrary	JJ
randomwalker-info-585	64	20	to	to	IN
randomwalker-info-585	64	21	intuition	intuition	NN
randomwalker-info-585	64	22	,	,	,
randomwalker-info-585	64	23	it	-PRON-	PRP
randomwalker-info-585	64	24	performs	perform	VBZ
randomwalker-info-585	64	25	even	even	RB
randomwalker-info-585	64	26	better	well	RBR
randomwalker-info-585	64	27	in	in	IN
randomwalker-info-585	64	28	the	the	DT
randomwalker-info-585	64	29	transaction	transaction	NN
randomwalker-info-585	64	30	-	-	HYPH
randomwalker-info-585	64	31	fee	fee	NN
randomwalker-info-585	64	32	regime	regime	NN
randomwalker-info-585	64	33	than	than	IN
randomwalker-info-585	64	34	in	in	IN
randomwalker-info-585	64	35	the	the	DT
randomwalker-info-585	64	36	block	block	NN
randomwalker-info-585	64	37	-	-	HYPH
randomwalker-info-585	64	38	reward	reward	NN
randomwalker-info-585	64	39	regime	regime	NN
randomwalker-info-585	64	40	.	.	.
randomwalker-info-585	65	1	Next	next	RB
randomwalker-info-585	65	2	,	,	,
randomwalker-info-585	65	3	we	-PRON-	PRP
randomwalker-info-585	65	4	propose	propose	VBP
randomwalker-info-585	65	5	a	a	DT
randomwalker-info-585	65	6	more	more	RBR
randomwalker-info-585	65	7	sophisticated	sophisticated	JJ
randomwalker-info-585	65	8	selfish	selfish	JJ
randomwalker-info-585	65	9	mining	mining	NN
randomwalker-info-585	65	10	strat-	strat-	NN
randomwalker-info-585	65	11	egy	egy	NN
randomwalker-info-585	65	12	that	that	WDT
randomwalker-info-585	65	13	accounts	account	VBZ
randomwalker-info-585	65	14	for	for	IN
randomwalker-info-585	65	15	the	the	DT
randomwalker-info-585	65	16	non	non	JJ
randomwalker-info-585	65	17	-	-	JJ
randomwalker-info-585	65	18	uniformity	uniformity	JJ
randomwalker-info-585	65	19	of	of	IN
randomwalker-info-585	65	20	rewards	reward	NNS
randomwalker-info-585	65	21	and	and	CC
randomwalker-info-585	65	22	out-	out-	NNP
randomwalker-info-585	65	23	performs	perform	VBZ
randomwalker-info-585	65	24	both	both	CC
randomwalker-info-585	65	25	default	default	NN
randomwalker-info-585	65	26	mining	mining	NN
randomwalker-info-585	65	27	and	and	CC
randomwalker-info-585	65	28	“	"	``
randomwalker-info-585	65	29	classic	classic	JJ
randomwalker-info-585	65	30	”	"	''
randomwalker-info-585	65	31	selfish	selfish	JJ
randomwalker-info-585	65	32	mining	mining	NN
randomwalker-info-585	65	33	.	.	.
randomwalker-info-585	66	1	Worse	bad	JJR
randomwalker-info-585	66	2	,	,	,
randomwalker-info-585	66	3	unlike	unlike	IN
randomwalker-info-585	66	4	classic	classic	JJ
randomwalker-info-585	66	5	selfish	selfish	JJ
randomwalker-info-585	66	6	mining	mining	NN
randomwalker-info-585	66	7	,	,	,
randomwalker-info-585	66	8	this	this	DT
randomwalker-info-585	66	9	strategy	strategy	NN
randomwalker-info-585	66	10	works	work	VBZ
randomwalker-info-585	66	11	for	for	IN
randomwalker-info-585	66	12	miners	miner	NNS
randomwalker-info-585	66	13	with	with	IN
randomwalker-info-585	66	14	arbitrarily	arbitrarily	RB
randomwalker-info-585	66	15	low	low	JJ
randomwalker-info-585	66	16	hash	hash	NN
randomwalker-info-585	66	17	power	power	NN
randomwalker-info-585	66	18	and	and	CC
randomwalker-info-585	66	19	regardless	regardless	RB
randomwalker-info-585	66	20	of	of	IN
randomwalker-info-585	66	21	their	-PRON-	PRP$
randomwalker-info-585	66	22	connectedness	connectedness	NN
randomwalker-info-585	66	23	in	in	IN
randomwalker-info-585	66	24	the	the	DT
randomwalker-info-585	66	25	Bitcoin	Bitcoin	NNP
randomwalker-info-585	66	26	network	network	NN
randomwalker-info-585	66	27	.	.	.
randomwalker-info-585	67	1	Moreover	moreover	RB
randomwalker-info-585	67	2	,	,	,
randomwalker-info-585	67	3	the	the	DT
randomwalker-info-585	67	4	attack	attack	NN
randomwalker-info-585	67	5	is	be	VBZ
randomwalker-info-585	67	6	profitable	profitable	JJ
randomwalker-info-585	67	7	as	as	RB
randomwalker-info-585	67	8	soon	soon	RB
randomwalker-info-585	67	9	as	as	IN
randomwalker-info-585	67	10	it	-PRON-	PRP
randomwalker-info-585	67	11	is	be	VBZ
randomwalker-info-585	67	12	deployed	deploy	VBN
randomwalker-info-585	67	13	,	,	,
randomwalker-info-585	67	14	whereas	whereas	IN
randomwalker-info-585	67	15	classic	classic	JJ
randomwalker-info-585	67	16	selfish	selfish	JJ
randomwalker-info-585	67	17	mining	mining	NN
randomwalker-info-585	67	18	only	only	RB
randomwalker-info-585	67	19	becomes	become	VBZ
randomwalker-info-585	67	20	profitable	profitable	JJ
randomwalker-info-585	67	21	after	after	IN
randomwalker-info-585	67	22	a	a	DT
randomwalker-info-585	67	23	two	two	CD
randomwalker-info-585	67	24	-	-	HYPH
randomwalker-info-585	67	25	week	week	NN
randomwalker-info-585	67	26	dif-	dif-	CC
randomwalker-info-585	67	27	ficulty	ficulty	NN
randomwalker-info-585	67	28	adjustment	adjustment	NN
randomwalker-info-585	67	29	period	period	NN
randomwalker-info-585	67	30	,	,	,
randomwalker-info-585	67	31	arguably	arguably	RB
randomwalker-info-585	67	32	giving	give	VBG
randomwalker-info-585	67	33	the	the	DT
randomwalker-info-585	67	34	community	community	NN
randomwalker-info-585	67	35	a	a	DT
randomwalker-info-585	67	36	crucial	crucial	JJ
randomwalker-info-585	67	37	window	window	NN
randomwalker-info-585	67	38	of	of	IN
randomwalker-info-585	67	39	time	time	NN
randomwalker-info-585	67	40	to	to	TO
randomwalker-info-585	67	41	detect	detect	VB
randomwalker-info-585	67	42	and	and	CC
randomwalker-info-585	67	43	respond	respond	VB
randomwalker-info-585	67	44	to	to	IN
randomwalker-info-585	67	45	such	such	PDT
randomwalker-info-585	67	46	an	an	DT
randomwalker-info-585	67	47	attack	attack	NN
randomwalker-info-585	67	48	[	[	-LRB-
randomwalker-info-585	67	49	10	10	CD
randomwalker-info-585	67	50	]	]	-RRB-
randomwalker-info-585	67	51	.	.	.
randomwalker-info-585	68	1	We	-PRON-	PRP
randomwalker-info-585	68	2	validate	validate	VBP
randomwalker-info-585	68	3	these	these	DT
randomwalker-info-585	68	4	results	result	NNS
randomwalker-info-585	68	5	via	via	IN
randomwalker-info-585	68	6	both	both	DT
randomwalker-info-585	68	7	theory	theory	NN
randomwalker-info-585	68	8	and	and	CC
randomwalker-info-585	68	9	simulation	simulation	NN
randomwalker-info-585	68	10	(	(	-LRB-
randomwalker-info-585	68	11	Section	section	NN
randomwalker-info-585	68	12	6	6	CD
randomwalker-info-585	68	13	)	)	-RRB-
randomwalker-info-585	68	14	.	.	.
randomwalker-info-585	69	1	Impact	impact	VB
randomwalker-info-585	69	2	on	on	IN
randomwalker-info-585	69	3	Bitcoin	Bitcoin	NNP
randomwalker-info-585	69	4	security	security	NN
randomwalker-info-585	69	5	.	.	.
randomwalker-info-585	70	1	If	if	IN
randomwalker-info-585	70	2	any	any	DT
randomwalker-info-585	70	3	of	of	IN
randomwalker-info-585	70	4	the	the	DT
randomwalker-info-585	70	5	deviant	deviant	NN
randomwalker-info-585	70	6	min-	min-	JJ
randomwalker-info-585	70	7	ing	ing	NNP
randomwalker-info-585	70	8	strategies	strategy	NNS
randomwalker-info-585	70	9	we	-PRON-	PRP
randomwalker-info-585	70	10	explore	explore	VBP
randomwalker-info-585	70	11	were	be	VBD
randomwalker-info-585	70	12	to	to	TO
randomwalker-info-585	70	13	be	be	VB
randomwalker-info-585	70	14	deployed	deploy	VBN
randomwalker-info-585	70	15	,	,	,
randomwalker-info-585	70	16	the	the	DT
randomwalker-info-585	70	17	impact	impact	NN
randomwalker-info-585	70	18	on	on	IN
randomwalker-info-585	70	19	Bitcoin	Bitcoin	NNP
randomwalker-info-585	70	20	’s	’s	POS
randomwalker-info-585	70	21	security	security	NN
randomwalker-info-585	70	22	would	would	MD
randomwalker-info-585	70	23	be	be	VB
randomwalker-info-585	70	24	serious	serious	JJ
randomwalker-info-585	70	25	.	.	.
randomwalker-info-585	71	1	At	at	IN
randomwalker-info-585	71	2	best	well	RBS
randomwalker-info-585	71	3	,	,	,
randomwalker-info-585	71	4	the	the	DT
randomwalker-info-585	71	5	block	block	NN
randomwalker-info-585	71	6	chain	chain	NN
randomwalker-info-585	71	7	will	will	MD
randomwalker-info-585	71	8	have	have	VB
randomwalker-info-585	71	9	a	a	DT
randomwalker-info-585	71	10	significant	significant	JJ
randomwalker-info-585	71	11	fraction	fraction	NN
randomwalker-info-585	71	12	of	of	IN
randomwalker-info-585	71	13	stale	stale	JJ
randomwalker-info-585	71	14	or	or	CC
randomwalker-info-585	71	15	orphaned	orphan	VBN
randomwalker-info-585	71	16	blocks	block	NNS
randomwalker-info-585	71	17	due	due	JJ
randomwalker-info-585	71	18	to	to	IN
randomwalker-info-585	71	19	constant	constant	JJ
randomwalker-info-585	71	20	forks	fork	NNS
randomwalker-info-585	71	21	,	,	,
randomwalker-info-585	71	22	making	make	VBG
randomwalker-info-585	71	23	51	51	CD
randomwalker-info-585	71	24	%	%	NN
randomwalker-info-585	71	25	attacks	attack	NNS
randomwalker-info-585	71	26	much	much	RB
randomwalker-info-585	71	27	eas-	eas-	RB
randomwalker-info-585	71	28	ier	ier	RBR
randomwalker-info-585	71	29	and	and	CC
randomwalker-info-585	71	30	increasing	increase	VBG
randomwalker-info-585	71	31	the	the	DT
randomwalker-info-585	71	32	transaction	transaction	NN
randomwalker-info-585	71	33	confirmation	confirmation	NN
randomwalker-info-585	71	34	time	time	NN
randomwalker-info-585	71	35	.	.	.
randomwalker-info-585	72	1	At	at	RB
randomwalker-info-585	72	2	worst	worst	RBS
randomwalker-info-585	72	3	,	,	,
randomwalker-info-585	72	4	consensus	consensus	NN
randomwalker-info-585	72	5	will	will	MD
randomwalker-info-585	72	6	break	break	VB
randomwalker-info-585	72	7	down	down	RP
randomwalker-info-585	72	8	due	due	IN
randomwalker-info-585	72	9	to	to	IN
randomwalker-info-585	72	10	block	block	NN
randomwalker-info-585	72	11	withholding	withholding	NN
randomwalker-info-585	72	12	or	or	CC
randomwalker-info-585	72	13	increasingly	increasingly	RB
randomwalker-info-585	72	14	aggressive	aggressive	JJ
randomwalker-info-585	72	15	undercutting	undercutting	NN
randomwalker-info-585	72	16	.	.	.
randomwalker-info-585	73	1	This	this	DT
randomwalker-info-585	73	2	suggests	suggest	VBZ
randomwalker-info-585	73	3	a	a	DT
randomwalker-info-585	73	4	fundamental	fundamental	JJ
randomwalker-info-585	73	5	rethinking	rethinking	NN
randomwalker-info-585	73	6	of	of	IN
randomwalker-info-585	73	7	the	the	DT
randomwalker-info-585	73	8	role	role	NN
randomwalker-info-585	73	9	of	of	IN
randomwalker-info-585	73	10	block	block	NN
randomwalker-info-585	73	11	rewards	reward	NNS
randomwalker-info-585	73	12	in	in	IN
randomwalker-info-585	73	13	cryptocurrency	cryptocurrency	NN
randomwalker-info-585	73	14	design	design	NN
randomwalker-info-585	73	15	.	.	.
randomwalker-info-585	74	1	Nakamoto	Nakamoto	NNP
randomwalker-info-585	74	2	appears	appear	VBZ
randomwalker-info-585	74	3	to	to	TO
randomwalker-info-585	74	4	have	have	VB
randomwalker-info-585	74	5	viewed	view	VBN
randomwalker-info-585	74	6	the	the	DT
randomwalker-info-585	74	7	block	block	NN
randomwalker-info-585	74	8	reward	reward	NN
randomwalker-info-585	74	9	as	as	IN
randomwalker-info-585	74	10	a	a	DT
randomwalker-info-585	74	11	necessary	necessary	JJ
randomwalker-info-585	74	12	but	but	CC
randomwalker-info-585	74	13	temporary	temporary	JJ
randomwalker-info-585	74	14	evil	evil	NN
randomwalker-info-585	74	15	to	to	TO
randomwalker-info-585	74	16	achieve	achieve	VB
randomwalker-info-585	74	17	an	an	DT
randomwalker-info-585	74	18	initial	initial	JJ
randomwalker-info-585	74	19	allocation	allocation	NN
randomwalker-info-585	74	20	of	of	IN
randomwalker-info-585	74	21	bitcoins	bitcoin	NNS
randomwalker-info-585	74	22	in	in	IN
randomwalker-info-585	74	23	the	the	DT
randomwalker-info-585	74	24	absence	absence	NN
randomwalker-info-585	74	25	of	of	IN
randomwalker-info-585	74	26	a	a	DT
randomwalker-info-585	74	27	central	central	JJ
randomwalker-info-585	74	28	authority	authority	NN
randomwalker-info-585	74	29	,	,	,
randomwalker-info-585	74	30	with	with	IN
randomwalker-info-585	74	31	the	the	DT
randomwalker-info-585	74	32	transaction	transaction	NN
randomwalker-info-585	74	33	fee	fee	NN
randomwalker-info-585	74	34	regime	regime	NN
randomwalker-info-585	74	35	being	be	VBG
randomwalker-info-585	74	36	the	the	DT
randomwalker-info-585	74	37	ideal	ideal	NN
randomwalker-info-585	74	38	,	,	,
randomwalker-info-585	74	39	inflation	inflation	NN
randomwalker-info-585	74	40	-	-	HYPH
randomwalker-info-585	74	41	free	free	JJ
randomwalker-info-585	74	42	steady	steady	JJ
randomwalker-info-585	74	43	state	state	NN
randomwalker-info-585	74	44	of	of	IN
randomwalker-info-585	74	45	the	the	DT
randomwalker-info-585	74	46	system	system	NN
randomwalker-info-585	74	47	.	.	.
randomwalker-info-585	75	1	But	but	CC
randomwalker-info-585	75	2	our	-PRON-	PRP$
randomwalker-info-585	75	3	work	work	NN
randomwalker-info-585	75	4	shows	show	VBZ
randomwalker-info-585	75	5	that	that	IN
randomwalker-info-585	75	6	incentivizing	incentivize	VBG
randomwalker-info-585	75	7	compliant	compliant	JJ
randomwalker-info-585	75	8	miner	miner	NN
randomwalker-info-585	75	9	behavior	behavior	NN
randomwalker-info-585	75	10	in	in	IN
randomwalker-info-585	75	11	the	the	DT
randomwalker-info-585	75	12	transaction	transaction	NN
randomwalker-info-585	75	13	fee	fee	NN
randomwalker-info-585	75	14	regime	regime	NN
randomwalker-info-585	75	15	is	be	VBZ
randomwalker-info-585	75	16	a	a	DT
randomwalker-info-585	75	17	significantly	significantly	RB
randomwalker-info-585	75	18	more	more	RBR
randomwalker-info-585	75	19	daunting	daunting	JJ
randomwalker-info-585	75	20	task	task	NN
randomwalker-info-585	75	21	than	than	IN
randomwalker-info-585	75	22	in	in	IN
randomwalker-info-585	75	23	the	the	DT
randomwalker-info-585	75	24	block	block	NN
randomwalker-info-585	75	25	reward	reward	NN
randomwalker-info-585	75	26	regime	regime	NN
randomwalker-info-585	75	27	.	.	.
randomwalker-info-585	76	1	Perhaps	perhaps	RB
randomwalker-info-585	76	2	instead	instead	RB
randomwalker-info-585	76	3	,	,	,
randomwalker-info-585	76	4	de-	de-	XX
randomwalker-info-585	76	5	signers	signer	NNS
randomwalker-info-585	76	6	of	of	IN
randomwalker-info-585	76	7	new	new	JJ
randomwalker-info-585	76	8	cryptocurrencies	cryptocurrencie	NNS
randomwalker-info-585	76	9	must	must	MD
randomwalker-info-585	76	10	resign	resign	VB
randomwalker-info-585	76	11	themselves	-PRON-	PRP
randomwalker-info-585	76	12	to	to	IN
randomwalker-info-585	76	13	the	the	DT
randomwalker-info-585	76	14	inevitability	inevitability	NN
randomwalker-info-585	76	15	of	of	IN
randomwalker-info-585	76	16	monetary	monetary	JJ
randomwalker-info-585	76	17	inflation	inflation	NN
randomwalker-info-585	76	18	and	and	CC
randomwalker-info-585	76	19	make	make	VB
randomwalker-info-585	76	20	the	the	DT
randomwalker-info-585	76	21	block	block	NN
randomwalker-info-585	76	22	reward	reward	NN
randomwalker-info-585	76	23	permanent	permanent	JJ
randomwalker-info-585	76	24	.	.	.
randomwalker-info-585	77	1	Transaction	transaction	NN
randomwalker-info-585	77	2	fees	fee	NNS
randomwalker-info-585	77	3	would	would	MD
randomwalker-info-585	77	4	still	still	RB
randomwalker-info-585	77	5	exist	exist	VB
randomwalker-info-585	77	6	,	,	,
randomwalker-info-585	77	7	but	but	CC
randomwalker-info-585	77	8	merely	merely	RB
randomwalker-info-585	77	9	as	as	IN
randomwalker-info-585	77	10	an	an	DT
randomwalker-info-585	77	11	incentive	incentive	NN
randomwalker-info-585	77	12	for	for	IN
randomwalker-info-585	77	13	miners	miner	NNS
randomwalker-info-585	77	14	to	to	TO
randomwalker-info-585	77	15	include	include	VB
randomwalker-info-585	77	16	transactions	transaction	NNS
randomwalker-info-585	77	17	in	in	IN
randomwalker-info-585	77	18	their	-PRON-	PRP$
randomwalker-info-585	77	19	blocks	block	NNS
randomwalker-info-585	77	20	.	.	.
randomwalker-info-585	78	1	2	2	LS
randomwalker-info-585	78	2	.	.	.
randomwalker-info-585	79	1	RELATED	related	JJ
randomwalker-info-585	79	2	WORK	work	NN
randomwalker-info-585	79	3	Several	several	JJ
randomwalker-info-585	79	4	recent	recent	JJ
randomwalker-info-585	79	5	works	work	NNS
randomwalker-info-585	79	6	analyze	analyze	VBP
randomwalker-info-585	79	7	incentives	incentive	NNS
randomwalker-info-585	79	8	in	in	IN
randomwalker-info-585	79	9	Bitcoin	Bitcoin	NNP
randomwalker-info-585	79	10	min-	min-	JJ
randomwalker-info-585	79	11	ing	ing	NN
randomwalker-info-585	79	12	.	.	.
randomwalker-info-585	80	1	Some	some	DT
randomwalker-info-585	80	2	examples	example	NNS
randomwalker-info-585	80	3	include	include	VBP
randomwalker-info-585	80	4	[	[	-LRB-
randomwalker-info-585	80	5	12	12	CD
randomwalker-info-585	80	6	]	]	-RRB-
randomwalker-info-585	80	7	and	and	CC
randomwalker-info-585	80	8	[	[	-LRB-
randomwalker-info-585	80	9	8	8	CD
randomwalker-info-585	80	10	]	]	-RRB-
randomwalker-info-585	80	11	,	,	,
randomwalker-info-585	80	12	which	which	WDT
randomwalker-info-585	80	13	analyze	analyze	VBP
randomwalker-info-585	80	14	how	how	WRB
randomwalker-info-585	80	15	strategic	strategic	JJ
randomwalker-info-585	80	16	mining	mining	NN
randomwalker-info-585	80	17	pools	pool	NNS
randomwalker-info-585	80	18	may	may	MD
randomwalker-info-585	80	19	attack	attack	VB
randomwalker-info-585	80	20	competing	compete	VBG
randomwalker-info-585	80	21	pools	pool	NNS
randomwalker-info-585	80	22	in	in	IN
randomwalker-info-585	80	23	vari-	vari-	NNP
randomwalker-info-585	80	24	ous	ous	JJ
randomwalker-info-585	80	25	ways	way	NNS
randomwalker-info-585	80	26	,	,	,
randomwalker-info-585	80	27	and	and	CC
randomwalker-info-585	80	28	[	[	-LRB-
randomwalker-info-585	80	29	16	16	CD
randomwalker-info-585	80	30	]	]	-RRB-
randomwalker-info-585	80	31	,	,	,
randomwalker-info-585	80	32	which	which	WDT
randomwalker-info-585	80	33	analyzes	analyze	VBZ
randomwalker-info-585	80	34	how	how	WRB
randomwalker-info-585	80	35	strategic	strategic	JJ
randomwalker-info-585	80	36	Ethereum	ethereum	JJ
randomwalker-info-585	80	37	miners	miner	NNS
randomwalker-info-585	80	38	can	can	MD
randomwalker-info-585	80	39	trick	trick	VB
randomwalker-info-585	80	40	others	other	NNS
randomwalker-info-585	80	41	into	into	IN
randomwalker-info-585	80	42	wasting	waste	VBG
randomwalker-info-585	80	43	their	-PRON-	PRP$
randomwalker-info-585	80	44	computational	computational	JJ
randomwalker-info-585	80	45	power	power	NN
randomwalker-info-585	80	46	verifying	verify	VBG
randomwalker-info-585	80	47	the	the	DT
randomwalker-info-585	80	48	validity	validity	NN
randomwalker-info-585	80	49	of	of	IN
randomwalker-info-585	80	50	complex	complex	JJ
randomwalker-info-585	80	51	scripts	script	NNS
randomwalker-info-585	80	52	.	.	.
randomwalker-info-585	81	1	Understand-	Understand-	NNP
randomwalker-info-585	81	2	ing	ing	NNP
randomwalker-info-585	81	3	miner	miner	NN
randomwalker-info-585	81	4	incentives	incentive	VBZ
randomwalker-info-585	81	5	in	in	IN
randomwalker-info-585	81	6	the	the	DT
randomwalker-info-585	81	7	Bitcoin	Bitcoin	NNP
randomwalker-info-585	81	8	system	system	NN
randomwalker-info-585	81	9	is	be	VBZ
randomwalker-info-585	81	10	important	important	JJ
randomwalker-info-585	81	11	—	—	:
randomwalker-info-585	81	12	there	there	EX
randomwalker-info-585	81	13	is	be	VBZ
randomwalker-info-585	81	14	empirical	empirical	JJ
randomwalker-info-585	81	15	evidence	evidence	NN
randomwalker-info-585	81	16	that	that	IN
randomwalker-info-585	81	17	miners	miner	NNS
randomwalker-info-585	81	18	/	/	SYM
randomwalker-info-585	81	19	mining	mining	NN
randomwalker-info-585	81	20	pools	pool	NNS
randomwalker-info-585	81	21	are	be	VBP
randomwalker-info-585	81	22	willing	willing	JJ
randomwalker-info-585	81	23	to	to	TO
randomwalker-info-585	81	24	attack	attack	VB
randomwalker-info-585	81	25	others	other	NNS
randomwalker-info-585	81	26	in	in	IN
randomwalker-info-585	81	27	order	order	NN
randomwalker-info-585	81	28	to	to	TO
randomwalker-info-585	81	29	maximize	maximize	VB
randomwalker-info-585	81	30	their	-PRON-	PRP$
randomwalker-info-585	81	31	own	own	JJ
randomwalker-info-585	81	32	prof-	prof-	NN
randomwalker-info-585	81	33	its	-PRON-	PRP$
randomwalker-info-585	81	34	(	(	-LRB-
randomwalker-info-585	81	35	e.g.	e.g.	RB
randomwalker-info-585	82	1	launching	launch	VBG
randomwalker-info-585	82	2	DDoS	DDoS	NNP
randomwalker-info-585	82	3	attacks	attack	NNS
randomwalker-info-585	82	4	against	against	IN
randomwalker-info-585	82	5	other	other	JJ
randomwalker-info-585	82	6	pools	pool	NNS
randomwalker-info-585	82	7	)	)	-RRB-
randomwalker-info-585	82	8	[	[	-LRB-
randomwalker-info-585	82	9	24	24	CD
randomwalker-info-585	82	10	]	]	-RRB-
randomwalker-info-585	82	11	.	.	.
randomwalker-info-585	83	1	Eyal	Eyal	NNP
randomwalker-info-585	83	2	and	and	CC
randomwalker-info-585	83	3	Sirer	Sirer	NNP
randomwalker-info-585	83	4	develop	develop	VBP
randomwalker-info-585	83	5	the	the	DT
randomwalker-info-585	83	6	selfish	selfish	JJ
randomwalker-info-585	83	7	mining	mining	NN
randomwalker-info-585	83	8	attack	attack	NN
randomwalker-info-585	83	9	[	[	-LRB-
randomwalker-info-585	83	10	9	9	CD
randomwalker-info-585	83	11	]	]	-RRB-
randomwalker-info-585	83	12	,	,	,
randomwalker-info-585	83	13	a	a	DT
randomwalker-info-585	83	14	de-	de-	RB
randomwalker-info-585	83	15	viant	viant	JJ
randomwalker-info-585	83	16	mining	mining	NN
randomwalker-info-585	83	17	strategy	strategy	NN
randomwalker-info-585	83	18	that	that	WDT
randomwalker-info-585	83	19	enables	enable	VBZ
randomwalker-info-585	83	20	miners	miner	NNS
randomwalker-info-585	83	21	to	to	TO
randomwalker-info-585	83	22	get	get	VB
randomwalker-info-585	83	23	more	more	JJR
randomwalker-info-585	83	24	than	than	IN
randomwalker-info-585	83	25	their	-PRON-	PRP$
randomwalker-info-585	83	26	fair	fair	JJ
randomwalker-info-585	83	27	share	share	NN
randomwalker-info-585	83	28	of	of	IN
randomwalker-info-585	83	29	rewards	reward	NNS
randomwalker-info-585	83	30	.	.	.
randomwalker-info-585	84	1	We	-PRON-	PRP
randomwalker-info-585	84	2	build	build	VBP
randomwalker-info-585	84	3	on	on	IN
randomwalker-info-585	84	4	their	-PRON-	PRP$
randomwalker-info-585	84	5	results	result	NNS
randomwalker-info-585	84	6	in	in	IN
randomwalker-info-585	84	7	Sec-	Sec-	NNP
randomwalker-info-585	84	8	tion	tion	NN
randomwalker-info-585	84	9	6	6	CD
randomwalker-info-585	84	10	.	.	.
randomwalker-info-585	85	1	Other	other	JJ
randomwalker-info-585	85	2	works	work	NNS
randomwalker-info-585	85	3	,	,	,
randomwalker-info-585	85	4	notably	notably	RB
randomwalker-info-585	85	5	Sapirshtein	Sapirshtein	NNP
randomwalker-info-585	85	6	et	et	FW
randomwalker-info-585	85	7	al	al	NNP
randomwalker-info-585	85	8	.	.	.
randomwalker-info-585	86	1	[	[	-LRB-
randomwalker-info-585	86	2	23	23	CD
randomwalker-info-585	86	3	]	]	-RRB-
randomwalker-info-585	86	4	have	have	VBP
randomwalker-info-585	86	5	analyzed	analyze	VBN
randomwalker-info-585	86	6	selfish	selfish	JJ
randomwalker-info-585	86	7	mining	mining	NN
randomwalker-info-585	86	8	in	in	IN
randomwalker-info-585	86	9	more	more	JJR
randomwalker-info-585	86	10	detail	detail	NN
randomwalker-info-585	86	11	using	use	VBG
randomwalker-info-585	86	12	Markov	Markov	NNP
randomwalker-info-585	86	13	Deci-	Deci-	NNP
randomwalker-info-585	86	14	sion	sion	NN
randomwalker-info-585	86	15	Processes	process	NNS
randomwalker-info-585	86	16	(	(	-LRB-
randomwalker-info-585	86	17	MDP	MDP	NNP
randomwalker-info-585	86	18	)	)	-RRB-
randomwalker-info-585	86	19	.	.	.
randomwalker-info-585	87	1	In	in	IN
randomwalker-info-585	87	2	an	an	DT
randomwalker-info-585	87	3	MDP	MDP	NNP
randomwalker-info-585	87	4	,	,	,
randomwalker-info-585	87	5	a	a	DT
randomwalker-info-585	87	6	player	player	NN
randomwalker-info-585	87	7	moves	move	VBZ
randomwalker-info-585	87	8	through	through	IN
randomwalker-info-585	87	9	a	a	DT
randomwalker-info-585	87	10	discrete	discrete	JJ
randomwalker-info-585	87	11	state	state	NN
randomwalker-info-585	87	12	space	space	NN
randomwalker-info-585	87	13	and	and	CC
randomwalker-info-585	87	14	tries	try	VBZ
randomwalker-info-585	87	15	to	to	TO
randomwalker-info-585	87	16	maximize	maximize	VB
randomwalker-info-585	87	17	reward	reward	NN
randomwalker-info-585	87	18	(	(	-LRB-
randomwalker-info-585	87	19	the	the	DT
randomwalker-info-585	87	20	state-	state-	NNP
randomwalker-info-585	87	21	transition	transition	NNP
randomwalker-info-585	87	22	function	function	NNP
randomwalker-info-585	87	23	and	and	CC
randomwalker-info-585	87	24	reward	reward	NN
randomwalker-info-585	87	25	function	function	NN
randomwalker-info-585	87	26	are	be	VBP
randomwalker-info-585	87	27	probabilistic	probabilistic	JJ
randomwalker-info-585	87	28	)	)	-RRB-
randomwalker-info-585	87	29	.	.	.
randomwalker-info-585	88	1	This	this	DT
randomwalker-info-585	88	2	makes	make	VBZ
randomwalker-info-585	88	3	it	-PRON-	PRP
randomwalker-info-585	88	4	a	a	DT
randomwalker-info-585	88	5	good	good	JJ
randomwalker-info-585	88	6	fit	fit	NN
randomwalker-info-585	88	7	for	for	IN
randomwalker-info-585	88	8	modeling	model	VBG
randomwalker-info-585	88	9	Bitcoin	Bitcoin	NNP
randomwalker-info-585	88	10	mining	mining	NN
randomwalker-info-585	88	11	.	.	.
randomwalker-info-585	89	1	In	in	IN
randomwalker-info-585	89	2	the	the	DT
randomwalker-info-585	89	3	fixed	fix	VBN
randomwalker-info-585	89	4	-	-	HYPH
randomwalker-info-585	89	5	reward	reward	NN
randomwalker-info-585	89	6	model	model	NN
randomwalker-info-585	89	7	,	,	,
randomwalker-info-585	89	8	states	state	NNS
randomwalker-info-585	89	9	are	be	VBP
randomwalker-info-585	89	10	discrete	discrete	JJ
randomwalker-info-585	89	11	.	.	.
randomwalker-info-585	90	1	In	in	IN
randomwalker-info-585	90	2	the	the	DT
randomwalker-info-585	90	3	transaction	transaction	NN
randomwalker-info-585	90	4	fees	fee	NNS
randomwalker-info-585	90	5	model	model	NN
randomwalker-info-585	90	6	,	,	,
randomwalker-info-585	90	7	states	state	NNS
randomwalker-info-585	90	8	are	be	VBP
randomwalker-info-585	90	9	continuous	continuous	JJ
randomwalker-info-585	90	10	,	,	,
randomwalker-info-585	90	11	so	so	IN
randomwalker-info-585	90	12	we	-PRON-	PRP
randomwalker-info-585	90	13	can	can	MD
randomwalker-info-585	90	14	not	not	RB
randomwalker-info-585	90	15	apply	apply	VB
randomwalker-info-585	90	16	MDP	MDP	NNP
randomwalker-info-585	90	17	machinery	machinery	NN
randomwalker-info-585	90	18	directly	directly	RB
randomwalker-info-585	90	19	.	.	.
randomwalker-info-585	91	1	Still	still	RB
randomwalker-info-585	91	2	,	,	,
randomwalker-info-585	91	3	our	-PRON-	PRP$
randomwalker-info-585	91	4	analysis	analysis	NN
randomwalker-info-585	91	5	takes	take	VBZ
randomwalker-info-585	91	6	an	an	DT
randomwalker-info-585	91	7	MDP	MDP	NNP
randomwalker-info-585	91	8	-	-	HYPH
randomwalker-info-585	91	9	like	like	JJ
randomwalker-info-585	91	10	approach	approach	NN
randomwalker-info-585	91	11	.	.	.
randomwalker-info-585	92	1	In	in	IN
randomwalker-info-585	92	2	more	more	JJR
randomwalker-info-585	92	3	recent	recent	JJ
randomwalker-info-585	92	4	work	work	NN
randomwalker-info-585	92	5	,	,	,
randomwalker-info-585	92	6	Kiayias	Kiayias	NNP
randomwalker-info-585	92	7	et	et	NNP
randomwalker-info-585	92	8	.	.	.
randomwalker-info-585	93	1	al	al	NNP
randomwalker-info-585	93	2	.	.	.
randomwalker-info-585	94	1	[	[	-LRB-
randomwalker-info-585	94	2	13	13	CD
randomwalker-info-585	94	3	]	]	-RRB-
randomwalker-info-585	94	4	perform	perform	VBP
randomwalker-info-585	94	5	a	a	DT
randomwalker-info-585	94	6	theoretical	theoretical	JJ
randomwalker-info-585	94	7	analysis	analysis	NN
randomwalker-info-585	94	8	of	of	IN
randomwalker-info-585	94	9	various	various	JJ
randomwalker-info-585	94	10	selfish	selfish	JJ
randomwalker-info-585	94	11	mining	mining	NN
randomwalker-info-585	94	12	strategies	strategy	NNS
randomwalker-info-585	94	13	in	in	IN
randomwalker-info-585	94	14	the	the	DT
randomwalker-info-585	94	15	fixed	fix	VBN
randomwalker-info-585	94	16	-	-	HYPH
randomwalker-info-585	94	17	reward	reward	NN
randomwalker-info-585	94	18	model	model	NN
randomwalker-info-585	94	19	,	,	,
randomwalker-info-585	94	20	and	and	CC
randomwalker-info-585	94	21	proves	prove	VBZ
randomwalker-info-585	94	22	that	that	IN
randomwalker-info-585	94	23	when	when	WRB
randomwalker-info-585	94	24	miners	miner	NNS
randomwalker-info-585	94	25	are	be	VBP
randomwalker-info-585	94	26	sufficiently	sufficiently	RB
randomwalker-info-585	94	27	small	small	JJ
randomwalker-info-585	94	28	,	,	,
randomwalker-info-585	94	29	the	the	DT
randomwalker-info-585	94	30	default	default	NN
randomwalker-info-585	94	31	mining	mining	NN
randomwalker-info-585	94	32	behavior	behavior	NN
randomwalker-info-585	94	33	is	be	VBZ
randomwalker-info-585	94	34	an	an	DT
randomwalker-info-585	94	35	equilib-	equilib-	JJ
randomwalker-info-585	94	36	rium	rium	NN
randomwalker-info-585	94	37	.	.	.
randomwalker-info-585	95	1	There	there	EX
randomwalker-info-585	95	2	is	be	VBZ
randomwalker-info-585	95	3	some	some	DT
randomwalker-info-585	95	4	work	work	NN
randomwalker-info-585	95	5	on	on	IN
randomwalker-info-585	95	6	understanding	understand	VBG
randomwalker-info-585	95	7	the	the	DT
randomwalker-info-585	95	8	market	market	NN
randomwalker-info-585	95	9	for	for	IN
randomwalker-info-585	95	10	trans-	trans-	JJ
randomwalker-info-585	95	11	action	action	NN
randomwalker-info-585	95	12	fees	fee	NNS
randomwalker-info-585	95	13	and	and	CC
randomwalker-info-585	95	14	its	-PRON-	PRP$
randomwalker-info-585	95	15	relation	relation	NN
randomwalker-info-585	95	16	to	to	IN
randomwalker-info-585	95	17	the	the	DT
randomwalker-info-585	95	18	block	block	NN
randomwalker-info-585	95	19	size	size	NN
randomwalker-info-585	95	20	(	(	-LRB-
randomwalker-info-585	95	21	i.e.	i.e.	FW
randomwalker-info-585	96	1	what	what	WDT
randomwalker-info-585	96	2	fees	fee	NNS
randomwalker-info-585	96	3	will	will	MD
randomwalker-info-585	96	4	users	user	NNS
randomwalker-info-585	96	5	have	have	VB
randomwalker-info-585	96	6	to	to	TO
randomwalker-info-585	96	7	pay	pay	VB
randomwalker-info-585	96	8	in	in	IN
randomwalker-info-585	96	9	order	order	NN
randomwalker-info-585	96	10	for	for	IN
randomwalker-info-585	96	11	transactions	transaction	NNS
randomwalker-info-585	96	12	to	to	TO
randomwalker-info-585	96	13	be	be	VB
randomwalker-info-585	96	14	in-	in-	RB
randomwalker-info-585	96	15	cluded	clude	VBN
randomwalker-info-585	96	16	in	in	IN
randomwalker-info-585	96	17	a	a	DT
randomwalker-info-585	96	18	block	block	NN
randomwalker-info-585	96	19	?	?	.
randomwalker-info-585	96	20	)	)	-RRB-
randomwalker-info-585	97	1	[	[	-LRB-
randomwalker-info-585	97	2	14	14	CD
randomwalker-info-585	97	3	,	,	,
randomwalker-info-585	97	4	11	11	CD
randomwalker-info-585	97	5	,	,	,
randomwalker-info-585	97	6	21	21	CD
randomwalker-info-585	97	7	,	,	,
randomwalker-info-585	97	8	18	18	CD
randomwalker-info-585	97	9	]	]	-RRB-
randomwalker-info-585	97	10	.	.	.
randomwalker-info-585	98	1	Our	-PRON-	PRP$
randomwalker-info-585	98	2	work	work	NN
randomwalker-info-585	98	3	avoids	avoid	VBZ
randomwalker-info-585	98	4	this	this	DT
randomwalker-info-585	98	5	discussion	discussion	NN
randomwalker-info-585	98	6	;	;	:
randomwalker-info-585	98	7	we	-PRON-	PRP
randomwalker-info-585	98	8	show	show	VBP
randomwalker-info-585	98	9	that	that	IN
randomwalker-info-585	98	10	undesirable	undesirable	JJ
randomwalker-info-585	98	11	behavior	behavior	NN
randomwalker-info-585	98	12	emerges	emerge	VBZ
randomwalker-info-585	98	13	even	even	RB
randomwalker-info-585	98	14	if	if	IN
randomwalker-info-585	98	15	the	the	DT
randomwalker-info-585	98	16	market	market	NN
randomwalker-info-585	98	17	reaches	reach	VBZ
randomwalker-info-585	98	18	an	an	DT
randomwalker-info-585	98	19	equilibrium	equilibrium	NN
randomwalker-info-585	98	20	where	where	WRB
randomwalker-info-585	98	21	transaction	transaction	NN
randomwalker-info-585	98	22	fees	fee	NNS
randomwalker-info-585	98	23	are	be	VBP
randomwalker-info-585	98	24	non	non	JJ
randomwalker-info-585	98	25	-	-	JJ
randomwalker-info-585	98	26	negligible	negligible	JJ
randomwalker-info-585	98	27	,	,	,
randomwalker-info-585	98	28	and	and	CC
randomwalker-info-585	98	29	arrive	arrive	VB
randomwalker-info-585	98	30	steadily	steadily	RB
randomwalker-info-585	98	31	and	and	CC
randomwalker-info-585	98	32	reliably	reliably	RB
randomwalker-info-585	98	33	.	.	.
randomwalker-info-585	99	1	Inter-	Inter-	NNP
randomwalker-info-585	99	2	estingly	estingly	RB
randomwalker-info-585	99	3	,	,	,
randomwalker-info-585	99	4	Möser	Möser	NNP
randomwalker-info-585	99	5	and	and	CC
randomwalker-info-585	99	6	Böhme	Böhme	NNP
randomwalker-info-585	99	7	reach	reach	VBP
randomwalker-info-585	99	8	the	the	DT
randomwalker-info-585	99	9	same	same	JJ
randomwalker-info-585	99	10	conclusion	conclusion	NN
randomwalker-info-585	99	11	as	as	IN
randomwalker-info-585	99	12	us	-PRON-	PRP
randomwalker-info-585	99	13	(	(	-LRB-
randomwalker-info-585	99	14	that	that	IN
randomwalker-info-585	99	15	monetary	monetary	JJ
randomwalker-info-585	99	16	inflation	inflation	NN
randomwalker-info-585	99	17	is	be	VBZ
randomwalker-info-585	99	18	a	a	DT
randomwalker-info-585	99	19	preferable	preferable	JJ
randomwalker-info-585	99	20	mechanism	mechanism	NN
randomwalker-info-585	99	21	to	to	IN
randomwalker-info-585	99	22	trans-	trans-	JJ
randomwalker-info-585	99	23	action	action	NN
randomwalker-info-585	99	24	fees	fee	NNS
randomwalker-info-585	99	25	)	)	-RRB-
randomwalker-info-585	99	26	through	through	IN
randomwalker-info-585	99	27	very	very	RB
randomwalker-info-585	99	28	different	different	JJ
randomwalker-info-585	99	29	methods	method	NNS
randomwalker-info-585	99	30	[	[	-LRB-
randomwalker-info-585	99	31	18	18	CD
randomwalker-info-585	99	32	]	]	-RRB-
randomwalker-info-585	99	33	.	.	.
randomwalker-info-585	100	1	On	on	IN
randomwalker-info-585	100	2	the	the	DT
randomwalker-info-585	100	3	simulation	simulation	NN
randomwalker-info-585	100	4	side	side	NN
randomwalker-info-585	100	5	,	,	,
randomwalker-info-585	100	6	numerous	numerous	JJ
randomwalker-info-585	100	7	prior	prior	JJ
randomwalker-info-585	100	8	works	work	NNS
randomwalker-info-585	100	9	have	have	VBP
randomwalker-info-585	100	10	devel-	devel-	FW
randomwalker-info-585	100	11	oped	ope	VBN
randomwalker-info-585	100	12	simulators	simulator	NNS
randomwalker-info-585	100	13	for	for	IN
randomwalker-info-585	100	14	some	some	DT
randomwalker-info-585	100	15	aspect	aspect	NN
randomwalker-info-585	100	16	of	of	IN
randomwalker-info-585	100	17	Bitcoin	Bitcoin	NNP
randomwalker-info-585	100	18	.	.	.
randomwalker-info-585	101	1	Some	some	DT
randomwalker-info-585	101	2	simulators	simulator	NNS
randomwalker-info-585	101	3	are	be	VBP
randomwalker-info-585	101	4	aimed	aim	VBN
randomwalker-info-585	101	5	at	at	IN
randomwalker-info-585	101	6	aspects	aspect	NNS
randomwalker-info-585	101	7	of	of	IN
randomwalker-info-585	101	8	Bitcoin	Bitcoin	NNP
randomwalker-info-585	101	9	aside	aside	RB
randomwalker-info-585	101	10	from	from	IN
randomwalker-info-585	101	11	strategic	strategic	JJ
randomwalker-info-585	101	12	min-	min-	JJ
randomwalker-info-585	101	13	ing	ing	NN
randomwalker-info-585	101	14	,	,	,
randomwalker-info-585	101	15	such	such	JJ
randomwalker-info-585	101	16	as	as	IN
randomwalker-info-585	101	17	privacy	privacy	NN
randomwalker-info-585	101	18	[	[	-LRB-
randomwalker-info-585	101	19	3	3	CD
randomwalker-info-585	101	20	]	]	-RRB-
randomwalker-info-585	101	21	,	,	,
randomwalker-info-585	101	22	or	or	CC
randomwalker-info-585	101	23	the	the	DT
randomwalker-info-585	101	24	peer	peer	NN
randomwalker-info-585	101	25	-	-	HYPH
randomwalker-info-585	101	26	to	to	IN
randomwalker-info-585	101	27	-	-	HYPH
randomwalker-info-585	101	28	peer	peer	NN
randomwalker-info-585	101	29	network	network	NN
randomwalker-info-585	101	30	[	[	-LRB-
randomwalker-info-585	101	31	17	17	CD
randomwalker-info-585	101	32	]	]	-RRB-
randomwalker-info-585	101	33	.	.	.
randomwalker-info-585	102	1	Those	those	DT
randomwalker-info-585	102	2	developed	develop	VBN
randomwalker-info-585	102	3	in	in	IN
randomwalker-info-585	102	4	[	[	-LRB-
randomwalker-info-585	102	5	9	9	CD
randomwalker-info-585	102	6	]	]	-RRB-
randomwalker-info-585	102	7	and	and	CC
randomwalker-info-585	102	8	[	[	-LRB-
randomwalker-info-585	102	9	8	8	CD
randomwalker-info-585	102	10	]	]	-RRB-
randomwalker-info-585	102	11	also	also	RB
randomwalker-info-585	102	12	focus	focus	VB
randomwalker-info-585	102	13	on	on	IN
randomwalker-info-585	102	14	simulating	simulate	VBG
randomwalker-info-585	102	15	de-	de-	RB
randomwalker-info-585	102	16	viant	viant	JJ
randomwalker-info-585	102	17	mining	mining	NN
randomwalker-info-585	102	18	strategies	strategy	NNS
randomwalker-info-585	102	19	,	,	,
randomwalker-info-585	102	20	but	but	CC
randomwalker-info-585	102	21	our	-PRON-	PRP$
randomwalker-info-585	102	22	understanding	understanding	NN
randomwalker-info-585	102	23	is	be	VBZ
randomwalker-info-585	102	24	that	that	IN
randomwalker-info-585	102	25	these	these	DT
randomwalker-info-585	102	26	simulators	simulator	NNS
randomwalker-info-585	102	27	are	be	VBP
randomwalker-info-585	102	28	tailor	tailor	NN
randomwalker-info-585	102	29	-	-	HYPH
randomwalker-info-585	102	30	made	make	VBN
randomwalker-info-585	102	31	for	for	IN
randomwalker-info-585	102	32	the	the	DT
randomwalker-info-585	102	33	specific	specific	JJ
randomwalker-info-585	102	34	deviant	deviant	NN
randomwalker-info-585	102	35	strategies	strategy	NNS
randomwalker-info-585	102	36	they	-PRON-	PRP
randomwalker-info-585	102	37	wish	wish	VBP
randomwalker-info-585	102	38	to	to	TO
randomwalker-info-585	102	39	test	test	VB
randomwalker-info-585	102	40	.	.	.
randomwalker-info-585	103	1	In	in	IN
randomwalker-info-585	103	2	comparison	comparison	NN
randomwalker-info-585	103	3	,	,	,
randomwalker-info-585	103	4	our	-PRON-	PRP$
randomwalker-info-585	103	5	simulator	simulator	NN
randomwalker-info-585	103	6	allows	allow	VBZ
randomwalker-info-585	103	7	for	for	IN
randomwalker-info-585	103	8	easy	easy	JJ
randomwalker-info-585	103	9	implementation	implementation	NN
randomwalker-info-585	103	10	of	of	IN
randomwalker-info-585	103	11	a	a	DT
randomwalker-info-585	103	12	broad	broad	JJ
randomwalker-info-585	103	13	range	range	NN
randomwalker-info-585	103	14	of	of	IN
randomwalker-info-585	103	15	strategies	strategy	NNS
randomwalker-info-585	103	16	in	in	IN
randomwalker-info-585	103	17	var-	var-	NN
randomwalker-info-585	103	18	ious	ious	JJ
randomwalker-info-585	103	19	environments	environment	NNS
randomwalker-info-585	103	20	.	.	.
randomwalker-info-585	104	1	Indeed	indeed	RB
randomwalker-info-585	104	2	,	,	,
randomwalker-info-585	104	3	the	the	DT
randomwalker-info-585	104	4	versatility	versatility	NN
randomwalker-info-585	104	5	of	of	IN
randomwalker-info-585	104	6	our	-PRON-	PRP$
randomwalker-info-585	104	7	simulator	simulator	NN
randomwalker-info-585	104	8	is	be	VBZ
randomwalker-info-585	104	9	crucial	crucial	JJ
randomwalker-info-585	104	10	for	for	IN
randomwalker-info-585	104	11	getting	get	VBG
randomwalker-info-585	104	12	intuition	intuition	NN
randomwalker-info-585	104	13	for	for	IN
randomwalker-info-585	104	14	every	every	DT
randomwalker-info-585	104	15	result	result	NN
randomwalker-info-585	104	16	in	in	IN
randomwalker-info-585	104	17	this	this	DT
randomwalker-info-585	104	18	paper	paper	NN
randomwalker-info-585	104	19	.	.	.
randomwalker-info-585	105	1	We	-PRON-	PRP
randomwalker-info-585	105	2	have	have	VBP
randomwalker-info-585	105	3	made	make	VBN
randomwalker-info-585	105	4	it	-PRON-	PRP
randomwalker-info-585	105	5	open	open	JJ
randomwalker-info-585	105	6	-	-	HYPH
randomwalker-info-585	105	7	source	source	NN
randomwalker-info-585	105	8	and	and	CC
randomwalker-info-585	105	9	hope	hope	VB
randomwalker-info-585	105	10	it	-PRON-	PRP
randomwalker-info-585	105	11	will	will	MD
randomwalker-info-585	105	12	be	be	VB
randomwalker-info-585	105	13	a	a	DT
randomwalker-info-585	105	14	useful	useful	JJ
randomwalker-info-585	105	15	tool	tool	NN
randomwalker-info-585	105	16	for	for	IN
randomwalker-info-585	105	17	future	future	JJ
randomwalker-info-585	105	18	research	research	NN
randomwalker-info-585	105	19	on	on	IN
randomwalker-info-585	105	20	strategic	strategic	JJ
randomwalker-info-585	105	21	miner	miner	NN
randomwalker-info-585	105	22	behavior	behavior	NN
randomwalker-info-585	105	23	.	.	.
randomwalker-info-585	106	1	3	3	LS
randomwalker-info-585	106	2	.	.	.
randomwalker-info-585	107	1	MODEL	MODEL	NNP
randomwalker-info-585	107	2	AND	and	CC
randomwalker-info-585	107	3	STRATEGIES	strategy	NNS
randomwalker-info-585	107	4	In	in	IN
randomwalker-info-585	107	5	this	this	DT
randomwalker-info-585	107	6	section	section	NN
randomwalker-info-585	107	7	,	,	,
randomwalker-info-585	107	8	we	-PRON-	PRP
randomwalker-info-585	107	9	cover	cover	VBP
randomwalker-info-585	107	10	the	the	DT
randomwalker-info-585	107	11	model	model	NN
randomwalker-info-585	107	12	of	of	IN
randomwalker-info-585	107	13	Bitcoin	Bitcoin	NNP
randomwalker-info-585	107	14	that	that	WDT
randomwalker-info-585	107	15	we	-PRON-	PRP
randomwalker-info-585	107	16	investigate	investigate	VBP
randomwalker-info-585	107	17	.	.	.
randomwalker-info-585	108	1	We	-PRON-	PRP
randomwalker-info-585	108	2	will	will	MD
randomwalker-info-585	108	3	use	use	VB
randomwalker-info-585	108	4	this	this	DT
randomwalker-info-585	108	5	model	model	NN
randomwalker-info-585	108	6	to	to	TO
randomwalker-info-585	108	7	quickly	quickly	RB
randomwalker-info-585	108	8	illustrate	illustrate	VB
randomwalker-info-585	108	9	how	how	WRB
randomwalker-info-585	108	10	the	the	DT
randomwalker-info-585	108	11	switch	switch	NN
randomwalker-info-585	108	12	to	to	IN
randomwalker-info-585	108	13	transaction	transaction	NN
randomwalker-info-585	108	14	-	-	HYPH
randomwalker-info-585	108	15	fee	fee	NN
randomwalker-info-585	108	16	dominated	dominate	VBN
randomwalker-info-585	108	17	rewards	reward	NNS
randomwalker-info-585	108	18	may	may	MD
randomwalker-info-585	108	19	lead	lead	VB
randomwalker-info-585	108	20	to	to	IN
randomwalker-info-585	108	21	interesting	interesting	JJ
randomwalker-info-585	108	22	and	and	CC
randomwalker-info-585	108	23	potentially	potentially	RB
randomwalker-info-585	108	24	harmful	harmful	JJ
randomwalker-info-585	108	25	effects	effect	NNS
randomwalker-info-585	108	26	for	for	IN
randomwalker-info-585	108	27	Bitcoin	Bitcoin	NNP
randomwalker-info-585	108	28	.	.	.
randomwalker-info-585	109	1	We	-PRON-	PRP
randomwalker-info-585	109	2	also	also	RB
randomwalker-info-585	109	3	introduce	introduce	VBP
randomwalker-info-585	109	4	a	a	DT
randomwalker-info-585	109	5	formal	formal	JJ
randomwalker-info-585	109	6	language	language	NN
randomwalker-info-585	109	7	for	for	IN
randomwalker-info-585	109	8	describing	describe	VBG
randomwalker-info-585	109	9	Bitcoin	Bitcoin	NNP
randomwalker-info-585	109	10	strategies	strategy	NNS
randomwalker-info-585	109	11	that	that	IN
randomwalker-info-585	109	12	we	-PRON-	PRP
randomwalker-info-585	109	13	will	will	MD
randomwalker-info-585	109	14	use	use	VB
randomwalker-info-585	109	15	throughout	throughout	IN
randomwalker-info-585	109	16	the	the	DT
randomwalker-info-585	109	17	paper	paper	NN
randomwalker-info-585	109	18	.	.	.
randomwalker-info-585	110	1	3.1	3.1	CD
randomwalker-info-585	110	2	Model	model	NN
randomwalker-info-585	110	3	of	of	IN
randomwalker-info-585	110	4	the	the	DT
randomwalker-info-585	110	5	system	system	NN
randomwalker-info-585	110	6	Briefly	briefly	RB
randomwalker-info-585	110	7	,	,	,
randomwalker-info-585	110	8	let	let	VB
randomwalker-info-585	110	9	us	-PRON-	PRP
randomwalker-info-585	110	10	describe	describe	VB
randomwalker-info-585	110	11	the	the	DT
randomwalker-info-585	110	12	theme	theme	NN
randomwalker-info-585	110	13	of	of	IN
randomwalker-info-585	110	14	our	-PRON-	PRP$
randomwalker-info-585	110	15	model	model	NN
randomwalker-info-585	110	16	before	before	IN
randomwalker-info-585	110	17	get-	get-	JJ
randomwalker-info-585	110	18	ting	ting	NNP
randomwalker-info-585	110	19	into	into	IN
randomwalker-info-585	110	20	specific	specific	JJ
randomwalker-info-585	110	21	details	detail	NNS
randomwalker-info-585	110	22	.	.	.
randomwalker-info-585	111	1	The	the	DT
randomwalker-info-585	111	2	goal	goal	NN
randomwalker-info-585	111	3	of	of	IN
randomwalker-info-585	111	4	this	this	DT
randomwalker-info-585	111	5	work	work	NN
randomwalker-info-585	111	6	is	be	VBZ
randomwalker-info-585	111	7	not	not	RB
randomwalker-info-585	111	8	to	to	TO
randomwalker-info-585	111	9	accurately	accurately	RB
randomwalker-info-585	111	10	predict	predict	VB
randomwalker-info-585	111	11	exactly	exactly	RB
randomwalker-info-585	111	12	what	what	WP
randomwalker-info-585	111	13	mining	mining	NN
randomwalker-info-585	111	14	behavior	behavior	NN
randomwalker-info-585	111	15	will	will	MD
randomwalker-info-585	111	16	arise	arise	VB
randomwalker-info-585	111	17	in	in	IN
randomwalker-info-585	111	18	practice	practice	NN
randomwalker-info-585	111	19	,	,	,
randomwalker-info-585	111	20	but	but	CC
randomwalker-info-585	111	21	instead	instead	RB
randomwalker-info-585	111	22	to	to	TO
randomwalker-info-585	111	23	uncover	uncover	VB
randomwalker-info-585	111	24	incentive	incentive	NN
randomwalker-info-585	111	25	issues	issue	NNS
randomwalker-info-585	111	26	that	that	WDT
randomwalker-info-585	111	27	arise	arise	VBP
randomwalker-info-585	111	28	solely	solely	RB
randomwalker-info-585	111	29	due	due	IN
randomwalker-info-585	111	30	to	to	IN
randomwalker-info-585	111	31	the	the	DT
randomwalker-info-585	111	32	time	time	NN
randomwalker-info-585	111	33	-	-	HYPH
randomwalker-info-585	111	34	varying	vary	VBG
randomwalker-info-585	111	35	nature	nature	NN
randomwalker-info-585	111	36	of	of	IN
randomwalker-info-585	111	37	transaction	transaction	NN
randomwalker-info-585	111	38	fees	fee	NNS
randomwalker-info-585	111	39	ver-	ver-	VBP
randomwalker-info-585	111	40	sus	sus	NNP
randomwalker-info-585	111	41	block	block	NN
randomwalker-info-585	111	42	rewards	reward	NNS
randomwalker-info-585	111	43	.	.	.
randomwalker-info-585	112	1	To	to	IN
randomwalker-info-585	112	2	this	this	DT
randomwalker-info-585	112	3	end	end	NN
randomwalker-info-585	112	4	,	,	,
randomwalker-info-585	112	5	our	-PRON-	PRP$
randomwalker-info-585	112	6	model	model	NN
randomwalker-info-585	112	7	is	be	VBZ
randomwalker-info-585	112	8	intentionally	intentionally	RB
randomwalker-info-585	112	9	simple	simple	JJ
randomwalker-info-585	112	10	because	because	IN
randomwalker-info-585	112	11	we	-PRON-	PRP
randomwalker-info-585	112	12	want	want	VBP
randomwalker-info-585	112	13	to	to	TO
randomwalker-info-585	112	14	isolate	isolate	VB
randomwalker-info-585	112	15	the	the	DT
randomwalker-info-585	112	16	effects	effect	NNS
randomwalker-info-585	112	17	of	of	IN
randomwalker-info-585	112	18	time	time	NN
randomwalker-info-585	112	19	-	-	HYPH
randomwalker-info-585	112	20	varying	vary	VBG
randomwalker-info-585	112	21	versus	versus	IN
randomwalker-info-585	112	22	fixed	fix	VBN
randomwalker-info-585	112	23	rewards	reward	NNS
randomwalker-info-585	112	24	.	.	.
randomwalker-info-585	113	1	As	as	IN
randomwalker-info-585	113	2	an	an	DT
randomwalker-info-585	113	3	example	example	NN
randomwalker-info-585	113	4	,	,	,
randomwalker-info-585	113	5	we	-PRON-	PRP
randomwalker-info-585	113	6	will	will	MD
randomwalker-info-585	113	7	assume	assume	VB
randomwalker-info-585	113	8	that	that	IN
randomwalker-info-585	113	9	transactions	transaction	NNS
randomwalker-info-585	113	10	(	(	-LRB-
randomwalker-info-585	113	11	and	and	CC
randomwalker-info-585	113	12	their	-PRON-	PRP$
randomwalker-info-585	113	13	associated	associate	VBN
randomwalker-info-585	113	14	fees	fee	NNS
randomwalker-info-585	113	15	)	)	-RRB-
randomwalker-info-585	113	16	arrive	arrive	VBP
randomwalker-info-585	113	17	at	at	IN
randomwalker-info-585	113	18	a	a	DT
randomwalker-info-585	113	19	constant	constant	JJ
randomwalker-info-585	113	20	and	and	CC
randomwalker-info-585	113	21	continuous	continuous	JJ
randomwalker-info-585	113	22	rate	rate	NN
randomwalker-info-585	113	23	.	.	.
randomwalker-info-585	114	1	We	-PRON-	PRP
randomwalker-info-585	114	2	make	make	VBP
randomwalker-info-585	114	3	this	this	DT
randomwalker-info-585	114	4	assumption	assumption	NN
randomwalker-info-585	114	5	not	not	RB
randomwalker-info-585	114	6	be-	be-	RB
randomwalker-info-585	114	7	cause	cause	IN
randomwalker-info-585	114	8	we	-PRON-	PRP
randomwalker-info-585	114	9	necessarily	necessarily	RB
randomwalker-info-585	114	10	predict	predict	VBP
randomwalker-info-585	114	11	it	-PRON-	PRP
randomwalker-info-585	114	12	will	will	MD
randomwalker-info-585	114	13	hold	hold	VB
randomwalker-info-585	114	14	in	in	IN
randomwalker-info-585	114	15	practice	practice	NN
randomwalker-info-585	114	16	,	,	,
randomwalker-info-585	114	17	but	but	CC
randomwalker-info-585	114	18	because	because	IN
randomwalker-info-585	114	19	without	without	IN
randomwalker-info-585	114	20	it	-PRON-	PRP
randomwalker-info-585	114	21	we	-PRON-	PRP
randomwalker-info-585	114	22	ca	can	MD
randomwalker-info-585	114	23	n’t	not	RB
randomwalker-info-585	114	24	guarantee	guarantee	VB
randomwalker-info-585	114	25	that	that	IN
randomwalker-info-585	114	26	we	-PRON-	PRP
randomwalker-info-585	114	27	’ve	have	VB
randomwalker-info-585	114	28	isolated	isolate	VBN
randomwalker-info-585	114	29	time	time	NN
randomwalker-info-585	114	30	-	-	HYPH
randomwalker-info-585	114	31	varying	vary	VBG
randomwalker-info-585	114	32	transaction	transaction	NN
randomwalker-info-585	114	33	fees	fee	NNS
randomwalker-info-585	114	34	as	as	IN
randomwalker-info-585	114	35	the	the	DT
randomwalker-info-585	114	36	cause	cause	NN
randomwalker-info-585	114	37	for	for	IN
randomwalker-info-585	114	38	any	any	DT
randomwalker-info-585	114	39	incentive	incentive	NN
randomwalker-info-585	114	40	issues	issue	NNS
randomwalker-info-585	114	41	we	-PRON-	PRP
randomwalker-info-585	114	42	uncover	uncover	VBP
randomwalker-info-585	114	43	.	.	.
randomwalker-info-585	115	1	Put	put	VB
randomwalker-info-585	115	2	another	another	DT
randomwalker-info-585	115	3	way	way	NN
randomwalker-info-585	115	4	,	,	,
randomwalker-info-585	115	5	our	-PRON-	PRP$
randomwalker-info-585	115	6	results	result	NNS
randomwalker-info-585	115	7	are	be	VBP
randomwalker-info-585	115	8	only	only	RB
randomwalker-info-585	115	9	made	make	VBN
randomwalker-info-585	115	10	stronger	strong	JJR
randomwalker-info-585	115	11	by	by	IN
randomwalker-info-585	115	12	simplifying	simplify	VBG
randomwalker-info-585	115	13	assumptions	assumption	NNS
randomwalker-info-585	115	14	,	,	,
randomwalker-info-585	115	15	because	because	IN
randomwalker-info-585	115	16	we	-PRON-	PRP
randomwalker-info-585	115	17	are	be	VBP
randomwalker-info-585	115	18	claiming	claim	VBG
randomwalker-info-585	115	19	that	that	DT
randomwalker-info-585	115	20	weird	weird	JJ
randomwalker-info-585	115	21	and	and	CC
randomwalker-info-585	115	22	undesirable	undesirable	JJ
randomwalker-info-585	115	23	consequences	consequence	NNS
randomwalker-info-585	115	24	arise	arise	VBP
randomwalker-info-585	115	25	even	even	RB
randomwalker-info-585	115	26	if	if	IN
randomwalker-info-585	115	27	one	one	PRP
randomwalker-info-585	115	28	is	be	VBZ
randomwalker-info-585	115	29	willing	willing	JJ
randomwalker-info-585	115	30	to	to	TO
randomwalker-info-585	115	31	grant	grant	VB
randomwalker-info-585	115	32	simplifying	simplifying	NN
randomwalker-info-585	115	33	assumptions	assumption	NNS
randomwalker-info-585	115	34	.	.	.
randomwalker-info-585	116	1	Getting	get	VBG
randomwalker-info-585	116	2	to	to	IN
randomwalker-info-585	116	3	details	detail	NNS
randomwalker-info-585	116	4	,	,	,
randomwalker-info-585	116	5	the	the	DT
randomwalker-info-585	116	6	model	model	NN
randomwalker-info-585	116	7	of	of	IN
randomwalker-info-585	116	8	Bitcoin	Bitcoin	NNP
randomwalker-info-585	116	9	that	that	WDT
randomwalker-info-585	116	10	we	-PRON-	PRP
randomwalker-info-585	116	11	analyze	analyze	VBP
randomwalker-info-585	116	12	is	be	VBZ
randomwalker-info-585	116	13	after	after	IN
randomwalker-info-585	116	14	the	the	DT
randomwalker-info-585	116	15	block	block	NN
randomwalker-info-585	116	16	reward	reward	NN
randomwalker-info-585	116	17	has	have	VBZ
randomwalker-info-585	116	18	dropped	drop	VBN
randomwalker-info-585	116	19	to	to	IN
randomwalker-info-585	116	20	zero	zero	CD
randomwalker-info-585	116	21	.	.	.
randomwalker-info-585	117	1	That	that	RB
randomwalker-info-585	117	2	is	is	RB
randomwalker-info-585	117	3	,	,	,
randomwalker-info-585	117	4	trans-	trans-	JJ
randomwalker-info-585	117	5	action	action	NN
randomwalker-info-585	117	6	fees	fee	NNS
randomwalker-info-585	117	7	are	be	VBP
randomwalker-info-585	117	8	the	the	DT
randomwalker-info-585	117	9	only	only	JJ
randomwalker-info-585	117	10	source	source	NN
randomwalker-info-585	117	11	of	of	IN
randomwalker-info-585	117	12	revenue	revenue	NN
randomwalker-info-585	117	13	for	for	IN
randomwalker-info-585	117	14	miners	miner	NNS
randomwalker-info-585	117	15	,	,	,
randomwalker-info-585	117	16	and	and	CC
randomwalker-info-585	117	17	we	-PRON-	PRP
randomwalker-info-585	117	18	model	model	VBP
randomwalker-info-585	117	19	available	available	JJ
randomwalker-info-585	117	20	transaction	transaction	NN
randomwalker-info-585	117	21	fees	fee	NNS
randomwalker-info-585	117	22	as	as	IN
randomwalker-info-585	117	23	arriving	arrive	VBG
randomwalker-info-585	117	24	to	to	IN
randomwalker-info-585	117	25	the	the	DT
randomwalker-info-585	117	26	Bit-	Bit-	NNP
randomwalker-info-585	117	27	coin	coin	NN
randomwalker-info-585	117	28	system	system	NN
randomwalker-info-585	117	29	at	at	IN
randomwalker-info-585	117	30	a	a	DT
randomwalker-info-585	117	31	constant	constant	JJ
randomwalker-info-585	117	32	rate	rate	NN
randomwalker-info-585	117	33	.	.	.
randomwalker-info-585	118	1	Specifically	specifically	RB
randomwalker-info-585	118	2	,	,	,
randomwalker-info-585	118	3	we	-PRON-	PRP
randomwalker-info-585	118	4	assume	assume	VBP
randomwalker-info-585	118	5	that	that	IN
randomwalker-info-585	118	6	for	for	IN
randomwalker-info-585	118	7	any	any	DT
randomwalker-info-585	118	8	time	time	NN
randomwalker-info-585	118	9	interval	interval	NN
randomwalker-info-585	118	10	I	-PRON-	PRP
randomwalker-info-585	118	11	of	of	IN
randomwalker-info-585	118	12	length	length	NN
randomwalker-info-585	118	13	t	t	NN
randomwalker-info-585	118	14	,	,	,
randomwalker-info-585	118	15	the	the	DT
randomwalker-info-585	118	16	total	total	JJ
randomwalker-info-585	118	17	sum	sum	NN
randomwalker-info-585	118	18	of	of	IN
randomwalker-info-585	118	19	transac-	transac-	NN
randomwalker-info-585	118	20	tion	tion	NN
randomwalker-info-585	118	21	fees	fee	NNS
randomwalker-info-585	118	22	for	for	IN
randomwalker-info-585	118	23	transactions	transaction	NNS
randomwalker-info-585	118	24	announced	announce	VBN
randomwalker-info-585	118	25	during	during	IN
randomwalker-info-585	118	26	I	-PRON-	PRP
randomwalker-info-585	118	27	is	be	VBZ
randomwalker-info-585	118	28	t	t	NN
randomwalker-info-585	118	29	(	(	-LRB-
randomwalker-info-585	118	30	the	the	DT
randomwalker-info-585	118	31	choice	choice	NN
randomwalker-info-585	118	32	of	of	IN
randomwalker-info-585	118	33	t	t	NNP
randomwalker-info-585	118	34	instead	instead	RB
randomwalker-info-585	118	35	of	of	IN
randomwalker-info-585	118	36	ct	ct	NNP
randomwalker-info-585	118	37	for	for	IN
randomwalker-info-585	118	38	some	some	DT
randomwalker-info-585	118	39	constant	constant	JJ
randomwalker-info-585	118	40	c	c	NN
randomwalker-info-585	118	41	is	be	VBZ
randomwalker-info-585	118	42	just	just	RB
randomwalker-info-585	118	43	normalization	normalization	NN
randomwalker-info-585	118	44	)	)	-RRB-
randomwalker-info-585	118	45	.	.	.
randomwalker-info-585	119	1	This	this	DT
randomwalker-info-585	119	2	is	be	VBZ
randomwalker-info-585	119	3	different	different	JJ
randomwalker-info-585	119	4	from	from	IN
randomwalker-info-585	119	5	Bitcoin	Bitcoin	NNP
randomwalker-info-585	119	6	as	as	IN
randomwalker-info-585	119	7	it	-PRON-	PRP
randomwalker-info-585	119	8	is	be	VBZ
randomwalker-info-585	119	9	today	today	NN
randomwalker-info-585	119	10	with	with	IN
randomwalker-info-585	119	11	a	a	DT
randomwalker-info-585	119	12	large	large	JJ
randomwalker-info-585	119	13	block	block	NN
randomwalker-info-585	119	14	reward	reward	NN
randomwalker-info-585	119	15	compared	compare	VBN
randomwalker-info-585	119	16	to	to	IN
randomwalker-info-585	119	17	the	the	DT
randomwalker-info-585	119	18	small	small	JJ
randomwalker-info-585	119	19	transaction	transaction	NN
randomwalker-info-585	119	20	fees	fee	NNS
randomwalker-info-585	119	21	,	,	,
randomwalker-info-585	119	22	but	but	CC
randomwalker-info-585	119	23	this	this	DT
randomwalker-info-585	119	24	sce-	sce-	NN
randomwalker-info-585	119	25	nario	nario	NN
randomwalker-info-585	119	26	is	be	VBZ
randomwalker-info-585	119	27	consistent	consistent	JJ
randomwalker-info-585	119	28	with	with	IN
randomwalker-info-585	119	29	the	the	DT
randomwalker-info-585	119	30	vision	vision	NN
randomwalker-info-585	119	31	of	of	IN
randomwalker-info-585	119	32	the	the	DT
randomwalker-info-585	119	33	long	long	JJ
randomwalker-info-585	119	34	-	-	HYPH
randomwalker-info-585	119	35	term	term	NN
randomwalker-info-585	119	36	steady	steady	JJ
randomwalker-info-585	119	37	state	state	NN
randomwalker-info-585	119	38	behaviour	behaviour	NN
randomwalker-info-585	119	39	of	of	IN
randomwalker-info-585	119	40	Bitcoin	Bitcoin	NNP
randomwalker-info-585	119	41	after	after	IN
randomwalker-info-585	119	42	all	all	DT
randomwalker-info-585	119	43	Bitcoins	Bitcoins	NNPS
randomwalker-info-585	119	44	have	have	VBP
randomwalker-info-585	119	45	eventually	eventually	RB
randomwalker-info-585	119	46	been	be	VBN
randomwalker-info-585	119	47	minted	mint	VBN
randomwalker-info-585	119	48	.	.	.
randomwalker-info-585	120	1	We	-PRON-	PRP
randomwalker-info-585	120	2	also	also	RB
randomwalker-info-585	120	3	assume	assume	VBP
randomwalker-info-585	120	4	that	that	IN
randomwalker-info-585	120	5	the	the	DT
randomwalker-info-585	120	6	difficulty	difficulty	NN
randomwalker-info-585	120	7	is	be	VBZ
randomwalker-info-585	120	8	set	set	VBN
randomwalker-info-585	120	9	so	so	IN
randomwalker-info-585	120	10	that	that	IN
randomwalker-info-585	120	11	a	a	DT
randomwalker-info-585	120	12	hash	hash	NN
randomwalker-info-585	120	13	puz-	puz-	NN
randomwalker-info-585	120	14	zle	zle	NN
randomwalker-info-585	120	15	is	be	VBZ
randomwalker-info-585	120	16	solved	solve	VBN
randomwalker-info-585	120	17	by	by	IN
randomwalker-info-585	120	18	someone	someone	NN
randomwalker-info-585	120	19	in	in	IN
randomwalker-info-585	120	20	the	the	DT
randomwalker-info-585	120	21	network	network	NN
randomwalker-info-585	120	22	every	every	DT
randomwalker-info-585	120	23	one	one	CD
randomwalker-info-585	120	24	time	time	NN
randomwalker-info-585	120	25	unit	unit	NN
randomwalker-info-585	120	26	in	in	IN
randomwalker-info-585	120	27	expectation	expectation	NN
randomwalker-info-585	120	28	(	(	-LRB-
randomwalker-info-585	120	29	this	this	DT
randomwalker-info-585	120	30	is	be	VBZ
randomwalker-info-585	120	31	again	again	RB
randomwalker-info-585	120	32	just	just	RB
randomwalker-info-585	120	33	a	a	DT
randomwalker-info-585	120	34	normalization	normalization	NN
randomwalker-info-585	120	35	)	)	-RRB-
randomwalker-info-585	120	36	.	.	.
randomwalker-info-585	121	1	Addition-	Addition-	NNP
randomwalker-info-585	121	2	ally	ally	NN
randomwalker-info-585	121	3	,	,	,
randomwalker-info-585	121	4	for	for	IN
randomwalker-info-585	121	5	simplicity	simplicity	NN
randomwalker-info-585	121	6	,	,	,
randomwalker-info-585	121	7	in	in	IN
randomwalker-info-585	121	8	our	-PRON-	PRP$
randomwalker-info-585	121	9	theoretical	theoretical	JJ
randomwalker-info-585	121	10	results	result	NNS
randomwalker-info-585	121	11	and	and	CC
randomwalker-info-585	121	12	reported	report	VBD
randomwalker-info-585	121	13	simulations	simulation	NNS
randomwalker-info-585	121	14	we	-PRON-	PRP
randomwalker-info-585	121	15	model	model	VBP
randomwalker-info-585	121	16	the	the	DT
randomwalker-info-585	121	17	network	network	NN
randomwalker-info-585	121	18	having	have	VBG
randomwalker-info-585	121	19	no	no	DT
randomwalker-info-585	121	20	latency	latency	NN
randomwalker-info-585	121	21	(	(	-LRB-
randomwalker-info-585	121	22	unless	unless	IN
randomwalker-info-585	121	23	otherwise	otherwise	RB
randomwalker-info-585	121	24	stated	state	VBN
randomwalker-info-585	121	25	)	)	-RRB-
randomwalker-info-585	121	26	.	.	.
randomwalker-info-585	122	1	Once	once	RB
randomwalker-info-585	122	2	a	a	DT
randomwalker-info-585	122	3	miner	miner	NN
randomwalker-info-585	122	4	publishes	publish	VBZ
randomwalker-info-585	122	5	a	a	DT
randomwalker-info-585	122	6	block	block	NN
randomwalker-info-585	122	7	,	,	,
randomwalker-info-585	122	8	all	all	DT
randomwalker-info-585	122	9	other	other	JJ
randomwalker-info-585	122	10	miners	miner	NNS
randomwalker-info-585	122	11	immediately	immediately	RB
randomwalker-info-585	122	12	gain	gain	VBP
randomwalker-info-585	122	13	knowledge	knowledge	NN
randomwalker-info-585	122	14	of	of	IN
randomwalker-info-585	122	15	it	-PRON-	PRP
randomwalker-info-585	122	16	.	.	.
randomwalker-info-585	123	1	Similarly	similarly	RB
randomwalker-info-585	123	2	,	,	,
randomwalker-info-585	123	3	once	once	RB
randomwalker-info-585	123	4	a	a	DT
randomwalker-info-585	123	5	transaction	transaction	NN
randomwalker-info-585	123	6	is	be	VBZ
randomwalker-info-585	123	7	announced	announce	VBN
randomwalker-info-585	123	8	,	,	,
randomwalker-info-585	123	9	all	all	DT
randomwalker-info-585	123	10	miners	miner	NNS
randomwalker-info-585	123	11	immediately	immediately	RB
randomwalker-info-585	123	12	learn	learn	VBP
randomwalker-info-585	123	13	of	of	IN
randomwalker-info-585	123	14	its	-PRON-	PRP$
randomwalker-info-585	123	15	existence	existence	NN
randomwalker-info-585	123	16	.	.	.
randomwalker-info-585	124	1	However	however	RB
randomwalker-info-585	124	2	,	,	,
randomwalker-info-585	124	3	our	-PRON-	PRP$
randomwalker-info-585	124	4	simulator	simulator	NN
randomwalker-info-585	124	5	is	be	VBZ
randomwalker-info-585	124	6	capable	capable	JJ
randomwalker-info-585	124	7	of	of	IN
randomwalker-info-585	124	8	simulating	simulate	VBG
randomwalker-info-585	124	9	latency	latency	NN
randomwalker-info-585	124	10	of	of	IN
randomwalker-info-585	124	11	both	both	DT
randomwalker-info-585	124	12	types	type	NNS
randomwalker-info-585	124	13	,	,	,
randomwalker-info-585	124	14	and	and	CC
randomwalker-info-585	124	15	we	-PRON-	PRP
randomwalker-info-585	124	16	do	do	VBP
randomwalker-info-585	124	17	not	not	RB
randomwalker-info-585	124	18	see	see	VB
randomwalker-info-585	124	19	any	any	DT
randomwalker-info-585	124	20	substantive	substantive	JJ
randomwalker-info-585	124	21	change	change	NN
randomwalker-info-585	124	22	in	in	IN
randomwalker-info-585	124	23	our	-PRON-	PRP$
randomwalker-info-585	124	24	results	result	NNS
randomwalker-info-585	124	25	as	as	IN
randomwalker-info-585	124	26	latency	latency	NN
randomwalker-info-585	124	27	changes	change	VBZ
randomwalker-info-585	124	28	.	.	.
randomwalker-info-585	125	1	Finally	finally	RB
randomwalker-info-585	125	2	,	,	,
randomwalker-info-585	125	3	we	-PRON-	PRP
randomwalker-info-585	125	4	assume	assume	VBP
randomwalker-info-585	125	5	that	that	IN
randomwalker-info-585	125	6	when	when	WRB
randomwalker-info-585	125	7	there	there	EX
randomwalker-info-585	125	8	are	be	VBP
randomwalker-info-585	125	9	R	r	NN
randomwalker-info-585	125	10	transaction	transaction	NN
randomwalker-info-585	125	11	fees	fee	NNS
randomwalker-info-585	125	12	available	available	JJ
randomwalker-info-585	125	13	,	,	,
randomwalker-info-585	125	14	the	the	DT
randomwalker-info-585	125	15	miner	miner	NN
randomwalker-info-585	125	16	can	can	MD
randomwalker-info-585	125	17	choose	choose	VB
randomwalker-info-585	125	18	to	to	TO
randomwalker-info-585	125	19	include	include	VB
randomwalker-info-585	125	20	any	any	DT
randomwalker-info-585	125	21	real	real	RB
randomwalker-info-585	125	22	-	-	HYPH
randomwalker-info-585	125	23	valued	value	VBN
randomwalker-info-585	125	24	number	number	NN
randomwalker-info-585	125	25	of	of	IN
randomwalker-info-585	125	26	transaction	transaction	NN
randomwalker-info-585	125	27	fees	fee	NNS
randomwalker-info-585	125	28	between	between	IN
randomwalker-info-585	125	29	0	0	CD
randomwalker-info-585	125	30	and	and	CC
randomwalker-info-585	125	31	R	r	NN
randomwalker-info-585	125	32	in	in	IN
randomwalker-info-585	125	33	their	-PRON-	PRP$
randomwalker-info-585	125	34	block	block	NN
randomwalker-info-585	125	35	.	.	.
randomwalker-info-585	126	1	That	that	RB
randomwalker-info-585	126	2	is	is	RB
randomwalker-info-585	126	3	,	,	,
randomwalker-info-585	126	4	transactions	transaction	NNS
randomwalker-info-585	126	5	are	be	VBP
randomwalker-info-585	126	6	fine	fine	RB
randomwalker-info-585	126	7	-	-	HYPH
randomwalker-info-585	126	8	grained	grained	JJ
randomwalker-info-585	126	9	enough	enough	RB
randomwalker-info-585	126	10	that	that	IN
randomwalker-info-585	126	11	a	a	DT
randomwalker-info-585	126	12	miner	miner	NN
randomwalker-info-585	126	13	can	can	MD
randomwalker-info-585	126	14	selectively	selectively	RB
randomwalker-info-585	126	15	choose	choose	VB
randomwalker-info-585	126	16	a	a	DT
randomwalker-info-585	126	17	set	set	NN
randomwalker-info-585	126	18	of	of	IN
randomwalker-info-585	126	19	transactions	transaction	NNS
randomwalker-info-585	126	20	whose	whose	WP$
randomwalker-info-585	126	21	fees	fee	NNS
randomwalker-info-585	126	22	are	be	VBP
randomwalker-info-585	126	23	very	very	RB
randomwalker-info-585	126	24	close	close	JJ
randomwalker-info-585	126	25	to	to	IN
randomwalker-info-585	126	26	whatever	whatever	WDT
randomwalker-info-585	126	27	real	real	RB
randomwalker-info-585	126	28	-	-	HYPH
randomwalker-info-585	126	29	valued	value	VBN
randomwalker-info-585	126	30	target	target	NN
randomwalker-info-585	126	31	they	-PRON-	PRP
randomwalker-info-585	126	32	have	have	VBP
randomwalker-info-585	126	33	in	in	IN
randomwalker-info-585	126	34	mind	mind	NN
randomwalker-info-585	126	35	.	.	.
randomwalker-info-585	127	1	We	-PRON-	PRP
randomwalker-info-585	127	2	believe	believe	VBP
randomwalker-info-585	127	3	this	this	DT
randomwalker-info-585	127	4	is	be	VBZ
randomwalker-info-585	127	5	a	a	DT
randomwalker-info-585	127	6	reasonable	reasonable	JJ
randomwalker-info-585	127	7	approximation	approximation	NN
randomwalker-info-585	127	8	due	due	IN
randomwalker-info-585	127	9	to	to	IN
randomwalker-info-585	127	10	the	the	DT
randomwalker-info-585	127	11	large	large	JJ
randomwalker-info-585	127	12	number	number	NN
randomwalker-info-585	127	13	of	of	IN
randomwalker-info-585	127	14	transactions	transaction	NNS
randomwalker-info-585	127	15	per	per	IN
randomwalker-info-585	127	16	block	block	NN
randomwalker-info-585	127	17	.	.	.
randomwalker-info-585	128	1	We	-PRON-	PRP
randomwalker-info-585	128	2	also	also	RB
randomwalker-info-585	128	3	assume	assume	VBP
randomwalker-info-585	128	4	that	that	IN
randomwalker-info-585	128	5	miners	miner	NNS
randomwalker-info-585	128	6	always	always	RB
randomwalker-info-585	128	7	have	have	VBP
randomwalker-info-585	128	8	space	space	NN
randomwalker-info-585	128	9	to	to	TO
randomwalker-info-585	128	10	include	include	VB
randomwalker-info-585	128	11	all	all	DT
randomwalker-info-585	128	12	available	available	JJ
randomwalker-info-585	128	13	transactions	transaction	NNS
randomwalker-info-585	128	14	.	.	.
randomwalker-info-585	129	1	If	if	IN
randomwalker-info-585	129	2	the	the	DT
randomwalker-info-585	129	3	block	block	NN
randomwalker-info-585	129	4	size	size	NN
randomwalker-info-585	129	5	is	be	VBZ
randomwalker-info-585	129	6	not	not	RB
randomwalker-info-585	129	7	large	large	JJ
randomwalker-info-585	129	8	enough	enough	RB
randomwalker-info-585	129	9	to	to	TO
randomwalker-info-585	129	10	meet	meet	VB
randomwalker-info-585	129	11	demand	demand	NN
randomwalker-info-585	129	12	for	for	IN
randomwalker-info-585	129	13	transactions	transaction	NNS
randomwalker-info-585	129	14	,	,	,
randomwalker-info-585	129	15	we	-PRON-	PRP
randomwalker-info-585	129	16	believe	believe	VBP
randomwalker-info-585	129	17	the	the	DT
randomwalker-info-585	129	18	qualitative	qualitative	JJ
randomwalker-info-585	129	19	content	content	NN
randomwalker-info-585	129	20	of	of	IN
randomwalker-info-585	129	21	all	all	PDT
randomwalker-info-585	129	22	our	-PRON-	PRP$
randomwalker-info-585	129	23	results	result	NNS
randomwalker-info-585	129	24	continue	continue	VBP
randomwalker-info-585	129	25	to	to	TO
randomwalker-info-585	129	26	hold	hold	VB
randomwalker-info-585	129	27	,	,	,
randomwalker-info-585	129	28	but	but	CC
randomwalker-info-585	129	29	the	the	DT
randomwalker-info-585	129	30	quantitative	quantitative	JJ
randomwalker-info-585	129	31	impact	impact	NN
randomwalker-info-585	129	32	is	be	VBZ
randomwalker-info-585	129	33	mitigated	mitigate	VBN
randomwalker-info-585	129	34	.	.	.
randomwalker-info-585	130	1	This	this	DT
randomwalker-info-585	130	2	belief	belief	NN
randomwalker-info-585	130	3	is	be	VBZ
randomwalker-info-585	130	4	supported	support	VBN
randomwalker-info-585	130	5	by	by	IN
randomwalker-info-585	130	6	the	the	DT
randomwalker-info-585	130	7	following	follow	VBG
randomwalker-info-585	130	8	data	datum	NNS
randomwalker-info-585	130	9	,	,	,
randomwalker-info-585	130	10	taken	take	VBN
randomwalker-info-585	130	11	from	from	IN
randomwalker-info-585	130	12	the	the	DT
randomwalker-info-585	130	13	most	most	RBS
randomwalker-info-585	130	14	recent	recent	JJ
randomwalker-info-585	130	15	1000	1000	CD
randomwalker-info-585	130	16	blocks	block	NNS
randomwalker-info-585	130	17	(	(	-LRB-
randomwalker-info-585	130	18	roughly	roughly	RB
randomwalker-info-585	130	19	one	one	CD
randomwalker-info-585	130	20	week	week	NN
randomwalker-info-585	130	21	’s	’s	,
randomwalker-info-585	130	22	worth	worth	JJ
randomwalker-info-585	130	23	)	)	-RRB-
randomwalker-info-585	130	24	as	as	IN
randomwalker-info-585	130	25	of	of	IN
randomwalker-info-585	130	26	July	July	NNP
randomwalker-info-585	130	27	11	11	CD
randomwalker-info-585	130	28	,	,	,
randomwalker-info-585	130	29	2016	2016	CD
randomwalker-info-585	130	30	:	:	:
randomwalker-info-585	130	31	of	of	IN
randomwalker-info-585	130	32	these	these	DT
randomwalker-info-585	130	33	1000	1000	CD
randomwalker-info-585	130	34	blocks	block	NNS
randomwalker-info-585	130	35	,	,	,
randomwalker-info-585	130	36	702	702	CD
randomwalker-info-585	130	37	are	be	VBP
randomwalker-info-585	130	38	full	full	JJ
randomwalker-info-585	130	39	.	.	.
randomwalker-info-585	131	1	Of	of	IN
randomwalker-info-585	131	2	the	the	DT
randomwalker-info-585	131	3	full	full	JJ
randomwalker-info-585	131	4	blocks	block	NNS
randomwalker-info-585	131	5	,	,	,
randomwalker-info-585	131	6	the	the	DT
randomwalker-info-585	131	7	total	total	JJ
randomwalker-info-585	131	8	sum	sum	NN
randomwalker-info-585	131	9	of	of	IN
randomwalker-info-585	131	10	transaction	transaction	NN
randomwalker-info-585	131	11	fees	fee	NNS
randomwalker-info-585	131	12	ranges	range	VBZ
randomwalker-info-585	131	13	from	from	IN
randomwalker-info-585	131	14	0.03	0.03	CD
randomwalker-info-585	131	15	BTC	BTC	NNP
randomwalker-info-585	131	16	to	to	IN
randomwalker-info-585	131	17	4.51	4.51	CD
randomwalker-info-585	131	18	BTC	BTC	NNP
randomwalker-info-585	131	19	.	.	.
randomwalker-info-585	132	1	The	the	DT
randomwalker-info-585	132	2	mean	mean	NN
randomwalker-info-585	132	3	is	be	VBZ
randomwalker-info-585	132	4	0.49	0.49	CD
randomwalker-info-585	132	5	BTC	BTC	NNP
randomwalker-info-585	132	6	and	and	CC
randomwalker-info-585	132	7	the	the	DT
randomwalker-info-585	132	8	standard	standard	JJ
randomwalker-info-585	132	9	deviation	deviation	NN
randomwalker-info-585	132	10	is	be	VBZ
randomwalker-info-585	132	11	0.25	0.25	CD
randomwalker-info-585	132	12	BTC	BTC	NNP
randomwalker-info-585	132	13	,	,	,
randomwalker-info-585	132	14	more	more	JJR
randomwalker-info-585	132	15	than	than	IN
randomwalker-info-585	132	16	half	half	PDT
randomwalker-info-585	132	17	the	the	DT
randomwalker-info-585	132	18	mean	mean	NN
randomwalker-info-585	132	19	.	.	.
randomwalker-info-585	133	1	It	-PRON-	PRP
randomwalker-info-585	133	2	’s	’	VBZ
randomwalker-info-585	133	3	unclear	unclear	JJ
randomwalker-info-585	133	4	how	how	WRB
randomwalker-info-585	133	5	to	to	TO
randomwalker-info-585	133	6	extrapolate	extrapolate	VB
randomwalker-info-585	133	7	these	these	DT
randomwalker-info-585	133	8	data	datum	NNS
randomwalker-info-585	133	9	to	to	IN
randomwalker-info-585	133	10	the	the	DT
randomwalker-info-585	133	11	future	future	NN
randomwalker-info-585	133	12	,	,	,
randomwalker-info-585	133	13	but	but	CC
randomwalker-info-585	133	14	it	-PRON-	PRP
randomwalker-info-585	133	15	is	be	VBZ
randomwalker-info-585	133	16	clear	clear	JJ
randomwalker-info-585	133	17	that	that	IN
randomwalker-info-585	133	18	there	there	EX
randomwalker-info-585	133	19	will	will	MD
randomwalker-info-585	133	20	indeed	indeed	RB
randomwalker-info-585	133	21	be	be	VB
randomwalker-info-585	133	22	fluctuation	fluctuation	NN
randomwalker-info-585	133	23	in	in	IN
randomwalker-info-585	133	24	the	the	DT
randomwalker-info-585	133	25	available	available	JJ
randomwalker-info-585	133	26	fees	fee	NNS
randomwalker-info-585	133	27	that	that	WDT
randomwalker-info-585	133	28	fit	fit	VBP
randomwalker-info-585	133	29	in	in	IN
randomwalker-info-585	133	30	a	a	DT
randomwalker-info-585	133	31	block	block	NN
randomwalker-info-585	133	32	.	.	.
randomwalker-info-585	134	1	So	so	RB
randomwalker-info-585	134	2	if	if	IN
randomwalker-info-585	134	3	the	the	DT
randomwalker-info-585	134	4	block	block	NN
randomwalker-info-585	134	5	size	size	NN
randomwalker-info-585	134	6	is	be	VBZ
randomwalker-info-585	134	7	not	not	RB
randomwalker-info-585	134	8	large	large	JJ
randomwalker-info-585	134	9	enough	enough	RB
randomwalker-info-585	134	10	to	to	TO
randomwalker-info-585	134	11	meet	meet	VB
randomwalker-info-585	134	12	demand	demand	NN
randomwalker-info-585	134	13	for	for	IN
randomwalker-info-585	134	14	trans-	trans-	JJ
randomwalker-info-585	134	15	actions	action	NNS
randomwalker-info-585	134	16	,	,	,
randomwalker-info-585	134	17	even	even	RB
randomwalker-info-585	134	18	though	though	IN
randomwalker-info-585	134	19	the	the	DT
randomwalker-info-585	134	20	available	available	JJ
randomwalker-info-585	134	21	fees	fee	NNS
randomwalker-info-585	134	22	immediately	immediately	RB
randomwalker-info-585	134	23	after	after	IN
randomwalker-info-585	134	24	a	a	DT
randomwalker-info-585	134	25	block	block	NN
randomwalker-info-585	134	26	is	be	VBZ
randomwalker-info-585	134	27	found	find	VBN
randomwalker-info-585	134	28	will	will	MD
randomwalker-info-585	134	29	not	not	RB
randomwalker-info-585	134	30	be	be	VB
randomwalker-info-585	134	31	zero	zero	CD
randomwalker-info-585	134	32	(	(	-LRB-
randomwalker-info-585	134	33	as	as	IN
randomwalker-info-585	134	34	in	in	IN
randomwalker-info-585	134	35	our	-PRON-	PRP$
randomwalker-info-585	134	36	analysis	analysis	NN
randomwalker-info-585	134	37	)	)	-RRB-
randomwalker-info-585	134	38	,	,	,
randomwalker-info-585	134	39	they	-PRON-	PRP
randomwalker-info-585	134	40	may	may	MD
randomwalker-info-585	134	41	be	be	VB
randomwalker-info-585	134	42	significantly	significantly	RB
randomwalker-info-585	134	43	lower	low	JJR
randomwalker-info-585	134	44	than	than	IN
randomwalker-info-585	134	45	(	(	-LRB-
randomwalker-info-585	134	46	say	say	VB
randomwalker-info-585	134	47	)	)	-RRB-
randomwalker-info-585	134	48	ten	ten	CD
randomwalker-info-585	134	49	minutes	minute	NNS
randomwalker-info-585	134	50	later	later	RB
randomwalker-info-585	134	51	.	.	.
randomwalker-info-585	135	1	So	so	RB
randomwalker-info-585	135	2	even	even	RB
randomwalker-info-585	135	3	though	though	IN
randomwalker-info-585	135	4	our	-PRON-	PRP$
randomwalker-info-585	135	5	exact	exact	JJ
randomwalker-info-585	135	6	analysis	analysis	NN
randomwalker-info-585	135	7	will	will	MD
randomwalker-info-585	135	8	not	not	RB
randomwalker-info-585	135	9	apply	apply	VB
randomwalker-info-585	135	10	in	in	IN
randomwalker-info-585	135	11	this	this	DT
randomwalker-info-585	135	12	setting	setting	NN
randomwalker-info-585	135	13	,	,	,
randomwalker-info-585	135	14	the	the	DT
randomwalker-info-585	135	15	intuition	intuition	NN
randomwalker-info-585	135	16	does	do	VBZ
randomwalker-info-585	135	17	carry	carry	VB
randomwalker-info-585	135	18	over	over	RP
randomwalker-info-585	135	19	.	.	.
randomwalker-info-585	136	1	3.2	3.2	CD
randomwalker-info-585	136	2	What	what	WP
randomwalker-info-585	136	3	could	could	MD
randomwalker-info-585	136	4	go	go	VB
randomwalker-info-585	136	5	wrong	wrong	JJ
randomwalker-info-585	136	6	?	?	.
randomwalker-info-585	137	1	The	the	DT
randomwalker-info-585	137	2	mining	mining	NN
randomwalker-info-585	137	3	gap	gap	NN
randomwalker-info-585	137	4	Without	without	IN
randomwalker-info-585	137	5	a	a	DT
randomwalker-info-585	137	6	block	block	NN
randomwalker-info-585	137	7	reward	reward	NN
randomwalker-info-585	137	8	,	,	,
randomwalker-info-585	137	9	immediately	immediately	RB
randomwalker-info-585	137	10	after	after	IN
randomwalker-info-585	137	11	a	a	DT
randomwalker-info-585	137	12	block	block	NN
randomwalker-info-585	137	13	is	be	VBZ
randomwalker-info-585	137	14	found	find	VBN
randomwalker-info-585	137	15	there	there	EX
randomwalker-info-585	137	16	is	be	VBZ
randomwalker-info-585	137	17	zero	zero	CD
randomwalker-info-585	137	18	expected	expect	VBN
randomwalker-info-585	137	19	reward	reward	NN
randomwalker-info-585	137	20	for	for	IN
randomwalker-info-585	137	21	min-	min-	RB
randomwalker-info-585	137	22	ing	ing	NNP
randomwalker-info-585	137	23	but	but	CC
randomwalker-info-585	137	24	nonzero	nonzero	NNP
randomwalker-info-585	137	25	electricity	electricity	NN
randomwalker-info-585	137	26	cost	cost	NN
randomwalker-info-585	137	27	,	,	,
randomwalker-info-585	137	28	making	make	VBG
randomwalker-info-585	137	29	it	-PRON-	PRP
randomwalker-info-585	137	30	unprof-	unprof-	JJ
randomwalker-info-585	137	31	itable	itable	JJ
randomwalker-info-585	137	32	for	for	IN
randomwalker-info-585	137	33	any	any	DT
randomwalker-info-585	137	34	miner	miner	NN
randomwalker-info-585	137	35	to	to	IN
randomwalker-info-585	137	36	mine	-PRON-	PRP
randomwalker-info-585	137	37	.	.	.
randomwalker-info-585	138	1	In	in	IN
randomwalker-info-585	138	2	order	order	NN
randomwalker-info-585	138	3	to	to	TO
randomwalker-info-585	138	4	provide	provide	VB
randomwalker-info-585	138	5	insight	insight	NN
randomwalker-info-585	138	6	as	as	IN
randomwalker-info-585	138	7	to	to	IN
randomwalker-info-585	138	8	how	how	WRB
randomwalker-info-585	138	9	time	time	NN
randomwalker-info-585	138	10	-	-	HYPH
randomwalker-info-585	138	11	varying	vary	VBG
randomwalker-info-585	138	12	rewards	reward	NNS
randomwalker-info-585	138	13	Figure	figure	NN
randomwalker-info-585	138	14	2	2	CD
randomwalker-info-585	138	15	:	:	:
randomwalker-info-585	138	16	Illustration	illustration	NN
randomwalker-info-585	138	17	of	of	IN
randomwalker-info-585	138	18	Mining	Mining	NNP
randomwalker-info-585	138	19	Gaps	Gaps	NNP
randomwalker-info-585	138	20	.	.	.
randomwalker-info-585	139	1	Miners	miner	NNS
randomwalker-info-585	139	2	will	will	MD
randomwalker-info-585	139	3	only	only	RB
randomwalker-info-585	139	4	mine	mine	VB
randomwalker-info-585	139	5	when	when	WRB
randomwalker-info-585	139	6	the	the	DT
randomwalker-info-585	139	7	instantaneous	instantaneous	JJ
randomwalker-info-585	139	8	expected	expect	VBN
randomwalker-info-585	139	9	reward	reward	NN
randomwalker-info-585	139	10	exceeds	exceed	VBZ
randomwalker-info-585	139	11	the	the	DT
randomwalker-info-585	139	12	instantaneous	instantaneous	JJ
randomwalker-info-585	139	13	cost	cost	NN
randomwalker-info-585	139	14	.	.	.
randomwalker-info-585	140	1	could	could	MD
randomwalker-info-585	140	2	be	be	VB
randomwalker-info-585	140	3	harmful	harmful	JJ
randomwalker-info-585	140	4	for	for	IN
randomwalker-info-585	140	5	Bitcoin	Bitcoin	NNP
randomwalker-info-585	140	6	,	,	,
randomwalker-info-585	140	7	let	let	VB
randomwalker-info-585	140	8	’s	-PRON-	PRP
randomwalker-info-585	140	9	walk	walk	VB
randomwalker-info-585	140	10	through	through	IN
randomwalker-info-585	140	11	an	an	DT
randomwalker-info-585	140	12	example	example	NN
randomwalker-info-585	140	13	.	.	.
randomwalker-info-585	141	1	Imagine	imagine	VB
randomwalker-info-585	141	2	that	that	IN
randomwalker-info-585	141	3	we	-PRON-	PRP
randomwalker-info-585	141	4	are	be	VBP
randomwalker-info-585	141	5	in	in	IN
randomwalker-info-585	141	6	the	the	DT
randomwalker-info-585	141	7	model	model	NN
randomwalker-info-585	141	8	previously	previously	RB
randomwalker-info-585	141	9	described	describe	VBN
randomwalker-info-585	141	10	,	,	,
randomwalker-info-585	141	11	that	that	IN
randomwalker-info-585	141	12	all	all	DT
randomwalker-info-585	141	13	miners	miner	NNS
randomwalker-info-585	141	14	are	be	VBP
randomwalker-info-585	141	15	using	use	VBG
randomwalker-info-585	141	16	the	the	DT
randomwalker-info-585	141	17	default	default	NN
randomwalker-info-585	141	18	compliant	compliant	JJ
randomwalker-info-585	141	19	strategy	strategy	NN
randomwalker-info-585	141	20	(	(	-LRB-
randomwalker-info-585	141	21	mine	mine	NN
randomwalker-info-585	141	22	on	on	IN
randomwalker-info-585	141	23	top	top	NN
randomwalker-info-585	141	24	of	of	IN
randomwalker-info-585	141	25	the	the	DT
randomwalker-info-585	141	26	longest	long	JJS
randomwalker-info-585	141	27	chain	chain	NN
randomwalker-info-585	141	28	,	,	,
randomwalker-info-585	141	29	authorize	authorize	VBP
randomwalker-info-585	141	30	all	all	DT
randomwalker-info-585	141	31	available	available	JJ
randomwalker-info-585	141	32	transactions	transaction	NNS
randomwalker-info-585	141	33	,	,	,
randomwalker-info-585	141	34	publish	publish	VB
randomwalker-info-585	141	35	immediately	immediately	RB
randomwalker-info-585	141	36	)	)	-RRB-
randomwalker-info-585	141	37	,	,	,
randomwalker-info-585	141	38	but	but	CC
randomwalker-info-585	141	39	also	also	RB
randomwalker-info-585	141	40	that	that	IN
randomwalker-info-585	141	41	that	that	IN
randomwalker-info-585	141	42	miners	miner	NNS
randomwalker-info-585	141	43	have	have	VBP
randomwalker-info-585	141	44	some	some	DT
randomwalker-info-585	141	45	cost	cost	NN
randomwalker-info-585	141	46	in	in	IN
randomwalker-info-585	141	47	electricity	electricity	NN
randomwalker-info-585	141	48	to	to	TO
randomwalker-info-585	141	49	run	run	VB
randomwalker-info-585	141	50	their	-PRON-	PRP$
randomwalker-info-585	141	51	mining	mining	NN
randomwalker-info-585	141	52	rigs	rig	NNS
randomwalker-info-585	141	53	(	(	-LRB-
randomwalker-info-585	141	54	i.e.	i.e.	FW
randomwalker-info-585	141	55	,	,	,
randomwalker-info-585	141	56	running	run	VBG
randomwalker-info-585	141	57	one	one	CD
randomwalker-info-585	141	58	rig	rig	NN
randomwalker-info-585	141	59	for	for	IN
randomwalker-info-585	141	60	t	t	NN
randomwalker-info-585	141	61	units	unit	NNS
randomwalker-info-585	141	62	of	of	IN
randomwalker-info-585	141	63	time	time	NN
randomwalker-info-585	141	64	costs	cost	NNS
randomwalker-info-585	141	65	pt	pt	IN
randomwalker-info-585	141	66	Bitcoin	Bitcoin	NNP
randomwalker-info-585	141	67	worth	worth	NN
randomwalker-info-585	141	68	of	of	IN
randomwalker-info-585	141	69	electricity	electricity	NN
randomwalker-info-585	141	70	)	)	-RRB-
randomwalker-info-585	141	71	.	.	.
randomwalker-info-585	142	1	Now	now	RB
randomwalker-info-585	142	2	,	,	,
randomwalker-info-585	142	3	immediately	immediately	RB
randomwalker-info-585	142	4	after	after	IN
randomwalker-info-585	142	5	a	a	DT
randomwalker-info-585	142	6	block	block	NN
randomwalker-info-585	142	7	is	be	VBZ
randomwalker-info-585	142	8	found	find	VBN
randomwalker-info-585	142	9	,	,	,
randomwalker-info-585	142	10	there	there	EX
randomwalker-info-585	142	11	will	will	MD
randomwalker-info-585	142	12	be	be	VB
randomwalker-info-585	142	13	no	no	DT
randomwalker-info-585	142	14	more	more	JJR
randomwalker-info-585	142	15	transactions	transaction	NNS
randomwalker-info-585	142	16	in	in	IN
randomwalker-info-585	142	17	the	the	DT
randomwalker-info-585	142	18	network	network	NN
randomwalker-info-585	142	19	to	to	TO
randomwalker-info-585	142	20	be	be	VB
randomwalker-info-585	142	21	claimed	claim	VBN
randomwalker-info-585	142	22	by	by	IN
randomwalker-info-585	142	23	a	a	DT
randomwalker-info-585	142	24	miner	miner	NN
randomwalker-info-585	142	25	making	make	VBG
randomwalker-info-585	142	26	the	the	DT
randomwalker-info-585	142	27	next	next	JJ
randomwalker-info-585	142	28	block	block	NN
randomwalker-info-585	142	29	.	.	.
randomwalker-info-585	143	1	This	this	DT
randomwalker-info-585	143	2	means	mean	VBZ
randomwalker-info-585	143	3	that	that	IN
randomwalker-info-585	143	4	for	for	IN
randomwalker-info-585	143	5	the	the	DT
randomwalker-info-585	143	6	instant	instant	JJ
randomwalker-info-585	143	7	fol-	fol-	NN
randomwalker-info-585	143	8	lowing	low	VBG
randomwalker-info-585	143	9	the	the	DT
randomwalker-info-585	143	10	discovery	discovery	NN
randomwalker-info-585	143	11	of	of	IN
randomwalker-info-585	143	12	a	a	DT
randomwalker-info-585	143	13	new	new	JJ
randomwalker-info-585	143	14	block	block	NN
randomwalker-info-585	143	15	,	,	,
randomwalker-info-585	143	16	there	there	EX
randomwalker-info-585	143	17	is	be	VBZ
randomwalker-info-585	143	18	actually	actually	RB
randomwalker-info-585	143	19	zero	zero	CD
randomwalker-info-585	143	20	expected	expect	VBN
randomwalker-info-585	143	21	reward	reward	NN
randomwalker-info-585	143	22	for	for	IN
randomwalker-info-585	143	23	mining	mining	NN
randomwalker-info-585	143	24	,	,	,
randomwalker-info-585	143	25	but	but	CC
randomwalker-info-585	143	26	a	a	DT
randomwalker-info-585	143	27	non	non	JJ
randomwalker-info-585	143	28	-	-	JJ
randomwalker-info-585	143	29	zero	zero	JJ
randomwalker-info-585	143	30	electricity	electricity	NN
randomwalker-info-585	143	31	cost	cost	NN
randomwalker-info-585	143	32	for	for	IN
randomwalker-info-585	143	33	doing	do	VBG
randomwalker-info-585	143	34	so	so	RB
randomwalker-info-585	143	35	!	!	.
randomwalker-info-585	144	1	Figure	figure	NN
randomwalker-info-585	144	2	2	2	CD
randomwalker-info-585	144	3	shows	show	VBZ
randomwalker-info-585	144	4	how	how	WRB
randomwalker-info-585	144	5	to	to	TO
randomwalker-info-585	144	6	extend	extend	VB
randomwalker-info-585	144	7	this	this	DT
randomwalker-info-585	144	8	reasoning	reasoning	NN
randomwalker-info-585	144	9	to	to	IN
randomwalker-info-585	144	10	the	the	DT
randomwalker-info-585	144	11	time	time	NN
randomwalker-info-585	144	12	period	period	NN
randomwalker-info-585	144	13	beyond	beyond	IN
randomwalker-info-585	144	14	.	.	.
randomwalker-info-585	145	1	Essentially	essentially	RB
randomwalker-info-585	145	2	,	,	,
randomwalker-info-585	145	3	every	every	DT
randomwalker-info-585	145	4	instant	instant	NN
randomwalker-info-585	145	5	your	-PRON-	PRP$
randomwalker-info-585	145	6	rig	rig	NN
randomwalker-info-585	145	7	is	be	VBZ
randomwalker-info-585	145	8	running	run	VBG
randomwalker-info-585	145	9	,	,	,
randomwalker-info-585	145	10	you	-PRON-	PRP
randomwalker-info-585	145	11	claim	claim	VBP
randomwalker-info-585	145	12	some	some	DT
randomwalker-info-585	145	13	expected	expected	JJ
randomwalker-info-585	145	14	reward	reward	NN
randomwalker-info-585	145	15	,	,	,
randomwalker-info-585	145	16	which	which	WDT
randomwalker-info-585	145	17	increases	increase	VBZ
randomwalker-info-585	145	18	depending	depend	VBG
randomwalker-info-585	145	19	on	on	IN
randomwalker-info-585	145	20	the	the	DT
randomwalker-info-585	145	21	available	available	JJ
randomwalker-info-585	145	22	transaction	transaction	NN
randomwalker-info-585	145	23	fees	fee	NNS
randomwalker-info-585	145	24	.	.	.
randomwalker-info-585	146	1	But	but	CC
randomwalker-info-585	146	2	every	every	DT
randomwalker-info-585	146	3	in-	in-	JJ
randomwalker-info-585	146	4	stant	stant	JJ
randomwalker-info-585	146	5	your	-PRON-	PRP$
randomwalker-info-585	146	6	rig	rig	NN
randomwalker-info-585	146	7	is	be	VBZ
randomwalker-info-585	146	8	running	run	VBG
randomwalker-info-585	146	9	,	,	,
randomwalker-info-585	146	10	you	-PRON-	PRP
randomwalker-info-585	146	11	also	also	RB
randomwalker-info-585	146	12	have	have	VBP
randomwalker-info-585	146	13	to	to	TO
randomwalker-info-585	146	14	pay	pay	VB
randomwalker-info-585	146	15	a	a	DT
randomwalker-info-585	146	16	constant	constant	JJ
randomwalker-info-585	146	17	amount	amount	NN
randomwalker-info-585	146	18	for	for	IN
randomwalker-info-585	146	19	electricity	electricity	NN
randomwalker-info-585	146	20	.	.	.
randomwalker-info-585	147	1	So	so	RB
randomwalker-info-585	147	2	the	the	DT
randomwalker-info-585	147	3	expected	expected	JJ
randomwalker-info-585	147	4	reward	reward	NN
randomwalker-info-585	147	5	for	for	IN
randomwalker-info-585	147	6	running	run	VBG
randomwalker-info-585	147	7	your	-PRON-	PRP$
randomwalker-info-585	147	8	rig	rig	NN
randomwalker-info-585	147	9	wo	will	MD
randomwalker-info-585	147	10	n’t	not	RB
randomwalker-info-585	147	11	exceed	exceed	VB
randomwalker-info-585	147	12	the	the	DT
randomwalker-info-585	147	13	cost	cost	NN
randomwalker-info-585	147	14	of	of	IN
randomwalker-info-585	147	15	electricity	electricity	NN
randomwalker-info-585	147	16	until	until	IN
randomwalker-info-585	147	17	some	some	DT
randomwalker-info-585	147	18	min-	min-	JJ
randomwalker-info-585	147	19	imum	imum	JJ
randomwalker-info-585	147	20	number	number	NN
randomwalker-info-585	147	21	of	of	IN
randomwalker-info-585	147	22	transaction	transaction	NN
randomwalker-info-585	147	23	fees	fee	NNS
randomwalker-info-585	147	24	are	be	VBP
randomwalker-info-585	147	25	available	available	JJ
randomwalker-info-585	147	26	to	to	TO
randomwalker-info-585	147	27	include	include	VB
randomwalker-info-585	147	28	.	.	.
randomwalker-info-585	148	1	If	if	IN
randomwalker-info-585	148	2	a	a	DT
randomwalker-info-585	148	3	is	be	VBZ
randomwalker-info-585	148	4	the	the	DT
randomwalker-info-585	148	5	fraction	fraction	NN
randomwalker-info-585	148	6	of	of	IN
randomwalker-info-585	148	7	the	the	DT
randomwalker-info-585	148	8	total	total	JJ
randomwalker-info-585	148	9	(	(	-LRB-
randomwalker-info-585	148	10	effective	effective	JJ
randomwalker-info-585	148	11	)	)	-RRB-
randomwalker-info-585	148	12	hash	hash	NN
randomwalker-info-585	148	13	power	power	NN
randomwalker-info-585	148	14	that	that	IN
randomwalker-info-585	148	15	a	a	DT
randomwalker-info-585	148	16	single	single	JJ
randomwalker-info-585	148	17	rig	rig	NN
randomwalker-info-585	148	18	generates	generate	NNS
randomwalker-info-585	148	19	,	,	,
randomwalker-info-585	148	20	then	then	RB
randomwalker-info-585	148	21	a	a	DT
randomwalker-info-585	148	22	miner	miner	NN
randomwalker-info-585	148	23	must	must	MD
randomwalker-info-585	148	24	wait	wait	VB
randomwalker-info-585	148	25	t	t	NNP
randomwalker-info-585	148	26	=	=	SYM
randomwalker-info-585	148	27	p	p	NN
randomwalker-info-585	148	28	/	/	SYM
randomwalker-info-585	148	29	a	a	DT
randomwalker-info-585	148	30	time	time	NN
randomwalker-info-585	148	31	steps	step	NNS
randomwalker-info-585	148	32	after	after	IN
randomwalker-info-585	148	33	a	a	DT
randomwalker-info-585	148	34	block	block	NN
randomwalker-info-585	148	35	is	be	VBZ
randomwalker-info-585	148	36	found	find	VBN
randomwalker-info-585	148	37	before	before	IN
randomwalker-info-585	148	38	mining	mining	NN
randomwalker-info-585	148	39	becomes	become	VBZ
randomwalker-info-585	148	40	profitable	profitable	JJ
randomwalker-info-585	148	41	again	again	RB
randomwalker-info-585	148	42	.	.	.
randomwalker-info-585	149	1	In	in	IN
randomwalker-info-585	149	2	Appendix	Appendix	NNP
randomwalker-info-585	149	3	A	A	NNP
randomwalker-info-585	149	4	,	,	,
randomwalker-info-585	149	5	we	-PRON-	PRP
randomwalker-info-585	149	6	discuss	discuss	VBP
randomwalker-info-585	149	7	in	in	IN
randomwalker-info-585	149	8	more	more	JJR
randomwalker-info-585	149	9	detail	detail	NN
randomwalker-info-585	149	10	the	the	DT
randomwalker-info-585	149	11	effects	effect	NNS
randomwalker-info-585	149	12	of	of	IN
randomwalker-info-585	149	13	such	such	PDT
randomwalker-info-585	149	14	a	a	DT
randomwalker-info-585	149	15	mining	mining	NN
randomwalker-info-585	149	16	gap	gap	NN
randomwalker-info-585	149	17	,	,	,
randomwalker-info-585	149	18	and	and	CC
randomwalker-info-585	149	19	find	find	VB
randomwalker-info-585	149	20	that	that	IN
randomwalker-info-585	149	21	it	-PRON-	PRP
randomwalker-info-585	149	22	leads	lead	VBZ
randomwalker-info-585	149	23	to	to	IN
randomwalker-info-585	149	24	miners	miner	NNS
randomwalker-info-585	149	25	mining	mining	NN
randomwalker-info-585	149	26	for	for	IN
randomwalker-info-585	149	27	a	a	DT
randomwalker-info-585	149	28	smaller	small	JJR
randomwalker-info-585	149	29	and	and	CC
randomwalker-info-585	149	30	smaller	small	JJR
randomwalker-info-585	149	31	fraction	fraction	NN
randomwalker-info-585	149	32	of	of	IN
randomwalker-info-585	149	33	the	the	DT
randomwalker-info-585	149	34	time	time	NN
randomwalker-info-585	149	35	between	between	IN
randomwalker-info-585	149	36	the	the	DT
randomwalker-info-585	149	37	ar-	ar-	NN
randomwalker-info-585	149	38	rival	rival	NN
randomwalker-info-585	149	39	of	of	IN
randomwalker-info-585	149	40	blocks	block	NNS
randomwalker-info-585	149	41	(	(	-LRB-
randomwalker-info-585	149	42	with	with	IN
randomwalker-info-585	149	43	the	the	DT
randomwalker-info-585	149	44	difficulty	difficulty	NN
randomwalker-info-585	149	45	dropping	drop	VBG
randomwalker-info-585	149	46	to	to	TO
randomwalker-info-585	149	47	compensate	compensate	VB
randomwalker-info-585	149	48	)	)	-RRB-
randomwalker-info-585	149	49	.	.	.
randomwalker-info-585	150	1	Clearly	clearly	RB
randomwalker-info-585	150	2	,	,	,
randomwalker-info-585	150	3	this	this	DT
randomwalker-info-585	150	4	would	would	MD
randomwalker-info-585	150	5	have	have	VB
randomwalker-info-585	150	6	a	a	DT
randomwalker-info-585	150	7	negative	negative	JJ
randomwalker-info-585	150	8	impact	impact	NN
randomwalker-info-585	150	9	for	for	IN
randomwalker-info-585	150	10	Bitcoin	Bitcoin	NNP
randomwalker-info-585	150	11	secu-	secu-	NN
randomwalker-info-585	150	12	rity	rity	NN
randomwalker-info-585	150	13	,	,	,
randomwalker-info-585	150	14	as	as	IN
randomwalker-info-585	150	15	the	the	DT
randomwalker-info-585	150	16	effective	effective	JJ
randomwalker-info-585	150	17	hash	hash	NN
randomwalker-info-585	150	18	power	power	NN
randomwalker-info-585	150	19	in	in	IN
randomwalker-info-585	150	20	the	the	DT
randomwalker-info-585	150	21	network	network	NN
randomwalker-info-585	150	22	would	would	MD
randomwalker-info-585	150	23	drop	drop	VB
randomwalker-info-585	150	24	,	,	,
randomwalker-info-585	150	25	and	and	CC
randomwalker-info-585	150	26	it	-PRON-	PRP
randomwalker-info-585	150	27	would	would	MD
randomwalker-info-585	150	28	become	become	VB
randomwalker-info-585	150	29	easier	easy	JJR
randomwalker-info-585	150	30	for	for	IN
randomwalker-info-585	150	31	a	a	DT
randomwalker-info-585	150	32	malicious	malicious	JJ
randomwalker-info-585	150	33	miner	miner	NN
randomwalker-info-585	150	34	to	to	TO
randomwalker-info-585	150	35	fork	fork	VB
randomwalker-info-585	150	36	.	.	.
randomwalker-info-585	151	1	Of	of	RB
randomwalker-info-585	151	2	course	course	RB
randomwalker-info-585	151	3	,	,	,
randomwalker-info-585	151	4	turning	turn	VBG
randomwalker-info-585	151	5	a	a	DT
randomwalker-info-585	151	6	rig	rig	NN
randomwalker-info-585	151	7	on	on	IN
randomwalker-info-585	151	8	and	and	CC
randomwalker-info-585	151	9	off	off	IN
randomwalker-info-585	151	10	every	every	DT
randomwalker-info-585	151	11	ten	ten	CD
randomwalker-info-585	151	12	minutes	minute	NNS
randomwalker-info-585	151	13	may	may	MD
randomwalker-info-585	151	14	be	be	VB
randomwalker-info-585	151	15	practically	practically	RB
randomwalker-info-585	151	16	infeasible	infeasible	JJ
randomwalker-info-585	151	17	.	.	.
randomwalker-info-585	152	1	Nevertheless	nevertheless	RB
randomwalker-info-585	152	2	,	,	,
randomwalker-info-585	152	3	this	this	DT
randomwalker-info-585	152	4	analysis	analysis	NN
randomwalker-info-585	152	5	illustrates	illustrate	VBZ
randomwalker-info-585	152	6	that	that	IN
randomwalker-info-585	152	7	strategic	strategic	JJ
randomwalker-info-585	152	8	miners	miner	NNS
randomwalker-info-585	152	9	might	may	MD
randomwalker-info-585	152	10	look	look	VB
randomwalker-info-585	152	11	for	for	IN
randomwalker-info-585	152	12	ways	way	NNS
randomwalker-info-585	152	13	to	to	TO
randomwalker-info-585	152	14	deviate	deviate	VB
randomwalker-info-585	152	15	when	when	WRB
randomwalker-info-585	152	16	the	the	DT
randomwalker-info-585	152	17	default	default	NN
randomwalker-info-585	152	18	protocol	protocol	NN
randomwalker-info-585	152	19	would	would	MD
randomwalker-info-585	152	20	have	have	VB
randomwalker-info-585	152	21	them	-PRON-	PRP
randomwalker-info-585	152	22	wasting	waste	VBG
randomwalker-info-585	152	23	electricity	electricity	NN
randomwalker-info-585	152	24	to	to	TO
randomwalker-info-585	152	25	mine	-PRON-	PRP
randomwalker-info-585	152	26	a	a	DT
randomwalker-info-585	152	27	near	near	JJ
randomwalker-info-585	152	28	-	-	HYPH
randomwalker-info-585	152	29	valueless	valueless	NN
randomwalker-info-585	152	30	block	block	NN
randomwalker-info-585	152	31	.	.	.
randomwalker-info-585	153	1	3.3	3.3	CD
randomwalker-info-585	153	2	Formal	formal	JJ
randomwalker-info-585	153	3	language	language	NN
randomwalker-info-585	153	4	for	for	IN
randomwalker-info-585	153	5	mining	mining	NN
randomwalker-info-585	153	6	strategies	strategy	NNS
randomwalker-info-585	153	7	In	in	IN
randomwalker-info-585	153	8	the	the	DT
randomwalker-info-585	153	9	rest	rest	NN
randomwalker-info-585	153	10	of	of	IN
randomwalker-info-585	153	11	this	this	DT
randomwalker-info-585	153	12	paper	paper	NN
randomwalker-info-585	153	13	,	,	,
randomwalker-info-585	153	14	we	-PRON-	PRP
randomwalker-info-585	153	15	focus	focus	VBP
randomwalker-info-585	153	16	on	on	IN
randomwalker-info-585	153	17	mining	mining	NN
randomwalker-info-585	153	18	strategies	strategy	NNS
randomwalker-info-585	153	19	that	that	WDT
randomwalker-info-585	153	20	always	always	RB
randomwalker-info-585	153	21	mine	-PRON-	PRP
randomwalker-info-585	153	22	within	within	IN
randomwalker-info-585	153	23	the	the	DT
randomwalker-info-585	153	24	same	same	JJ
randomwalker-info-585	153	25	cryptocurrency	cryptocurrency	NN
randomwalker-info-585	153	26	,	,	,
randomwalker-info-585	153	27	but	but	CC
randomwalker-info-585	153	28	may	may	MD
randomwalker-info-585	153	29	deviate	deviate	VB
randomwalker-info-585	153	30	from	from	IN
randomwalker-info-585	153	31	the	the	DT
randomwalker-info-585	153	32	default	default	NN
randomwalker-info-585	153	33	protocol	protocol	NN
randomwalker-info-585	153	34	in	in	IN
randomwalker-info-585	153	35	choosing	choose	VBG
randomwalker-info-585	153	36	how	how	WRB
randomwalker-info-585	153	37	to	to	TO
randomwalker-info-585	153	38	build	build	VB
randomwalker-info-585	153	39	blocks	block	NNS
randomwalker-info-585	153	40	and	and	CC
randomwalker-info-585	153	41	what	what	WP
randomwalker-info-585	153	42	to	to	TO
randomwalker-info-585	153	43	do	do	VB
randomwalker-info-585	153	44	with	with	IN
randomwalker-info-585	153	45	them	-PRON-	PRP
randomwalker-info-585	153	46	once	once	IN
randomwalker-info-585	153	47	they	-PRON-	PRP
randomwalker-info-585	153	48	’re	be	VBZ
randomwalker-info-585	153	49	found	find	VBN
randomwalker-info-585	153	50	.	.	.
randomwalker-info-585	154	1	We	-PRON-	PRP
randomwalker-info-585	154	2	consider	consider	VBP
randomwalker-info-585	154	3	a	a	DT
randomwalker-info-585	154	4	variety	variety	NN
randomwalker-info-585	154	5	of	of	IN
randomwalker-info-585	154	6	known	known	JJ
randomwalker-info-585	154	7	and	and	CC
randomwalker-info-585	154	8	novel	novel	JJ
randomwalker-info-585	154	9	Bitcoin	Bitcoin	NNP
randomwalker-info-585	154	10	mining	mining	NN
randomwalker-info-585	154	11	strate-	strate-	XX
randomwalker-info-585	154	12	gies	gy	NNS
randomwalker-info-585	154	13	.	.	.
randomwalker-info-585	155	1	All	all	DT
randomwalker-info-585	155	2	of	of	IN
randomwalker-info-585	155	3	these	these	DT
randomwalker-info-585	155	4	can	can	MD
randomwalker-info-585	155	5	be	be	VB
randomwalker-info-585	155	6	formalized	formalize	VBN
randomwalker-info-585	155	7	into	into	IN
randomwalker-info-585	155	8	the	the	DT
randomwalker-info-585	155	9	same	same	JJ
randomwalker-info-585	155	10	general	general	JJ
randomwalker-info-585	155	11	structure	structure	NN
randomwalker-info-585	155	12	.	.	.
randomwalker-info-585	156	1	At	at	IN
randomwalker-info-585	156	2	each	each	DT
randomwalker-info-585	156	3	instant	instant	NN
randomwalker-info-585	156	4	,	,	,
randomwalker-info-585	156	5	every	every	DT
randomwalker-info-585	156	6	miner	miner	NN
randomwalker-info-585	156	7	makes	make	VBZ
randomwalker-info-585	156	8	several	several	JJ
randomwalker-info-585	156	9	dis-	dis-	IN
randomwalker-info-585	156	10	tinct	tinct	JJ
randomwalker-info-585	156	11	decisions	decision	NNS
randomwalker-info-585	156	12	:	:	:
randomwalker-info-585	156	13	•	•	ADD
randomwalker-info-585	156	14	Which	which	WDT
randomwalker-info-585	156	15	block	block	NN
randomwalker-info-585	156	16	to	to	TO
randomwalker-info-585	156	17	extend	extend	VB
randomwalker-info-585	156	18	.	.	.
randomwalker-info-585	157	1	•	•	VB
randomwalker-info-585	157	2	How	how	WRB
randomwalker-info-585	157	3	much	much	JJ
randomwalker-info-585	157	4	of	of	IN
randomwalker-info-585	157	5	the	the	DT
randomwalker-info-585	157	6	available	available	JJ
randomwalker-info-585	157	7	transactions	transaction	NNS
randomwalker-info-585	157	8	(	(	-LRB-
randomwalker-info-585	157	9	and	and	CC
randomwalker-info-585	157	10	associated	associate	VBN
randomwalker-info-585	157	11	fees	fee	NNS
randomwalker-info-585	157	12	)	)	-RRB-
randomwalker-info-585	157	13	to	to	TO
randomwalker-info-585	157	14	include	include	VB
randomwalker-info-585	157	15	in	in	IN
randomwalker-info-585	157	16	the	the	DT
randomwalker-info-585	157	17	block	block	NN
randomwalker-info-585	157	18	they	-PRON-	PRP
randomwalker-info-585	157	19	are	be	VBP
randomwalker-info-585	157	20	solving	solve	VBG
randomwalker-info-585	157	21	.	.	.
randomwalker-info-585	158	1	•	•	VB
randomwalker-info-585	158	2	For	for	IN
randomwalker-info-585	158	3	each	each	DT
randomwalker-info-585	158	4	unpublished	unpublished	JJ
randomwalker-info-585	158	5	block	block	NN
randomwalker-info-585	158	6	,	,	,
randomwalker-info-585	158	7	whether	whether	IN
randomwalker-info-585	158	8	or	or	CC
randomwalker-info-585	158	9	not	not	RB
randomwalker-info-585	158	10	to	to	TO
randomwalker-info-585	158	11	publish	publish	VB
randomwalker-info-585	158	12	.	.	.
randomwalker-info-585	159	1	The	the	DT
randomwalker-info-585	159	2	first	first	JJ
randomwalker-info-585	159	3	decision	decision	NN
randomwalker-info-585	159	4	is	be	VBZ
randomwalker-info-585	159	5	which	which	WDT
randomwalker-info-585	159	6	block	block	NN
randomwalker-info-585	159	7	to	to	TO
randomwalker-info-585	159	8	extend	extend	VB
randomwalker-info-585	159	9	.	.	.
randomwalker-info-585	160	1	As	as	IN
randomwalker-info-585	160	2	an	an	DT
randomwalker-info-585	160	3	ex-	ex-	JJ
randomwalker-info-585	160	4	ample	ample	NN
randomwalker-info-585	160	5	,	,	,
randomwalker-info-585	160	6	the	the	DT
randomwalker-info-585	160	7	default	default	NN
randomwalker-info-585	160	8	compliant	compliant	JJ
randomwalker-info-585	160	9	miner	miner	NN
randomwalker-info-585	160	10	chooses	choose	NNS
randomwalker-info-585	160	11	to	to	IN
randomwalker-info-585	160	12	mine	-PRON-	PRP
randomwalker-info-585	160	13	on	on	IN
randomwalker-info-585	160	14	the	the	DT
randomwalker-info-585	160	15	longest	long	JJS
randomwalker-info-585	160	16	chain	chain	NN
randomwalker-info-585	160	17	that	that	IN
randomwalker-info-585	160	18	they	-PRON-	PRP
randomwalker-info-585	160	19	are	be	VBP
randomwalker-info-585	160	20	aware	aware	JJ
randomwalker-info-585	160	21	of	of	IN
randomwalker-info-585	160	22	,	,	,
randomwalker-info-585	160	23	and	and	CC
randomwalker-info-585	160	24	in	in	IN
randomwalker-info-585	160	25	the	the	DT
randomwalker-info-585	160	26	case	case	NN
randomwalker-info-585	160	27	of	of	IN
randomwalker-info-585	160	28	multi-	multi-	NNP
randomwalker-info-585	160	29	ple	ple	NN
randomwalker-info-585	160	30	blocks	block	NNS
randomwalker-info-585	160	31	that	that	WDT
randomwalker-info-585	160	32	are	be	VBP
randomwalker-info-585	160	33	tied	tie	VBN
randomwalker-info-585	160	34	for	for	IN
randomwalker-info-585	160	35	the	the	DT
randomwalker-info-585	160	36	longest	long	JJS
randomwalker-info-585	160	37	chain	chain	NN
randomwalker-info-585	160	38	,	,	,
randomwalker-info-585	160	39	they	-PRON-	PRP
randomwalker-info-585	160	40	will	will	MD
randomwalker-info-585	160	41	favor	favor	VB
randomwalker-info-585	160	42	mining	mining	NN
randomwalker-info-585	160	43	on	on	IN
randomwalker-info-585	160	44	the	the	DT
randomwalker-info-585	160	45	first	first	JJ
randomwalker-info-585	160	46	of	of	IN
randomwalker-info-585	160	47	these	these	DT
randomwalker-info-585	160	48	blocks	block	NNS
randomwalker-info-585	160	49	that	that	WDT
randomwalker-info-585	160	50	they	-PRON-	PRP
randomwalker-info-585	160	51	became	become	VBD
randomwalker-info-585	160	52	aware	aware	JJ
randomwalker-info-585	160	53	of	of	IN
randomwalker-info-585	160	54	.	.	.
randomwalker-info-585	161	1	This	this	DT
randomwalker-info-585	161	2	decision	decision	NN
randomwalker-info-585	161	3	forms	form	VBZ
randomwalker-info-585	161	4	the	the	DT
randomwalker-info-585	161	5	basis	basis	NN
randomwalker-info-585	161	6	for	for	IN
randomwalker-info-585	161	7	how	how	WRB
randomwalker-info-585	161	8	a	a	DT
randomwalker-info-585	161	9	mining	mining	NN
randomwalker-info-585	161	10	strat-	strat-	NN
randomwalker-info-585	161	11	egy	egy	NN
randomwalker-info-585	161	12	will	will	MD
randomwalker-info-585	161	13	determine	determine	VB
randomwalker-info-585	161	14	which	which	WDT
randomwalker-info-585	161	15	side	side	NN
randomwalker-info-585	161	16	of	of	IN
randomwalker-info-585	161	17	a	a	DT
randomwalker-info-585	161	18	fork	fork	NN
randomwalker-info-585	161	19	it	-PRON-	PRP
randomwalker-info-585	161	20	wants	want	VBZ
randomwalker-info-585	161	21	to	to	TO
randomwalker-info-585	161	22	support	support	VB
randomwalker-info-585	161	23	,	,	,
randomwalker-info-585	161	24	or	or	CC
randomwalker-info-585	161	25	,	,	,
randomwalker-info-585	161	26	alternatively	alternatively	RB
randomwalker-info-585	161	27	,	,	,
randomwalker-info-585	161	28	if	if	IN
randomwalker-info-585	161	29	the	the	DT
randomwalker-info-585	161	30	miner	miner	NN
randomwalker-info-585	161	31	wants	want	VBZ
randomwalker-info-585	161	32	to	to	TO
randomwalker-info-585	161	33	create	create	VB
randomwalker-info-585	161	34	a	a	DT
randomwalker-info-585	161	35	new	new	JJ
randomwalker-info-585	161	36	fork	fork	NN
randomwalker-info-585	161	37	.	.	.
randomwalker-info-585	162	1	The	the	DT
randomwalker-info-585	162	2	next	next	JJ
randomwalker-info-585	162	3	decision	decision	NN
randomwalker-info-585	162	4	is	be	VBZ
randomwalker-info-585	162	5	how	how	WRB
randomwalker-info-585	162	6	much	much	JJ
randomwalker-info-585	162	7	of	of	IN
randomwalker-info-585	162	8	the	the	DT
randomwalker-info-585	162	9	available	available	JJ
randomwalker-info-585	162	10	transaction	transaction	NN
randomwalker-info-585	162	11	fees	fee	NNS
randomwalker-info-585	162	12	to	to	TO
randomwalker-info-585	162	13	claim	claim	VB
randomwalker-info-585	162	14	.	.	.
randomwalker-info-585	163	1	Again	again	RB
randomwalker-info-585	163	2	,	,	,
randomwalker-info-585	163	3	as	as	IN
randomwalker-info-585	163	4	an	an	DT
randomwalker-info-585	163	5	example	example	NN
randomwalker-info-585	163	6	,	,	,
randomwalker-info-585	163	7	the	the	DT
randomwalker-info-585	163	8	default	default	NN
randomwalker-info-585	163	9	compliant	compliant	JJ
randomwalker-info-585	163	10	miner	miner	NN
randomwalker-info-585	163	11	will	will	MD
randomwalker-info-585	163	12	include	include	VB
randomwalker-info-585	163	13	all	all	DT
randomwalker-info-585	163	14	of	of	IN
randomwalker-info-585	163	15	the	the	DT
randomwalker-info-585	163	16	unclaimed	unclaimed	JJ
randomwalker-info-585	163	17	transaction	transaction	NN
randomwalker-info-585	163	18	fees	fee	NNS
randomwalker-info-585	163	19	they	-PRON-	PRP
randomwalker-info-585	163	20	are	be	VBP
randomwalker-info-585	163	21	aware	aware	JJ
randomwalker-info-585	163	22	of	of	IN
randomwalker-info-585	163	23	in	in	IN
randomwalker-info-585	163	24	their	-PRON-	PRP$
randomwalker-info-585	163	25	block	block	NN
randomwalker-info-585	163	26	.	.	.
randomwalker-info-585	164	1	The	the	DT
randomwalker-info-585	164	2	final	final	JJ
randomwalker-info-585	164	3	decision	decision	NN
randomwalker-info-585	164	4	is	be	VBZ
randomwalker-info-585	164	5	when	when	WRB
randomwalker-info-585	164	6	to	to	TO
randomwalker-info-585	164	7	publish	publish	VB
randomwalker-info-585	164	8	blocks	block	NNS
randomwalker-info-585	164	9	.	.	.
randomwalker-info-585	165	1	When	when	WRB
randomwalker-info-585	165	2	a	a	DT
randomwalker-info-585	165	3	miner	miner	NN
randomwalker-info-585	165	4	mines	mine	VBZ
randomwalker-info-585	165	5	a	a	DT
randomwalker-info-585	165	6	block	block	NN
randomwalker-info-585	165	7	,	,	,
randomwalker-info-585	165	8	only	only	RB
randomwalker-info-585	165	9	they	-PRON-	PRP
randomwalker-info-585	165	10	are	be	VBP
randomwalker-info-585	165	11	aware	aware	JJ
randomwalker-info-585	165	12	of	of	IN
randomwalker-info-585	165	13	its	-PRON-	PRP$
randomwalker-info-585	165	14	existence	existence	NN
randomwalker-info-585	165	15	.	.	.
randomwalker-info-585	166	1	At	at	IN
randomwalker-info-585	166	2	each	each	DT
randomwalker-info-585	166	3	moment	moment	NN
randomwalker-info-585	166	4	,	,	,
randomwalker-info-585	166	5	miners	miner	NNS
randomwalker-info-585	166	6	can	can	MD
randomwalker-info-585	166	7	choose	choose	VB
randomwalker-info-585	166	8	whether	whether	IN
randomwalker-info-585	166	9	or	or	CC
randomwalker-info-585	166	10	not	not	RB
randomwalker-info-585	166	11	to	to	TO
randomwalker-info-585	166	12	alert	alert	VB
randomwalker-info-585	166	13	the	the	DT
randomwalker-info-585	166	14	other	other	JJ
randomwalker-info-585	166	15	miners	miner	NNS
randomwalker-info-585	166	16	of	of	IN
randomwalker-info-585	166	17	the	the	DT
randomwalker-info-585	166	18	block	block	NN
randomwalker-info-585	166	19	that	that	WDT
randomwalker-info-585	166	20	they	-PRON-	PRP
randomwalker-info-585	166	21	have	have	VBP
randomwalker-info-585	166	22	found	find	VBN
randomwalker-info-585	166	23	.	.	.
randomwalker-info-585	167	1	This	this	DT
randomwalker-info-585	167	2	allows	allow	VBZ
randomwalker-info-585	167	3	for	for	IN
randomwalker-info-585	167	4	mining	mining	NN
randomwalker-info-585	167	5	strategies	strategy	NNS
randomwalker-info-585	167	6	where	where	WRB
randomwalker-info-585	167	7	miners	miner	NNS
randomwalker-info-585	167	8	intentionally	intentionally	RB
randomwalker-info-585	167	9	choose	choose	VBP
randomwalker-info-585	167	10	to	to	TO
randomwalker-info-585	167	11	not	not	RB
randomwalker-info-585	167	12	reveal	reveal	VB
randomwalker-info-585	167	13	their	-PRON-	PRP$
randomwalker-info-585	167	14	blocks	block	NNS
randomwalker-info-585	167	15	(	(	-LRB-
randomwalker-info-585	167	16	such	such	JJ
randomwalker-info-585	167	17	as	as	IN
randomwalker-info-585	167	18	selfish	selfish	JJ
randomwalker-info-585	167	19	mining	mining	NN
randomwalker-info-585	167	20	[	[	-LRB-
randomwalker-info-585	167	21	9	9	CD
randomwalker-info-585	167	22	]	]	-RRB-
randomwalker-info-585	167	23	)	)	-RRB-
randomwalker-info-585	167	24	.	.	.
randomwalker-info-585	168	1	We	-PRON-	PRP
randomwalker-info-585	168	2	define	define	VBP
randomwalker-info-585	168	3	the	the	DT
randomwalker-info-585	168	4	following	follow	VBG
randomwalker-info-585	168	5	concepts	concept	NNS
randomwalker-info-585	168	6	in	in	IN
randomwalker-info-585	168	7	order	order	NN
randomwalker-info-585	168	8	to	to	IN
randomwalker-info-585	168	9	more	more	RBR
randomwalker-info-585	168	10	rig-	rig-	NN
randomwalker-info-585	168	11	orously	orously	RB
randomwalker-info-585	168	12	describe	describe	VB
randomwalker-info-585	168	13	the	the	DT
randomwalker-info-585	168	14	mining	mining	NN
randomwalker-info-585	168	15	strategies	strategy	NNS
randomwalker-info-585	168	16	:	:	:
randomwalker-info-585	168	17	First	first	RB
randomwalker-info-585	168	18	,	,	,
randomwalker-info-585	168	19	for	for	IN
randomwalker-info-585	168	20	a	a	DT
randomwalker-info-585	168	21	set	set	NN
randomwalker-info-585	168	22	of	of	IN
randomwalker-info-585	168	23	transactions	transaction	NNS
randomwalker-info-585	168	24	T	t	NN
randomwalker-info-585	168	25	,	,	,
randomwalker-info-585	168	26	we	-PRON-	PRP
randomwalker-info-585	168	27	will	will	MD
randomwalker-info-585	168	28	abuse	abuse	VB
randomwalker-info-585	168	29	notation	notation	NN
randomwalker-info-585	168	30	and	and	CC
randomwalker-info-585	168	31	use	use	VB
randomwalker-info-585	168	32	T	T	NNP
randomwalker-info-585	168	33	to	to	TO
randomwalker-info-585	168	34	also	also	RB
randomwalker-info-585	168	35	denote	denote	VB
randomwalker-info-585	168	36	the	the	DT
randomwalker-info-585	168	37	total	total	JJ
randomwalker-info-585	168	38	transaction	transaction	NN
randomwalker-info-585	168	39	fees	fee	NNS
randomwalker-info-585	168	40	included	include	VBN
randomwalker-info-585	168	41	for	for	IN
randomwalker-info-585	168	42	transactions	transaction	NNS
randomwalker-info-585	168	43	in	in	IN
randomwalker-info-585	168	44	T.	t.	NN
randomwalker-info-585	168	45	For	for	IN
randomwalker-info-585	168	46	a	a	DT
randomwalker-info-585	168	47	block	block	NN
randomwalker-info-585	168	48	,	,	,
randomwalker-info-585	168	49	B	b	UH
randomwalker-info-585	168	50	,	,	,
randomwalker-info-585	168	51	we	-PRON-	PRP
randomwalker-info-585	168	52	will	will	MD
randomwalker-info-585	168	53	denote	denote	VB
randomwalker-info-585	168	54	Tx(B	Tx(B	NNP
randomwalker-info-585	168	55	)	)	-RRB-
randomwalker-info-585	168	56	to	to	TO
randomwalker-info-585	168	57	be	be	VB
randomwalker-info-585	168	58	the	the	DT
randomwalker-info-585	168	59	set	set	NN
randomwalker-info-585	168	60	of	of	IN
randomwalker-info-585	168	61	transactions	transaction	NNS
randomwalker-info-585	168	62	included	include	VBN
randomwalker-info-585	168	63	in	in	IN
randomwalker-info-585	168	64	block	block	NN
randomwalker-info-585	168	65	B	B	NNP
randomwalker-info-585	168	66	,	,	,
randomwalker-info-585	168	67	and	and	CC
randomwalker-info-585	168	68	Rem(B	Rem(B	NNP
randomwalker-info-585	168	69	)	)	-RRB-
randomwalker-info-585	168	70	to	to	TO
randomwalker-info-585	168	71	denote	denote	VB
randomwalker-info-585	168	72	the	the	DT
randomwalker-info-585	168	73	remaining	remain	VBG
randomwalker-info-585	168	74	transactions	transaction	NNS
randomwalker-info-585	168	75	after	after	IN
randomwalker-info-585	168	76	block	block	NNP
randomwalker-info-585	168	77	B.	B.	NNP
randomwalker-info-585	169	1	That	that	RB
randomwalker-info-585	169	2	is	is	RB
randomwalker-info-585	169	3	,	,	,
randomwalker-info-585	169	4	Rem(B	Rem(B	NNP
randomwalker-info-585	169	5	)	)	-RRB-
randomwalker-info-585	169	6	contains	contain	VBZ
randomwalker-info-585	169	7	all	all	DT
randomwalker-info-585	169	8	announced	announce	VBN
randomwalker-info-585	169	9	transactions	transaction	NNS
randomwalker-info-585	169	10	in	in	IN
randomwalker-info-585	169	11	that	that	DT
randomwalker-info-585	169	12	are	be	VBP
randomwalker-info-585	169	13	not	not	RB
randomwalker-info-585	169	14	included	include	VBN
randomwalker-info-585	169	15	in	in	IN
randomwalker-info-585	169	16	B	b	NN
randomwalker-info-585	169	17	or	or	CC
randomwalker-info-585	169	18	any	any	DT
randomwalker-info-585	169	19	of	of	IN
randomwalker-info-585	169	20	its	-PRON-	PRP$
randomwalker-info-585	169	21	predecessors	predecessor	NNS
randomwalker-info-585	169	22	(	(	-LRB-
randomwalker-info-585	169	23	thus	thus	RB
randomwalker-info-585	169	24	,	,	,
randomwalker-info-585	169	25	this	this	DT
randomwalker-info-585	169	26	is	be	VBZ
randomwalker-info-585	169	27	a	a	DT
randomwalker-info-585	169	28	set	set	NN
randomwalker-info-585	169	29	that	that	WDT
randomwalker-info-585	169	30	varies	vary	VBZ
randomwalker-info-585	169	31	over	over	IN
randomwalker-info-585	169	32	time	time	NN
randomwalker-info-585	169	33	)	)	-RRB-
randomwalker-info-585	169	34	.	.	.
randomwalker-info-585	170	1	We	-PRON-	PRP
randomwalker-info-585	170	2	will	will	MD
randomwalker-info-585	170	3	also	also	RB
randomwalker-info-585	170	4	use	use	VB
randomwalker-info-585	170	5	Height(B	Height(B	NNP
randomwalker-info-585	170	6	)	)	-RRB-
randomwalker-info-585	170	7	to	to	TO
randomwalker-info-585	170	8	denote	denote	VB
randomwalker-info-585	170	9	the	the	DT
randomwalker-info-585	170	10	height	height	NN
randomwalker-info-585	170	11	of	of	IN
randomwalker-info-585	170	12	a	a	DT
randomwalker-info-585	170	13	block	block	NN
randomwalker-info-585	170	14	(	(	-LRB-
randomwalker-info-585	170	15	i.e.	i.e.	FW
randomwalker-info-585	171	1	the	the	DT
randomwalker-info-585	171	2	height	height	NN
randomwalker-info-585	171	3	of	of	IN
randomwalker-info-585	171	4	a	a	DT
randomwalker-info-585	171	5	chain	chain	NN
randomwalker-info-585	171	6	that	that	WDT
randomwalker-info-585	171	7	ends	end	VBZ
randomwalker-info-585	171	8	at	at	IN
randomwalker-info-585	171	9	block	block	NNP
randomwalker-info-585	171	10	B	B	NNP
randomwalker-info-585	171	11	)	)	-RRB-
randomwalker-info-585	171	12	,	,	,
randomwalker-info-585	171	13	denoting	denote	VBG
randomwalker-info-585	171	14	by	by	IN
randomwalker-info-585	171	15	H	h	NN
randomwalker-info-585	171	16	the	the	DT
randomwalker-info-585	171	17	height	height	NN
randomwalker-info-585	171	18	of	of	IN
randomwalker-info-585	171	19	the	the	DT
randomwalker-info-585	171	20	current	current	JJ
randomwalker-info-585	171	21	longest	long	JJS
randomwalker-info-585	171	22	chain	chain	NN
randomwalker-info-585	171	23	that	that	WDT
randomwalker-info-585	171	24	has	have	VBZ
randomwalker-info-585	171	25	been	be	VBN
randomwalker-info-585	171	26	announced,2	announced,2	CD
randomwalker-info-585	171	27	and	and	CC
randomwalker-info-585	171	28	Owner(B	owner(b	NN
randomwalker-info-585	171	29	)	)	-RRB-
randomwalker-info-585	171	30	to	to	TO
randomwalker-info-585	171	31	denote	denote	VB
randomwalker-info-585	171	32	the	the	DT
randomwalker-info-585	171	33	miner	miner	NN
randomwalker-info-585	171	34	that	that	WDT
randomwalker-info-585	171	35	produced	produce	VBD
randomwalker-info-585	171	36	block	block	NNP
randomwalker-info-585	171	37	B.	B.	NNP
randomwalker-info-585	172	1	When	when	WRB
randomwalker-info-585	172	2	a	a	DT
randomwalker-info-585	172	3	miner	miner	NN
randomwalker-info-585	172	4	m	m	NN
randomwalker-info-585	172	5	is	be	VBZ
randomwalker-info-585	172	6	deciding	decide	VBG
randomwalker-info-585	172	7	which	which	WDT
randomwalker-info-585	172	8	block	block	NN
randomwalker-info-585	172	9	of	of	IN
randomwalker-info-585	172	10	height	height	NN
randomwalker-info-585	172	11	i	i	PRP
randomwalker-info-585	172	12	to	to	TO
randomwalker-info-585	172	13	extend	extend	VB
randomwalker-info-585	172	14	in	in	IN
randomwalker-info-585	172	15	the	the	DT
randomwalker-info-585	172	16	case	case	NN
randomwalker-info-585	172	17	of	of	IN
randomwalker-info-585	172	18	a	a	DT
randomwalker-info-585	172	19	tie	tie	NN
randomwalker-info-585	172	20	,	,	,
randomwalker-info-585	172	21	all	all	DT
randomwalker-info-585	172	22	strategies	strategy	NNS
randomwalker-info-585	172	23	considered	consider	VBN
randomwalker-info-585	172	24	in	in	IN
randomwalker-info-585	172	25	this	this	DT
randomwalker-info-585	172	26	pa-	pa-	NN
randomwalker-info-585	172	27	per	per	IN
randomwalker-info-585	172	28	first	first	RB
randomwalker-info-585	172	29	select	select	VB
randomwalker-info-585	172	30	a	a	DT
randomwalker-info-585	172	31	block	block	NN
randomwalker-info-585	172	32	that	that	IN
randomwalker-info-585	172	33	they	-PRON-	PRP
randomwalker-info-585	172	34	themselves	-PRON-	PRP
randomwalker-info-585	172	35	mined	mine	VBD
randomwalker-info-585	172	36	(	(	-LRB-
randomwalker-info-585	172	37	Owner(B	owner(b	NN
randomwalker-info-585	172	38	)	)	-RRB-
randomwalker-info-585	172	39	=	=	NFP
randomwalker-info-585	172	40	m	m	NN
randomwalker-info-585	172	41	)	)	-RRB-
randomwalker-info-585	172	42	.	.	.
randomwalker-info-585	173	1	Also	also	RB
randomwalker-info-585	173	2	,	,	,
randomwalker-info-585	173	3	all	all	DT
randomwalker-info-585	173	4	strategies	strategy	NNS
randomwalker-info-585	173	5	in	in	IN
randomwalker-info-585	173	6	this	this	DT
randomwalker-info-585	173	7	paper	paper	NN
randomwalker-info-585	173	8	avoid	avoid	NN
randomwalker-info-585	173	9	mining	mine	VBG
randomwalker-info-585	173	10	multiple	multiple	JJ
randomwalker-info-585	173	11	blocks	block	NNS
randomwalker-info-585	173	12	at	at	IN
randomwalker-info-585	173	13	the	the	DT
randomwalker-info-585	173	14	same	same	JJ
randomwalker-info-585	173	15	height	height	NN
randomwalker-info-585	173	16	,	,	,
randomwalker-info-585	173	17	so	so	CC
randomwalker-info-585	173	18	if	if	IN
randomwalker-info-585	173	19	a	a	DT
randomwalker-info-585	173	20	block	block	NN
randomwalker-info-585	173	21	with	with	IN
randomwalker-info-585	173	22	Owner(B	owner(b	NN
randomwalker-info-585	173	23	)	)	-RRB-
randomwalker-info-585	173	24	=	=	NFP
randomwalker-info-585	173	25	m	m	NN
randomwalker-info-585	173	26	at	at	IN
randomwalker-info-585	173	27	height	height	NN
randomwalker-info-585	173	28	i	i	PRP
randomwalker-info-585	173	29	exists	exist	VBZ
randomwalker-info-585	173	30	,	,	,
randomwalker-info-585	173	31	it	-PRON-	PRP
randomwalker-info-585	173	32	would	would	MD
randomwalker-info-585	173	33	be	be	VB
randomwalker-info-585	173	34	unique	unique	JJ
randomwalker-info-585	173	35	.	.	.
randomwalker-info-585	174	1	If	if	IN
randomwalker-info-585	174	2	m	m	NNP
randomwalker-info-585	174	3	did	do	VBD
randomwalker-info-585	174	4	not	not	RB
randomwalker-info-585	174	5	pro-	pro-	VB
randomwalker-info-585	174	6	duce	duce	VB
randomwalker-info-585	174	7	any	any	DT
randomwalker-info-585	174	8	blocks	block	NNS
randomwalker-info-585	174	9	at	at	IN
randomwalker-info-585	174	10	height	height	NN
randomwalker-info-585	174	11	i	i	PRP
randomwalker-info-585	174	12	,	,	,
randomwalker-info-585	174	13	the	the	DT
randomwalker-info-585	174	14	default	default	NN
randomwalker-info-585	174	15	client	client	NN
randomwalker-info-585	174	16	would	would	MD
randomwalker-info-585	174	17	then	then	RB
randomwalker-info-585	174	18	select	select	VB
randomwalker-info-585	174	19	the	the	DT
randomwalker-info-585	174	20	first	first	JJ
randomwalker-info-585	174	21	block	block	NN
randomwalker-info-585	174	22	that	that	WDT
randomwalker-info-585	174	23	m	m	NNP
randomwalker-info-585	174	24	became	become	VBD
randomwalker-info-585	174	25	aware	aware	JJ
randomwalker-info-585	174	26	of	of	IN
randomwalker-info-585	174	27	.	.	.
randomwalker-info-585	175	1	So	so	RB
randomwalker-info-585	175	2	we	-PRON-	PRP
randomwalker-info-585	175	3	define	define	VBP
randomwalker-info-585	175	4	Oldestmi	Oldestmi	NNP
randomwalker-info-585	175	5	to	to	TO
randomwalker-info-585	175	6	be	be	VB
randomwalker-info-585	175	7	the	the	DT
randomwalker-info-585	175	8	unique	unique	JJ
randomwalker-info-585	175	9	block	block	NN
randomwalker-info-585	175	10	of	of	IN
randomwalker-info-585	175	11	height	height	NN
randomwalker-info-585	175	12	i	i	PRP
randomwalker-info-585	175	13	produced	produce	VBD
randomwalker-info-585	175	14	by	by	IN
randomwalker-info-585	175	15	miner	miner	NN
randomwalker-info-585	175	16	m	m	NNP
randomwalker-info-585	175	17	if	if	IN
randomwalker-info-585	175	18	it	-PRON-	PRP
randomwalker-info-585	175	19	exists	exist	VBZ
randomwalker-info-585	175	20	,	,	,
randomwalker-info-585	175	21	or	or	CC
randomwalker-info-585	175	22	the	the	DT
randomwalker-info-585	175	23	first	first	JJ
randomwalker-info-585	175	24	block	block	NN
randomwalker-info-585	175	25	of	of	IN
randomwalker-info-585	175	26	height	height	NN
randomwalker-info-585	175	27	i	i	PRP
randomwalker-info-585	175	28	that	that	DT
randomwalker-info-585	175	29	m	m	NNP
randomwalker-info-585	175	30	became	become	VBD
randomwalker-info-585	175	31	aware	aware	JJ
randomwalker-info-585	175	32	of	of	IN
randomwalker-info-585	175	33	.	.	.
randomwalker-info-585	176	1	Note	note	VB
randomwalker-info-585	176	2	that	that	IN
randomwalker-info-585	176	3	if	if	IN
randomwalker-info-585	176	4	i	i	PRP
randomwalker-info-585	176	5	=	=	SYM
randomwalker-info-585	176	6	H	h	NN
randomwalker-info-585	176	7	,	,	,
randomwalker-info-585	176	8	then	then	RB
randomwalker-info-585	176	9	this	this	DT
randomwalker-info-585	176	10	is	be	VBZ
randomwalker-info-585	176	11	the	the	DT
randomwalker-info-585	176	12	block	block	NN
randomwalker-info-585	176	13	m	m	NNP
randomwalker-info-585	176	14	would	would	MD
randomwalker-info-585	176	15	extend	extend	VB
randomwalker-info-585	176	16	using	use	VBG
randomwalker-info-585	176	17	the	the	DT
randomwalker-info-585	176	18	default	default	NN
randomwalker-info-585	176	19	strategy	strategy	NN
randomwalker-info-585	176	20	.	.	.
randomwalker-info-585	177	1	We	-PRON-	PRP
randomwalker-info-585	177	2	also	also	RB
randomwalker-info-585	177	3	define	define	VBP
randomwalker-info-585	177	4	Mosti	Mosti	NNP
randomwalker-info-585	177	5	to	to	TO
randomwalker-info-585	177	6	be	be	VB
randomwalker-info-585	177	7	the	the	DT
randomwalker-info-585	177	8	block	block	NN
randomwalker-info-585	177	9	of	of	IN
randomwalker-info-585	177	10	height	height	NN
randomwalker-info-585	177	11	i	i	PRP
randomwalker-info-585	177	12	that	that	DT
randomwalker-info-585	177	13	maximizes	maximize	VBZ
randomwalker-info-585	177	14	the	the	DT
randomwalker-info-585	177	15	remain-	remain-	NN
randomwalker-info-585	177	16	ing	ing	NNP
randomwalker-info-585	177	17	transaction	transaction	NN
randomwalker-info-585	177	18	fees	fee	NNS
randomwalker-info-585	177	19	(	(	-LRB-
randomwalker-info-585	177	20	formally	formally	RB
randomwalker-info-585	177	21	:	:	:
randomwalker-info-585	177	22	argmaxB|Height(B)=i{Rem(B	argmaxb|height(b)=i{rem(b	NN
randomwalker-info-585	177	23	)	)	-RRB-
randomwalker-info-585	177	24	}	}	-RRB-
randomwalker-info-585	177	25	)	)	-RRB-
randomwalker-info-585	177	26	.	.	.
randomwalker-info-585	178	1	Note	note	VB
randomwalker-info-585	178	2	that	that	IN
randomwalker-info-585	178	3	while	while	IN
randomwalker-info-585	178	4	Rem(B	Rem(B	NNP
randomwalker-info-585	178	5	)	)	-RRB-
randomwalker-info-585	178	6	changes	change	VBZ
randomwalker-info-585	178	7	over	over	IN
randomwalker-info-585	178	8	time	time	NN
randomwalker-info-585	178	9	,	,	,
randomwalker-info-585	178	10	the	the	DT
randomwalker-info-585	178	11	block	block	NN
randomwalker-info-585	178	12	Mosti	Mosti	NNP
randomwalker-info-585	178	13	can	can	MD
randomwalker-info-585	178	14	only	only	RB
randomwalker-info-585	178	15	change	change	VB
randomwalker-info-585	178	16	if	if	IN
randomwalker-info-585	178	17	a	a	DT
randomwalker-info-585	178	18	new	new	JJ
randomwalker-info-585	178	19	block	block	NN
randomwalker-info-585	178	20	of	of	IN
randomwalker-info-585	178	21	height	height	NN
randomwalker-info-585	178	22	i	i	PRP
randomwalker-info-585	178	23	is	be	VBZ
randomwalker-info-585	178	24	published	publish	VBN
randomwalker-info-585	178	25	.	.	.
randomwalker-info-585	179	1	Fi-	fi-	RB
randomwalker-info-585	179	2	nally	nally	RB
randomwalker-info-585	179	3	,	,	,
randomwalker-info-585	179	4	we	-PRON-	PRP
randomwalker-info-585	179	5	denote	denote	VBP
randomwalker-info-585	179	6	by	by	IN
randomwalker-info-585	179	7	Mostmi	Mostmi	NNP
randomwalker-info-585	179	8	the	the	DT
randomwalker-info-585	179	9	block	block	NN
randomwalker-info-585	179	10	of	of	IN
randomwalker-info-585	179	11	height	height	NN
randomwalker-info-585	179	12	i	i	PRP
randomwalker-info-585	179	13	produced	produce	VBD
randomwalker-info-585	179	14	by	by	IN
randomwalker-info-585	179	15	m	m	NNP
randomwalker-info-585	179	16	(	(	-LRB-
randomwalker-info-585	179	17	if	if	IN
randomwalker-info-585	179	18	it	-PRON-	PRP
randomwalker-info-585	179	19	exists	exist	VBZ
randomwalker-info-585	179	20	)	)	-RRB-
randomwalker-info-585	179	21	,	,	,
randomwalker-info-585	179	22	or	or	CC
randomwalker-info-585	179	23	the	the	DT
randomwalker-info-585	179	24	block	block	NN
randomwalker-info-585	179	25	of	of	IN
randomwalker-info-585	179	26	height	height	NN
randomwalker-info-585	179	27	i	i	PRP
randomwalker-info-585	179	28	that	that	DT
randomwalker-info-585	179	29	maximizes	maximize	VBZ
randomwalker-info-585	179	30	the	the	DT
randomwalker-info-585	179	31	remaining	remain	VBG
randomwalker-info-585	179	32	transaction	transaction	NN
randomwalker-info-585	179	33	fees	fee	NNS
randomwalker-info-585	179	34	otherwise	otherwise	RB
randomwalker-info-585	179	35	.	.	.
randomwalker-info-585	180	1	2So	2so	CD
randomwalker-info-585	180	2	for	for	IN
randomwalker-info-585	180	3	instance	instance	NN
randomwalker-info-585	180	4	,	,	,
randomwalker-info-585	180	5	if	if	IN
randomwalker-info-585	180	6	a	a	DT
randomwalker-info-585	180	7	chain	chain	NN
randomwalker-info-585	180	8	of	of	IN
randomwalker-info-585	180	9	height	height	NN
randomwalker-info-585	180	10	2	2	CD
randomwalker-info-585	180	11	has	have	VBZ
randomwalker-info-585	180	12	been	be	VBN
randomwalker-info-585	180	13	announced	announce	VBN
randomwalker-info-585	180	14	,	,	,
randomwalker-info-585	180	15	but	but	CC
randomwalker-info-585	180	16	some	some	DT
randomwalker-info-585	180	17	miner	miner	NN
randomwalker-info-585	180	18	is	be	VBZ
randomwalker-info-585	180	19	privately	privately	RB
randomwalker-info-585	180	20	storing	store	VBG
randomwalker-info-585	180	21	a	a	DT
randomwalker-info-585	180	22	chain	chain	NN
randomwalker-info-585	180	23	of	of	IN
randomwalker-info-585	180	24	length	length	NN
randomwalker-info-585	180	25	10	10	CD
randomwalker-info-585	180	26	,	,	,
randomwalker-info-585	180	27	we	-PRON-	PRP
randomwalker-info-585	180	28	would	would	MD
randomwalker-info-585	180	29	define	define	VB
randomwalker-info-585	180	30	H	h	NN
randomwalker-info-585	180	31	=	=	SYM
randomwalker-info-585	180	32	2	2	CD
randomwalker-info-585	180	33	.	.	.
randomwalker-info-585	181	1	We	-PRON-	PRP
randomwalker-info-585	181	2	can	can	MD
randomwalker-info-585	181	3	now	now	RB
randomwalker-info-585	181	4	formally	formally	RB
randomwalker-info-585	181	5	define	define	VB
randomwalker-info-585	181	6	mining	mining	NN
randomwalker-info-585	181	7	strategies	strategy	NNS
randomwalker-info-585	181	8	we	-PRON-	PRP
randomwalker-info-585	181	9	consider	consider	VBP
randomwalker-info-585	181	10	.	.	.
randomwalker-info-585	182	1	We	-PRON-	PRP
randomwalker-info-585	182	2	model	model	VBP
randomwalker-info-585	182	3	strategies	strategy	NNS
randomwalker-info-585	182	4	as	as	IN
randomwalker-info-585	182	5	time	time	NN
randomwalker-info-585	182	6	-	-	HYPH
randomwalker-info-585	182	7	driven	drive	VBN
randomwalker-info-585	182	8	(	(	-LRB-
randomwalker-info-585	182	9	rather	rather	RB
randomwalker-info-585	182	10	than	than	IN
randomwalker-info-585	182	11	event	event	NN
randomwalker-info-585	182	12	-	-	HYPH
randomwalker-info-585	182	13	driven	drive	VBN
randomwalker-info-585	182	14	)	)	-RRB-
randomwalker-info-585	182	15	:	:	:
randomwalker-info-585	182	16	in	in	IN
randomwalker-info-585	182	17	every	every	DT
randomwalker-info-585	182	18	infinitesimally	infinitesimally	RB
randomwalker-info-585	182	19	small	small	JJ
randomwalker-info-585	182	20	time	time	NN
randomwalker-info-585	182	21	step	step	NN
randomwalker-info-585	182	22	,	,	,
randomwalker-info-585	182	23	the	the	DT
randomwalker-info-585	182	24	miner	miner	NN
randomwalker-info-585	182	25	must	must	MD
randomwalker-info-585	182	26	de-	de-	RB
randomwalker-info-585	182	27	cide	cide	VB
randomwalker-info-585	182	28	which	which	WDT
randomwalker-info-585	182	29	block	block	NN
randomwalker-info-585	182	30	to	to	TO
randomwalker-info-585	182	31	extend	extend	VB
randomwalker-info-585	182	32	(	(	-LRB-
randomwalker-info-585	182	33	denoted	denote	VBN
randomwalker-info-585	182	34	by	by	IN
randomwalker-info-585	182	35	Mining(m	Mining(m	NNP
randomwalker-info-585	182	36	)	)	-RRB-
randomwalker-info-585	182	37	)	)	-RRB-
randomwalker-info-585	182	38	,	,	,
randomwalker-info-585	182	39	what	what	WDT
randomwalker-info-585	182	40	set	set	NN
randomwalker-info-585	182	41	of	of	IN
randomwalker-info-585	182	42	transactions	transaction	NNS
randomwalker-info-585	182	43	to	to	TO
randomwalker-info-585	182	44	include	include	VB
randomwalker-info-585	182	45	,	,	,
randomwalker-info-585	182	46	and	and	CC
randomwalker-info-585	182	47	for	for	IN
randomwalker-info-585	182	48	each	each	DT
randomwalker-info-585	182	49	of	of	IN
randomwalker-info-585	182	50	their	-PRON-	PRP$
randomwalker-info-585	182	51	own	own	JJ
randomwalker-info-585	182	52	unpublished	unpublished	JJ
randomwalker-info-585	182	53	blocks	block	NNS
randomwalker-info-585	182	54	,	,	,
randomwalker-info-585	182	55	whether	whether	IN
randomwalker-info-585	182	56	to	to	TO
randomwalker-info-585	182	57	publish	publish	VB
randomwalker-info-585	182	58	.	.	.
randomwalker-info-585	183	1	Note	note	VB
randomwalker-info-585	183	2	that	that	IN
randomwalker-info-585	183	3	by	by	IN
randomwalker-info-585	183	4	pub-	pub-	NN
randomwalker-info-585	183	5	lishing	lishe	VBG
randomwalker-info-585	183	6	a	a	DT
randomwalker-info-585	183	7	block	block	NN
randomwalker-info-585	183	8	B	b	NN
randomwalker-info-585	183	9	,	,	,
randomwalker-info-585	183	10	we	-PRON-	PRP
randomwalker-info-585	183	11	mean	mean	VBP
randomwalker-info-585	183	12	ensuring	ensure	VBG
randomwalker-info-585	183	13	that	that	IN
randomwalker-info-585	183	14	every	every	DT
randomwalker-info-585	183	15	node	node	NN
randomwalker-info-585	183	16	in	in	IN
randomwalker-info-585	183	17	the	the	DT
randomwalker-info-585	183	18	network	network	NN
randomwalker-info-585	183	19	is	be	VBZ
randomwalker-info-585	183	20	aware	aware	JJ
randomwalker-info-585	183	21	of	of	IN
randomwalker-info-585	183	22	B	b	NN
randomwalker-info-585	183	23	and	and	CC
randomwalker-info-585	183	24	all	all	PDT
randomwalker-info-585	183	25	its	-PRON-	PRP$
randomwalker-info-585	183	26	predecessors	predecessor	NNS
randomwalker-info-585	183	27	,	,	,
randomwalker-info-585	183	28	and	and	CC
randomwalker-info-585	183	29	are	be	VBP
randomwalker-info-585	183	30	n’t	not	RB
randomwalker-info-585	183	31	concerned	concerned	JJ
randomwalker-info-585	183	32	with	with	IN
randomwalker-info-585	183	33	exactly	exactly	RB
randomwalker-info-585	183	34	what	what	WP
randomwalker-info-585	183	35	physical	physical	JJ
randomwalker-info-585	183	36	measures	measure	NNS
randomwalker-info-585	183	37	m	m	NNP
randomwalker-info-585	183	38	takes	take	VBZ
randomwalker-info-585	183	39	to	to	TO
randomwalker-info-585	183	40	ensure	ensure	VB
randomwalker-info-585	183	41	this	this	DT
randomwalker-info-585	183	42	.	.	.
randomwalker-info-585	184	1	In	in	IN
randomwalker-info-585	184	2	this	this	DT
randomwalker-info-585	184	3	language	language	NN
randomwalker-info-585	184	4	,	,	,
randomwalker-info-585	184	5	the	the	DT
randomwalker-info-585	184	6	default	default	NN
randomwalker-info-585	184	7	mining	mining	NN
randomwalker-info-585	184	8	strategy	strategy	NN
randomwalker-info-585	184	9	would	would	MD
randomwalker-info-585	184	10	be	be	VB
randomwalker-info-585	184	11	formalized	formalize	VBN
randomwalker-info-585	184	12	as	as	IN
randomwalker-info-585	184	13	follows	follow	VBZ
randomwalker-info-585	184	14	:	:	:
randomwalker-info-585	184	15	DefaultCompliant	defaultcompliant	JJ
randomwalker-info-585	184	16	:	:	:
randomwalker-info-585	184	17	The	the	DT
randomwalker-info-585	184	18	default	default	NN
randomwalker-info-585	184	19	Bitcoin	Bitcoin	NNP
randomwalker-info-585	184	20	mining	mining	NN
randomwalker-info-585	184	21	strategy	strategy	NN
randomwalker-info-585	184	22	,	,	,
randomwalker-info-585	184	23	including	include	VBG
randomwalker-info-585	184	24	all	all	DT
randomwalker-info-585	184	25	avail-	avail-	JJ
randomwalker-info-585	184	26	able	able	JJ
randomwalker-info-585	184	27	transactions	transaction	NNS
randomwalker-info-585	184	28	,	,	,
randomwalker-info-585	184	29	mining	mine	VBG
randomwalker-info-585	184	30	on	on	IN
randomwalker-info-585	184	31	the	the	DT
randomwalker-info-585	184	32	end	end	NN
randomwalker-info-585	184	33	of	of	IN
randomwalker-info-585	184	34	the	the	DT
randomwalker-info-585	184	35	longest	long	JJS
randomwalker-info-585	184	36	chain	chain	NN
randomwalker-info-585	184	37	,	,	,
randomwalker-info-585	184	38	choosing	choose	VBG
randomwalker-info-585	184	39	the	the	DT
randomwalker-info-585	184	40	older	old	JJR
randomwalker-info-585	184	41	block	block	NN
randomwalker-info-585	184	42	in	in	IN
randomwalker-info-585	184	43	a	a	DT
randomwalker-info-585	184	44	tie	tie	NN
randomwalker-info-585	184	45	,	,	,
randomwalker-info-585	184	46	and	and	CC
randomwalker-info-585	184	47	publishing	publish	VBG
randomwalker-info-585	184	48	all	all	DT
randomwalker-info-585	184	49	blocks	block	NNS
randomwalker-info-585	184	50	.	.	.
randomwalker-info-585	185	1	Which	which	WDT
randomwalker-info-585	185	2	Block	Block	NNP
randomwalker-info-585	185	3	:	:	:
randomwalker-info-585	185	4	Mining(m	mining(m	LS
randomwalker-info-585	185	5	)	)	-RRB-
randomwalker-info-585	185	6	=	=	NFP
randomwalker-info-585	185	7	OldestmH	OldestmH	NNS
randomwalker-info-585	185	8	.	.	.
randomwalker-info-585	186	1	How	how	WRB
randomwalker-info-585	186	2	much	much	JJ
randomwalker-info-585	186	3	:	:	:
randomwalker-info-585	186	4	include	include	VBP
randomwalker-info-585	186	5	Rem(Mining(m	Rem(Mining(m	NNP
randomwalker-info-585	186	6	)	)	-RRB-
randomwalker-info-585	186	7	)	)	-RRB-
randomwalker-info-585	186	8	.	.	.
randomwalker-info-585	187	1	Publish(B	Publish(B	VBN
randomwalker-info-585	187	2	)	)	-RRB-
randomwalker-info-585	187	3	?	?	.
randomwalker-info-585	188	1	:	:	:
randomwalker-info-585	188	2	yes	yes	UH
randomwalker-info-585	188	3	.	.	.
randomwalker-info-585	189	1	4	4	LS
randomwalker-info-585	189	2	.	.	.
randomwalker-info-585	190	1	MINING	mining	NN
randomwalker-info-585	190	2	STRATEGY	STRATEGY	NNP
randomwalker-info-585	190	3	SIMULATOR	SIMULATOR	VBN
randomwalker-info-585	190	4	In	in	IN
randomwalker-info-585	190	5	order	order	NN
randomwalker-info-585	190	6	to	to	TO
randomwalker-info-585	190	7	more	more	RBR
randomwalker-info-585	190	8	clearly	clearly	RB
randomwalker-info-585	190	9	analyze	analyze	VB
randomwalker-info-585	190	10	what	what	WP
randomwalker-info-585	190	11	the	the	DT
randomwalker-info-585	190	12	game	game	NN
randomwalker-info-585	190	13	theoretic	theoretic	JJ
randomwalker-info-585	190	14	landscape	landscape	NN
randomwalker-info-585	190	15	will	will	MD
randomwalker-info-585	190	16	look	look	VB
randomwalker-info-585	190	17	like	like	IN
randomwalker-info-585	190	18	once	once	RB
randomwalker-info-585	190	19	the	the	DT
randomwalker-info-585	190	20	Bitcoin	Bitcoin	NNP
randomwalker-info-585	190	21	mining	mining	NN
randomwalker-info-585	190	22	incentive	incentive	NN
randomwalker-info-585	190	23	be-	be-	XX
randomwalker-info-585	190	24	comes	come	VBZ
randomwalker-info-585	190	25	transaction	transaction	NN
randomwalker-info-585	190	26	fee	fee	NN
randomwalker-info-585	190	27	based	base	VBN
randomwalker-info-585	190	28	instead	instead	RB
randomwalker-info-585	190	29	of	of	IN
randomwalker-info-585	190	30	block	block	NN
randomwalker-info-585	190	31	reward	reward	NN
randomwalker-info-585	190	32	based	base	VBN
randomwalker-info-585	190	33	,	,	,
randomwalker-info-585	190	34	we	-PRON-	PRP
randomwalker-info-585	190	35	have	have	VBP
randomwalker-info-585	190	36	developed	develop	VBN
randomwalker-info-585	190	37	a	a	DT
randomwalker-info-585	190	38	versatile	versatile	JJ
randomwalker-info-585	190	39	Bitcoin	Bitcoin	NNP
randomwalker-info-585	190	40	mining	mining	NN
randomwalker-info-585	190	41	strategy	strategy	NN
randomwalker-info-585	190	42	sim-	sim-	NN
randomwalker-info-585	190	43	ulator.3	ulator.3	UH
randomwalker-info-585	190	44	Here	here	RB
randomwalker-info-585	190	45	we	-PRON-	PRP
randomwalker-info-585	190	46	discuss	discuss	VBP
randomwalker-info-585	190	47	the	the	DT
randomwalker-info-585	190	48	strategies	strategy	NNS
randomwalker-info-585	190	49	our	-PRON-	PRP$
randomwalker-info-585	190	50	simulator	simulator	NN
randomwalker-info-585	190	51	is	be	VBZ
randomwalker-info-585	190	52	ca-	ca-	VBN
randomwalker-info-585	190	53	pable	pable	JJ
randomwalker-info-585	190	54	of	of	IN
randomwalker-info-585	190	55	implementing	implement	VBG
randomwalker-info-585	190	56	,	,	,
randomwalker-info-585	190	57	the	the	DT
randomwalker-info-585	190	58	process	process	NN
randomwalker-info-585	190	59	by	by	IN
randomwalker-info-585	190	60	which	which	WDT
randomwalker-info-585	190	61	our	-PRON-	PRP$
randomwalker-info-585	190	62	simulator	simulator	NN
randomwalker-info-585	190	63	can	can	MD
randomwalker-info-585	190	64	explore	explore	VB
randomwalker-info-585	190	65	a	a	DT
randomwalker-info-585	190	66	strategy	strategy	NN
randomwalker-info-585	190	67	space	space	NN
randomwalker-info-585	190	68	,	,	,
randomwalker-info-585	190	69	the	the	DT
randomwalker-info-585	190	70	configurable	configurable	JJ
randomwalker-info-585	190	71	parameters	parameter	NNS
randomwalker-info-585	190	72	of	of	IN
randomwalker-info-585	190	73	the	the	DT
randomwalker-info-585	190	74	simulator	simulator	NN
randomwalker-info-585	190	75	,	,	,
randomwalker-info-585	190	76	and	and	CC
randomwalker-info-585	190	77	its	-PRON-	PRP$
randomwalker-info-585	190	78	limitations	limitation	NNS
randomwalker-info-585	190	79	.	.	.
randomwalker-info-585	191	1	4.1	4.1	CD
randomwalker-info-585	191	2	Strategies	Strategies	NNPS
randomwalker-info-585	191	3	,	,	,
randomwalker-info-585	191	4	Rounds	Rounds	NNPS
randomwalker-info-585	191	5	,	,	,
randomwalker-info-585	191	6	and	and	CC
randomwalker-info-585	191	7	Games	Games	NNPS
randomwalker-info-585	191	8	We	-PRON-	PRP
randomwalker-info-585	191	9	first	first	RB
randomwalker-info-585	191	10	describe	describe	VBP
randomwalker-info-585	191	11	the	the	DT
randomwalker-info-585	191	12	basic	basic	JJ
randomwalker-info-585	191	13	units	unit	NNS
randomwalker-info-585	191	14	of	of	IN
randomwalker-info-585	191	15	our	-PRON-	PRP$
randomwalker-info-585	191	16	simulator	simulator	NN
randomwalker-info-585	191	17	and	and	CC
randomwalker-info-585	191	18	how	how	WRB
randomwalker-info-585	191	19	they	-PRON-	PRP
randomwalker-info-585	191	20	interact	interact	VBP
randomwalker-info-585	191	21	with	with	IN
randomwalker-info-585	191	22	each	each	DT
randomwalker-info-585	191	23	other	other	JJ
randomwalker-info-585	191	24	before	before	IN
randomwalker-info-585	191	25	getting	get	VBG
randomwalker-info-585	191	26	into	into	IN
randomwalker-info-585	191	27	details	detail	NNS
randomwalker-info-585	191	28	.	.	.
randomwalker-info-585	192	1	Strategies	strategy	NNS
randomwalker-info-585	192	2	.	.	.
randomwalker-info-585	193	1	The	the	DT
randomwalker-info-585	193	2	simulator	simulator	NN
randomwalker-info-585	193	3	is	be	VBZ
randomwalker-info-585	193	4	designed	design	VBN
randomwalker-info-585	193	5	in	in	IN
randomwalker-info-585	193	6	such	such	PDT
randomwalker-info-585	193	7	a	a	DT
randomwalker-info-585	193	8	way	way	NN
randomwalker-info-585	193	9	to	to	TO
randomwalker-info-585	193	10	be	be	VB
randomwalker-info-585	193	11	able	able	JJ
randomwalker-info-585	193	12	to	to	TO
randomwalker-info-585	193	13	run	run	VB
randomwalker-info-585	193	14	any	any	DT
randomwalker-info-585	193	15	strategy	strategy	NN
randomwalker-info-585	193	16	that	that	WDT
randomwalker-info-585	193	17	fits	fit	VBZ
randomwalker-info-585	193	18	the	the	DT
randomwalker-info-585	193	19	strategy	strategy	NN
randomwalker-info-585	193	20	space	space	NN
randomwalker-info-585	193	21	detailed	detail	VBN
randomwalker-info-585	193	22	in	in	IN
randomwalker-info-585	193	23	Section	Section	NNP
randomwalker-info-585	193	24	3.3	3.3	CD
randomwalker-info-585	193	25	.	.	.
randomwalker-info-585	194	1	That	that	RB
randomwalker-info-585	194	2	is	is	RB
randomwalker-info-585	194	3	,	,	,
randomwalker-info-585	194	4	every	every	DT
randomwalker-info-585	194	5	strategy	strategy	NN
randomwalker-info-585	194	6	is	be	VBZ
randomwalker-info-585	194	7	fully	fully	RB
randomwalker-info-585	194	8	defined	define	VBN
randomwalker-info-585	194	9	by	by	IN
randomwalker-info-585	194	10	a	a	DT
randomwalker-info-585	194	11	function	function	NN
randomwalker-info-585	194	12	that	that	WDT
randomwalker-info-585	194	13	outputs	output	VBZ
randomwalker-info-585	194	14	a	a	DT
randomwalker-info-585	194	15	block	block	NN
randomwalker-info-585	194	16	to	to	TO
randomwalker-info-585	194	17	extend	extend	VB
randomwalker-info-585	194	18	,	,	,
randomwalker-info-585	194	19	a	a	DT
randomwalker-info-585	194	20	set	set	NN
randomwalker-info-585	194	21	of	of	IN
randomwalker-info-585	194	22	trans-	trans-	JJ
randomwalker-info-585	194	23	actions	action	NNS
randomwalker-info-585	194	24	to	to	TO
randomwalker-info-585	194	25	include	include	VB
randomwalker-info-585	194	26	,	,	,
randomwalker-info-585	194	27	and	and	CC
randomwalker-info-585	194	28	a	a	DT
randomwalker-info-585	194	29	rule	rule	NN
randomwalker-info-585	194	30	to	to	TO
randomwalker-info-585	194	31	decide	decide	VB
randomwalker-info-585	194	32	whether	whether	IN
randomwalker-info-585	194	33	to	to	TO
randomwalker-info-585	194	34	publish	publish	VB
randomwalker-info-585	194	35	any	any	DT
randomwalker-info-585	194	36	found	find	VBN
randomwalker-info-585	194	37	blocks	block	NNS
randomwalker-info-585	194	38	.	.	.
randomwalker-info-585	195	1	All	all	DT
randomwalker-info-585	195	2	of	of	IN
randomwalker-info-585	195	3	these	these	DT
randomwalker-info-585	195	4	functions	function	NNS
randomwalker-info-585	195	5	may	may	MD
randomwalker-info-585	195	6	take	take	VB
randomwalker-info-585	195	7	as	as	RB
randomwalker-info-585	195	8	input	input	NN
randomwalker-info-585	195	9	any	any	DT
randomwalker-info-585	195	10	public	public	JJ
randomwalker-info-585	195	11	information	information	NN
randomwalker-info-585	195	12	,	,	,
randomwalker-info-585	195	13	including	include	VBG
randomwalker-info-585	195	14	all	all	DT
randomwalker-info-585	195	15	published	publish	VBN
randomwalker-info-585	195	16	blocks	block	NNS
randomwalker-info-585	195	17	and	and	CC
randomwalker-info-585	195	18	all	all	DT
randomwalker-info-585	195	19	announced	announce	VBN
randomwalker-info-585	195	20	transactions	transaction	NNS
randomwalker-info-585	195	21	.	.	.
randomwalker-info-585	196	1	Rounds	round	NNS
randomwalker-info-585	196	2	.	.	.
randomwalker-info-585	197	1	Our	-PRON-	PRP$
randomwalker-info-585	197	2	simulator	simulator	NN
randomwalker-info-585	197	3	is	be	VBZ
randomwalker-info-585	197	4	time	time	NN
randomwalker-info-585	197	5	-	-	HYPH
randomwalker-info-585	197	6	driven	drive	VBN
randomwalker-info-585	197	7	,	,	,
randomwalker-info-585	197	8	as	as	IN
randomwalker-info-585	197	9	opposed	oppose	VBN
randomwalker-info-585	197	10	to	to	TO
randomwalker-info-585	197	11	event-	event-	VB
randomwalker-info-585	197	12	driven	drive	VBN
randomwalker-info-585	197	13	.	.	.
randomwalker-info-585	198	1	We	-PRON-	PRP
randomwalker-info-585	198	2	made	make	VBD
randomwalker-info-585	198	3	this	this	DT
randomwalker-info-585	198	4	decision	decision	NN
randomwalker-info-585	198	5	because	because	IN
randomwalker-info-585	198	6	we	-PRON-	PRP
randomwalker-info-585	198	7	want	want	VBP
randomwalker-info-585	198	8	it	-PRON-	PRP
randomwalker-info-585	198	9	to	to	TO
randomwalker-info-585	198	10	be	be	VB
randomwalker-info-585	198	11	easy	easy	JJ
randomwalker-info-585	198	12	to	to	TO
randomwalker-info-585	198	13	add	add	VB
randomwalker-info-585	198	14	new	new	JJ
randomwalker-info-585	198	15	strategies	strategy	NNS
randomwalker-info-585	198	16	to	to	IN
randomwalker-info-585	198	17	the	the	DT
randomwalker-info-585	198	18	simulator	simulator	NN
randomwalker-info-585	198	19	.	.	.
randomwalker-info-585	199	1	In	in	IN
randomwalker-info-585	199	2	an	an	DT
randomwalker-info-585	199	3	event	event	NN
randomwalker-info-585	199	4	-	-	HYPH
randomwalker-info-585	199	5	driven	drive	VBN
randomwalker-info-585	199	6	simulation	simulation	NN
randomwalker-info-585	199	7	,	,	,
randomwalker-info-585	199	8	new	new	JJ
randomwalker-info-585	199	9	strategies	strategy	NNS
randomwalker-info-585	199	10	would	would	MD
randomwalker-info-585	199	11	be	be	VB
randomwalker-info-585	199	12	limited	limit	VBN
randomwalker-info-585	199	13	by	by	IN
randomwalker-info-585	199	14	the	the	DT
randomwalker-info-585	199	15	current	current	JJ
randomwalker-info-585	199	16	list	list	NN
randomwalker-info-585	199	17	of	of	IN
randomwalker-info-585	199	18	possible	possible	JJ
randomwalker-info-585	199	19	events	event	NNS
randomwalker-info-585	199	20	.	.	.
randomwalker-info-585	200	1	However	however	RB
randomwalker-info-585	200	2	,	,	,
randomwalker-info-585	200	3	in	in	IN
randomwalker-info-585	200	4	our	-PRON-	PRP$
randomwalker-info-585	200	5	time	time	NN
randomwalker-info-585	200	6	-	-	HYPH
randomwalker-info-585	200	7	based	base	VBN
randomwalker-info-585	200	8	simula-	simula-	NN
randomwalker-info-585	200	9	tions	tion	NNS
randomwalker-info-585	200	10	,	,	,
randomwalker-info-585	200	11	any	any	DT
randomwalker-info-585	200	12	strategy	strategy	NN
randomwalker-info-585	200	13	that	that	WDT
randomwalker-info-585	200	14	details	detail	VBZ
randomwalker-info-585	200	15	how	how	WRB
randomwalker-info-585	200	16	to	to	TO
randomwalker-info-585	200	17	make	make	VB
randomwalker-info-585	200	18	the	the	DT
randomwalker-info-585	200	19	decisions	decision	NNS
randomwalker-info-585	200	20	above	above	IN
randomwalker-info-585	200	21	at	at	IN
randomwalker-info-585	200	22	any	any	DT
randomwalker-info-585	200	23	moment	moment	NN
randomwalker-info-585	200	24	can	can	MD
randomwalker-info-585	200	25	be	be	VB
randomwalker-info-585	200	26	easily	easily	RB
randomwalker-info-585	200	27	implemented	implement	VBN
randomwalker-info-585	200	28	.	.	.
randomwalker-info-585	201	1	A	a	DT
randomwalker-info-585	201	2	round	round	NN
randomwalker-info-585	201	3	is	be	VBZ
randomwalker-info-585	201	4	the	the	DT
randomwalker-info-585	201	5	smallest	small	JJS
randomwalker-info-585	201	6	unit	unit	NN
randomwalker-info-585	201	7	of	of	IN
randomwalker-info-585	201	8	time	time	NN
randomwalker-info-585	201	9	in	in	IN
randomwalker-info-585	201	10	our	-PRON-	PRP$
randomwalker-info-585	201	11	simulator	simulator	NN
randomwalker-info-585	201	12	(	(	-LRB-
randomwalker-info-585	201	13	cur-	cur-	RB
randomwalker-info-585	201	14	rently	rently	RB
randomwalker-info-585	201	15	,	,	,
randomwalker-info-585	201	16	1/600	1/600	CD
randomwalker-info-585	201	17	of	of	IN
randomwalker-info-585	201	18	the	the	DT
randomwalker-info-585	201	19	time	time	NN
randomwalker-info-585	201	20	it	-PRON-	PRP
randomwalker-info-585	201	21	takes	take	VBZ
randomwalker-info-585	201	22	for	for	IN
randomwalker-info-585	201	23	the	the	DT
randomwalker-info-585	201	24	entire	entire	JJ
randomwalker-info-585	201	25	network	network	NN
randomwalker-info-585	201	26	to	to	TO
randomwalker-info-585	201	27	find	find	VB
randomwalker-info-585	201	28	a	a	DT
randomwalker-info-585	201	29	block	block	NN
randomwalker-info-585	201	30	)	)	-RRB-
randomwalker-info-585	201	31	.	.	.
randomwalker-info-585	202	1	During	during	IN
randomwalker-info-585	202	2	a	a	DT
randomwalker-info-585	202	3	round	round	NN
randomwalker-info-585	202	4	,	,	,
randomwalker-info-585	202	5	every	every	DT
randomwalker-info-585	202	6	miner	miner	NN
randomwalker-info-585	202	7	first	first	RB
randomwalker-info-585	202	8	takes	take	VBZ
randomwalker-info-585	202	9	as	as	RB
randomwalker-info-585	202	10	in-	in-	CD
randomwalker-info-585	202	11	put	put	VBD
randomwalker-info-585	202	12	the	the	DT
randomwalker-info-585	202	13	block	block	NN
randomwalker-info-585	202	14	chain	chain	NN
randomwalker-info-585	202	15	(	(	-LRB-
randomwalker-info-585	202	16	that	that	IN
randomwalker-info-585	202	17	they	-PRON-	PRP
randomwalker-info-585	202	18	’re	be	VBZ
randomwalker-info-585	202	19	aware	aware	JJ
randomwalker-info-585	202	20	of	of	IN
randomwalker-info-585	202	21	)	)	-RRB-
randomwalker-info-585	202	22	and	and	CC
randomwalker-info-585	202	23	all	all	DT
randomwalker-info-585	202	24	transac-	transac-	NN
randomwalker-info-585	202	25	tions	tion	NNS
randomwalker-info-585	202	26	(	(	-LRB-
randomwalker-info-585	202	27	that	that	IN
randomwalker-info-585	202	28	they	-PRON-	PRP
randomwalker-info-585	202	29	’re	be	VBZ
randomwalker-info-585	202	30	aware	aware	JJ
randomwalker-info-585	202	31	of	of	IN
randomwalker-info-585	202	32	)	)	-RRB-
randomwalker-info-585	202	33	and	and	CC
randomwalker-info-585	202	34	decides	decide	VBZ
randomwalker-info-585	202	35	which	which	WDT
randomwalker-info-585	202	36	block	block	NN
randomwalker-info-585	202	37	to	to	IN
randomwalker-info-585	202	38	(	(	-LRB-
randomwalker-info-585	202	39	try	try	VB
randomwalker-info-585	202	40	to	to	TO
randomwalker-info-585	202	41	)	)	-RRB-
randomwalker-info-585	202	42	extend	extend	VB
randomwalker-info-585	202	43	,	,	,
randomwalker-info-585	202	44	and	and	CC
randomwalker-info-585	202	45	which	which	WDT
randomwalker-info-585	202	46	transactions	transaction	NNS
randomwalker-info-585	202	47	to	to	TO
randomwalker-info-585	202	48	include	include	VB
randomwalker-info-585	202	49	.	.	.
randomwalker-info-585	203	1	Then	then	RB
randomwalker-info-585	203	2	there	there	EX
randomwalker-info-585	203	3	is	be	VBZ
randomwalker-info-585	203	4	a	a	DT
randomwalker-info-585	203	5	random	random	JJ
randomwalker-info-585	203	6	check	check	NN
randomwalker-info-585	203	7	(	(	-LRB-
randomwalker-info-585	203	8	as	as	IN
randomwalker-info-585	203	9	a	a	DT
randomwalker-info-585	203	10	function	function	NN
randomwalker-info-585	203	11	of	of	IN
randomwalker-info-585	203	12	that	that	DT
randomwalker-info-585	203	13	miner	miner	NN
randomwalker-info-585	203	14	’s	’s	POS
randomwalker-info-585	203	15	hash	hash	NN
randomwalker-info-585	203	16	rate	rate	NN
randomwalker-info-585	203	17	3While	3While	NNP
randomwalker-info-585	203	18	this	this	DT
randomwalker-info-585	203	19	is	be	VBZ
randomwalker-info-585	203	20	the	the	DT
randomwalker-info-585	203	21	original	original	JJ
randomwalker-info-585	203	22	motivation	motivation	NN
randomwalker-info-585	203	23	for	for	IN
randomwalker-info-585	203	24	developing	develop	VBG
randomwalker-info-585	203	25	our	-PRON-	PRP$
randomwalker-info-585	203	26	simulator	simulator	NN
randomwalker-info-585	203	27	,	,	,
randomwalker-info-585	203	28	it	-PRON-	PRP
randomwalker-info-585	203	29	is	be	VBZ
randomwalker-info-585	203	30	indeed	indeed	RB
randomwalker-info-585	203	31	capable	capable	JJ
randomwalker-info-585	203	32	of	of	IN
randomwalker-info-585	203	33	simulating	simulate	VBG
randomwalker-info-585	203	34	non	non	JJ
randomwalker-info-585	203	35	-	-	JJ
randomwalker-info-585	203	36	zero	zero	CD
randomwalker-info-585	203	37	block	block	NN
randomwalker-info-585	203	38	reward	reward	NN
randomwalker-info-585	203	39	as	as	RB
randomwalker-info-585	203	40	well	well	RB
randomwalker-info-585	203	41	—	—	:
randomwalker-info-585	203	42	more	more	RBR
randomwalker-info-585	203	43	on	on	IN
randomwalker-info-585	203	44	that	that	DT
randomwalker-info-585	203	45	in	in	IN
randomwalker-info-585	203	46	Section	Section	NNP
randomwalker-info-585	203	47	4.3	4.3	CD
randomwalker-info-585	203	48	.	.	.
randomwalker-info-585	203	49	and	and	CC
randomwalker-info-585	203	50	the	the	DT
randomwalker-info-585	203	51	current	current	JJ
randomwalker-info-585	203	52	network	network	NN
randomwalker-info-585	203	53	difficulty	difficulty	NN
randomwalker-info-585	203	54	)	)	-RRB-
randomwalker-info-585	203	55	to	to	TO
randomwalker-info-585	203	56	determine	determine	VB
randomwalker-info-585	203	57	whether	whether	IN
randomwalker-info-585	203	58	the	the	DT
randomwalker-info-585	203	59	miner	miner	NN
randomwalker-info-585	203	60	successfully	successfully	RB
randomwalker-info-585	203	61	found	find	VBD
randomwalker-info-585	203	62	a	a	DT
randomwalker-info-585	203	63	block	block	NN
randomwalker-info-585	203	64	or	or	CC
randomwalker-info-585	203	65	not	not	RB
randomwalker-info-585	203	66	.	.	.
randomwalker-info-585	204	1	Then	then	RB
randomwalker-info-585	204	2	,	,	,
randomwalker-info-585	204	3	the	the	DT
randomwalker-info-585	204	4	miner	miner	NN
randomwalker-info-585	204	5	de-	de-	NNP
randomwalker-info-585	204	6	cides	cide	VBZ
randomwalker-info-585	204	7	which	which	WDT
randomwalker-info-585	204	8	unpublished	unpublishe	VBD
randomwalker-info-585	204	9	blocks	block	NNS
randomwalker-info-585	204	10	to	to	TO
randomwalker-info-585	204	11	publish	publish	VB
randomwalker-info-585	204	12	.	.	.
randomwalker-info-585	205	1	The	the	DT
randomwalker-info-585	205	2	duration	duration	NN
randomwalker-info-585	205	3	of	of	IN
randomwalker-info-585	205	4	a	a	DT
randomwalker-info-585	205	5	round	round	NN
randomwalker-info-585	205	6	is	be	VBZ
randomwalker-info-585	205	7	a	a	DT
randomwalker-info-585	205	8	configurable	configurable	JJ
randomwalker-info-585	205	9	parameter	parameter	NN
randomwalker-info-585	205	10	,	,	,
randomwalker-info-585	205	11	which	which	WDT
randomwalker-info-585	205	12	we	-PRON-	PRP
randomwalker-info-585	205	13	discuss	discuss	VBP
randomwalker-info-585	205	14	shortly	shortly	RB
randomwalker-info-585	205	15	in	in	IN
randomwalker-info-585	205	16	Section	section	NN
randomwalker-info-585	205	17	4.3	4.3	CD
randomwalker-info-585	205	18	.	.	.
randomwalker-info-585	206	1	Games	game	NNS
randomwalker-info-585	206	2	.	.	.
randomwalker-info-585	207	1	A	a	DT
randomwalker-info-585	207	2	game	game	NN
randomwalker-info-585	207	3	involves	involve	VBZ
randomwalker-info-585	207	4	setting	set	VBG
randomwalker-info-585	207	5	parameters	parameter	NNS
randomwalker-info-585	207	6	such	such	JJ
randomwalker-info-585	207	7	as	as	IN
randomwalker-info-585	207	8	choos-	choos-	NNP
randomwalker-info-585	207	9	ing	ing	NNP
randomwalker-info-585	207	10	a	a	DT
randomwalker-info-585	207	11	number	number	NN
randomwalker-info-585	207	12	of	of	IN
randomwalker-info-585	207	13	miners	miner	NNS
randomwalker-info-585	207	14	,	,	,
randomwalker-info-585	207	15	assigning	assign	VBG
randomwalker-info-585	207	16	their	-PRON-	PRP$
randomwalker-info-585	207	17	strategies	strategy	NNS
randomwalker-info-585	207	18	and	and	CC
randomwalker-info-585	207	19	hash	hash	NN
randomwalker-info-585	207	20	power	power	NN
randomwalker-info-585	207	21	,	,	,
randomwalker-info-585	207	22	etc	etc	FW
randomwalker-info-585	207	23	.	.	.
randomwalker-info-585	208	1	(	(	-LRB-
randomwalker-info-585	208	2	all	all	DT
randomwalker-info-585	208	3	detailed	detailed	JJ
randomwalker-info-585	208	4	in	in	IN
randomwalker-info-585	208	5	Section	Section	NNP
randomwalker-info-585	208	6	4.3	4.3	CD
randomwalker-info-585	208	7	)	)	-RRB-
randomwalker-info-585	208	8	.	.	.
randomwalker-info-585	209	1	Once	once	IN
randomwalker-info-585	209	2	these	these	DT
randomwalker-info-585	209	3	parame-	parame-	NN
randomwalker-info-585	209	4	ters	ter	NNS
randomwalker-info-585	209	5	are	be	VBP
randomwalker-info-585	209	6	set	set	VBN
randomwalker-info-585	209	7	,	,	,
randomwalker-info-585	209	8	a	a	DT
randomwalker-info-585	209	9	game	game	NN
randomwalker-info-585	209	10	runs	run	VBZ
randomwalker-info-585	209	11	for	for	IN
randomwalker-info-585	209	12	several	several	JJ
randomwalker-info-585	209	13	rounds	round	NNS
randomwalker-info-585	209	14	,	,	,
randomwalker-info-585	209	15	and	and	CC
randomwalker-info-585	209	16	keeps	keep	VBZ
randomwalker-info-585	209	17	track	track	NN
randomwalker-info-585	209	18	of	of	IN
randomwalker-info-585	209	19	the	the	DT
randomwalker-info-585	209	20	rewards	reward	NNS
randomwalker-info-585	209	21	earned	earn	VBN
randomwalker-info-585	209	22	by	by	IN
randomwalker-info-585	209	23	each	each	DT
randomwalker-info-585	209	24	miner	miner	NN
randomwalker-info-585	209	25	.	.	.
randomwalker-info-585	210	1	Simulations	simulation	NNS
randomwalker-info-585	210	2	.	.	.
randomwalker-info-585	211	1	A	a	DT
randomwalker-info-585	211	2	simulation	simulation	NN
randomwalker-info-585	211	3	might	may	MD
randomwalker-info-585	211	4	consist	consist	VB
randomwalker-info-585	211	5	of	of	IN
randomwalker-info-585	211	6	a	a	DT
randomwalker-info-585	211	7	single	single	JJ
randomwalker-info-585	211	8	game	game	NN
randomwalker-info-585	211	9	(	(	-LRB-
randomwalker-info-585	211	10	to	to	TO
randomwalker-info-585	211	11	see	see	VB
randomwalker-info-585	211	12	how	how	WRB
randomwalker-info-585	211	13	certain	certain	JJ
randomwalker-info-585	211	14	strategies	strategy	NNS
randomwalker-info-585	211	15	fare	fare	VBP
randomwalker-info-585	211	16	against	against	IN
randomwalker-info-585	211	17	each	each	DT
randomwalker-info-585	211	18	other	other	JJ
randomwalker-info-585	211	19	)	)	-RRB-
randomwalker-info-585	211	20	,	,	,
randomwalker-info-585	211	21	or	or	CC
randomwalker-info-585	211	22	several	several	JJ
randomwalker-info-585	211	23	games	game	NNS
randomwalker-info-585	211	24	with	with	IN
randomwalker-info-585	211	25	parameter	parameter	NN
randomwalker-info-585	211	26	adjustments	adjustment	NNS
randomwalker-info-585	211	27	in	in	IN
randomwalker-info-585	211	28	between	between	IN
randomwalker-info-585	211	29	.	.	.
randomwalker-info-585	212	1	For	for	IN
randomwalker-info-585	212	2	example	example	NN
randomwalker-info-585	212	3	,	,	,
randomwalker-info-585	212	4	in	in	IN
randomwalker-info-585	212	5	order	order	NN
randomwalker-info-585	212	6	to	to	TO
randomwalker-info-585	212	7	model	model	VB
randomwalker-info-585	212	8	miners	miner	NNS
randomwalker-info-585	212	9	who	who	WP
randomwalker-info-585	212	10	learn	learn	VBP
randomwalker-info-585	212	11	over	over	IN
randomwalker-info-585	212	12	time	time	NN
randomwalker-info-585	212	13	,	,	,
randomwalker-info-585	212	14	we	-PRON-	PRP
randomwalker-info-585	212	15	have	have	VBP
randomwalker-info-585	212	16	them	-PRON-	PRP
randomwalker-info-585	212	17	play	play	VB
randomwalker-info-585	212	18	several	several	JJ
randomwalker-info-585	212	19	games	game	NNS
randomwalker-info-585	212	20	and	and	CC
randomwalker-info-585	212	21	decide	decide	VB
randomwalker-info-585	212	22	which	which	WDT
randomwalker-info-585	212	23	strategies	strategy	NNS
randomwalker-info-585	212	24	to	to	TO
randomwalker-info-585	212	25	use	use	VB
randomwalker-info-585	212	26	in	in	IN
randomwalker-info-585	212	27	future	future	JJ
randomwalker-info-585	212	28	games	game	NNS
randomwalker-info-585	212	29	based	base	VBN
randomwalker-info-585	212	30	on	on	IN
randomwalker-info-585	212	31	results	result	NNS
randomwalker-info-585	212	32	of	of	IN
randomwalker-info-585	212	33	past	past	JJ
randomwalker-info-585	212	34	games	game	NNS
randomwalker-info-585	212	35	.	.	.
randomwalker-info-585	213	1	In	in	IN
randomwalker-info-585	213	2	principle	principle	NN
randomwalker-info-585	213	3	,	,	,
randomwalker-info-585	213	4	any	any	DT
randomwalker-info-585	213	5	parameters	parameter	NNS
randomwalker-info-585	213	6	can	can	MD
randomwalker-info-585	213	7	be	be	VB
randomwalker-info-585	213	8	adjusted	adjust	VBN
randomwalker-info-585	213	9	between	between	IN
randomwalker-info-585	213	10	games	game	NNS
randomwalker-info-585	213	11	.	.	.
randomwalker-info-585	214	1	4.2	4.2	CD
randomwalker-info-585	214	2	Strategy	Strategy	NNP
randomwalker-info-585	214	3	exploration	exploration	NN
randomwalker-info-585	214	4	For	for	IN
randomwalker-info-585	214	5	several	several	JJ
randomwalker-info-585	214	6	of	of	IN
randomwalker-info-585	214	7	our	-PRON-	PRP$
randomwalker-info-585	214	8	simulations	simulation	NNS
randomwalker-info-585	214	9	we	-PRON-	PRP
randomwalker-info-585	214	10	want	want	VBP
randomwalker-info-585	214	11	miners	miner	NNS
randomwalker-info-585	214	12	to	to	TO
randomwalker-info-585	214	13	utilize	utilize	VB
randomwalker-info-585	214	14	the	the	DT
randomwalker-info-585	214	15	strategies	strategy	NNS
randomwalker-info-585	214	16	that	that	WDT
randomwalker-info-585	214	17	are	be	VBP
randomwalker-info-585	214	18	doing	do	VBG
randomwalker-info-585	214	19	the	the	DT
randomwalker-info-585	214	20	best	good	JJS
randomwalker-info-585	214	21	,	,	,
randomwalker-info-585	214	22	to	to	TO
randomwalker-info-585	214	23	simulate	simulate	VB
randomwalker-info-585	214	24	how	how	WRB
randomwalker-info-585	214	25	strate-	strate-	FW
randomwalker-info-585	214	26	gic	gic	NNP
randomwalker-info-585	214	27	miners	miner	NNS
randomwalker-info-585	214	28	might	may	MD
randomwalker-info-585	214	29	adapt	adapt	VB
randomwalker-info-585	214	30	over	over	IN
randomwalker-info-585	214	31	time	time	NN
randomwalker-info-585	214	32	.	.	.
randomwalker-info-585	215	1	In	in	IN
randomwalker-info-585	215	2	order	order	NN
randomwalker-info-585	215	3	to	to	TO
randomwalker-info-585	215	4	accomplish	accomplish	VB
randomwalker-info-585	215	5	this	this	DT
randomwalker-info-585	215	6	,	,	,
randomwalker-info-585	215	7	we	-PRON-	PRP
randomwalker-info-585	215	8	run	run	VBP
randomwalker-info-585	215	9	several	several	JJ
randomwalker-info-585	215	10	games	game	NNS
randomwalker-info-585	215	11	,	,	,
randomwalker-info-585	215	12	with	with	IN
randomwalker-info-585	215	13	hundreds	hundred	NNS
randomwalker-info-585	215	14	of	of	IN
randomwalker-info-585	215	15	miners	miner	NNS
randomwalker-info-585	215	16	in	in	IN
randomwalker-info-585	215	17	each	each	DT
randomwalker-info-585	215	18	game	game	NN
randomwalker-info-585	215	19	.	.	.
randomwalker-info-585	216	1	Miners	miner	NNS
randomwalker-info-585	216	2	choose	choose	VBP
randomwalker-info-585	216	3	strategies	strategy	NNS
randomwalker-info-585	216	4	proportional	proportional	JJ
randomwalker-info-585	216	5	to	to	IN
randomwalker-info-585	216	6	how	how	WRB
randomwalker-info-585	216	7	success-	success-	JJ
randomwalker-info-585	216	8	ful	ful	JJ
randomwalker-info-585	216	9	those	those	DT
randomwalker-info-585	216	10	strategies	strategy	NNS
randomwalker-info-585	216	11	have	have	VBP
randomwalker-info-585	216	12	historically	historically	RB
randomwalker-info-585	216	13	done	do	VBN
randomwalker-info-585	216	14	.	.	.
randomwalker-info-585	217	1	Formally	formally	RB
randomwalker-info-585	217	2	,	,	,
randomwalker-info-585	217	3	min-	min-	JJ
randomwalker-info-585	217	4	ers	er	NNS
randomwalker-info-585	217	5	in	in	IN
randomwalker-info-585	217	6	our	-PRON-	PRP$
randomwalker-info-585	217	7	simulator	simulator	NN
randomwalker-info-585	217	8	perform	perform	VBP
randomwalker-info-585	217	9	no	no	DT
randomwalker-info-585	217	10	-	-	HYPH
randomwalker-info-585	217	11	regret	regret	NN
randomwalker-info-585	217	12	learning	learning	NN
randomwalker-info-585	217	13	,	,	,
randomwalker-info-585	217	14	a	a	DT
randomwalker-info-585	217	15	standard	standard	JJ
randomwalker-info-585	217	16	notion	notion	NN
randomwalker-info-585	217	17	of	of	IN
randomwalker-info-585	217	18	learning	learning	NN
randomwalker-info-585	217	19	that	that	WDT
randomwalker-info-585	217	20	is	be	VBZ
randomwalker-info-585	217	21	popular	popular	JJ
randomwalker-info-585	217	22	in	in	IN
randomwalker-info-585	217	23	game	game	NN
randomwalker-info-585	217	24	theoretic	theoretic	JJ
randomwalker-info-585	217	25	con-	con-	NN
randomwalker-info-585	217	26	texts	text	NNS
randomwalker-info-585	217	27	.	.	.
randomwalker-info-585	218	1	This	this	DT
randomwalker-info-585	218	2	is	be	VBZ
randomwalker-info-585	218	3	due	due	JJ
randomwalker-info-585	218	4	to	to	IN
randomwalker-info-585	218	5	the	the	DT
randomwalker-info-585	218	6	fact	fact	NN
randomwalker-info-585	218	7	that	that	IN
randomwalker-info-585	218	8	in	in	IN
randomwalker-info-585	218	9	any	any	DT
randomwalker-info-585	218	10	repeated	repeat	VBN
randomwalker-info-585	218	11	game	game	NN
randomwalker-info-585	218	12	where	where	WRB
randomwalker-info-585	218	13	each	each	DT
randomwalker-info-585	218	14	player	player	NN
randomwalker-info-585	218	15	separately	separately	RB
randomwalker-info-585	218	16	performs	perform	VBZ
randomwalker-info-585	218	17	no	no	DT
randomwalker-info-585	218	18	-	-	HYPH
randomwalker-info-585	218	19	regret	regret	NN
randomwalker-info-585	218	20	learning	learning	NN
randomwalker-info-585	218	21	,	,	,
randomwalker-info-585	218	22	the	the	DT
randomwalker-info-585	218	23	repeated	repeat	VBN
randomwalker-info-585	218	24	play	play	NN
randomwalker-info-585	218	25	converges	converge	NNS
randomwalker-info-585	218	26	to	to	IN
randomwalker-info-585	218	27	a	a	DT
randomwalker-info-585	218	28	coarse	coarse	RB
randomwalker-info-585	218	29	correlated	correlate	VBN
randomwalker-info-585	218	30	equilib-	equilib-	VBN
randomwalker-info-585	218	31	rium	rium	NN
randomwalker-info-585	218	32	[	[	-LRB-
randomwalker-info-585	218	33	1	1	CD
randomwalker-info-585	218	34	,	,	,
randomwalker-info-585	218	35	2	2	CD
randomwalker-info-585	218	36	]	]	-RRB-
randomwalker-info-585	218	37	.	.	.
randomwalker-info-585	219	1	Moreover	moreover	RB
randomwalker-info-585	219	2	,	,	,
randomwalker-info-585	219	3	numerous	numerous	JJ
randomwalker-info-585	219	4	simple	simple	JJ
randomwalker-info-585	219	5	no	no	DT
randomwalker-info-585	219	6	-	-	HYPH
randomwalker-info-585	219	7	regret	regret	NN
randomwalker-info-585	219	8	learning	learning	NN
randomwalker-info-585	219	9	algorithms	algorithm	NNS
randomwalker-info-585	219	10	are	be	VBP
randomwalker-info-585	219	11	known	know	VBN
randomwalker-info-585	219	12	that	that	WDT
randomwalker-info-585	219	13	converge	converge	NN
randomwalker-info-585	219	14	quickly	quickly	RB
randomwalker-info-585	219	15	(	(	-LRB-
randomwalker-info-585	219	16	i.e.	i.e.	FW
randomwalker-info-585	220	1	in	in	IN
randomwalker-info-585	220	2	a	a	DT
randomwalker-info-585	220	3	num-	num-	JJ
randomwalker-info-585	220	4	ber	ber	NN
randomwalker-info-585	220	5	of	of	IN
randomwalker-info-585	220	6	rounds	round	NNS
randomwalker-info-585	220	7	sublinear	sublinear	JJ
randomwalker-info-585	220	8	in	in	IN
randomwalker-info-585	220	9	the	the	DT
randomwalker-info-585	220	10	number	number	NN
randomwalker-info-585	220	11	of	of	IN
randomwalker-info-585	220	12	possible	possible	JJ
randomwalker-info-585	220	13	strate-	strate-	NN
randomwalker-info-585	220	14	gies	gy	NNS
randomwalker-info-585	220	15	)	)	-RRB-
randomwalker-info-585	220	16	[	[	-LRB-
randomwalker-info-585	220	17	5	5	CD
randomwalker-info-585	220	18	,	,	,
randomwalker-info-585	220	19	6	6	CD
randomwalker-info-585	220	20	,	,	,
randomwalker-info-585	220	21	4	4	CD
randomwalker-info-585	220	22	,	,	,
randomwalker-info-585	220	23	15	15	CD
randomwalker-info-585	220	24	]	]	-RRB-
randomwalker-info-585	220	25	.	.	.
randomwalker-info-585	221	1	If	if	IN
randomwalker-info-585	221	2	a	a	DT
randomwalker-info-585	221	3	miner	miner	NN
randomwalker-info-585	221	4	has	have	VBZ
randomwalker-info-585	221	5	no	no	DT
randomwalker-info-585	221	6	regret	regret	NN
randomwalker-info-585	221	7	,	,	,
randomwalker-info-585	221	8	their	-PRON-	PRP$
randomwalker-info-585	221	9	total	total	JJ
randomwalker-info-585	221	10	re-	re-	RB
randomwalker-info-585	221	11	ward	ward	RB
randomwalker-info-585	221	12	across	across	IN
randomwalker-info-585	221	13	all	all	DT
randomwalker-info-585	221	14	of	of	IN
randomwalker-info-585	221	15	time	time	NN
randomwalker-info-585	221	16	is	be	VBZ
randomwalker-info-585	221	17	at	at	IN
randomwalker-info-585	221	18	least	least	JJS
randomwalker-info-585	221	19	as	as	RB
randomwalker-info-585	221	20	good	good	JJ
randomwalker-info-585	221	21	as	as	IN
randomwalker-info-585	221	22	had	have	VBD
randomwalker-info-585	221	23	they	-PRON-	PRP
randomwalker-info-585	221	24	instead	instead	RB
randomwalker-info-585	221	25	picked	pick	VBD
randomwalker-info-585	221	26	“	"	``
randomwalker-info-585	221	27	the	the	DT
randomwalker-info-585	221	28	best	good	JJS
randomwalker-info-585	221	29	”	"	''
randomwalker-info-585	221	30	strategy	strategy	NN
randomwalker-info-585	221	31	and	and	CC
randomwalker-info-585	221	32	used	use	VBD
randomwalker-info-585	221	33	it	-PRON-	PRP
randomwalker-info-585	221	34	in	in	IN
randomwalker-info-585	221	35	every	every	DT
randomwalker-info-585	221	36	game	game	NN
randomwalker-info-585	221	37	.	.	.
randomwalker-info-585	222	1	Sim-	Sim-	NNP
randomwalker-info-585	222	2	ilarly	ilarly	RB
randomwalker-info-585	222	3	,	,	,
randomwalker-info-585	222	4	a	a	DT
randomwalker-info-585	222	5	coarse	coarse	RB
randomwalker-info-585	222	6	correlated	correlate	VBN
randomwalker-info-585	222	7	equilibrium	equilibrium	NN
randomwalker-info-585	222	8	is	be	VBZ
randomwalker-info-585	222	9	a	a	DT
randomwalker-info-585	222	10	joint	joint	JJ
randomwalker-info-585	222	11	distribution	distribution	NN
randomwalker-info-585	222	12	over	over	IN
randomwalker-info-585	222	13	strategy	strategy	NN
randomwalker-info-585	222	14	profiles	profile	NNS
randomwalker-info-585	222	15	such	such	JJ
randomwalker-info-585	222	16	that	that	IN
randomwalker-info-585	222	17	every	every	DT
randomwalker-info-585	222	18	miner	miner	NN
randomwalker-info-585	222	19	gets	get	VBZ
randomwalker-info-585	222	20	more	more	RBR
randomwalker-info-585	222	21	ex-	ex-	DT
randomwalker-info-585	222	22	pected	pecte	VBN
randomwalker-info-585	222	23	payoff	payoff	NN
randomwalker-info-585	222	24	by	by	IN
randomwalker-info-585	222	25	following	follow	VBG
randomwalker-info-585	222	26	the	the	DT
randomwalker-info-585	222	27	equilibrium	equilibrium	NN
randomwalker-info-585	222	28	than	than	IN
randomwalker-info-585	222	29	deviating	deviate	VBG
randomwalker-info-585	222	30	to	to	IN
randomwalker-info-585	222	31	any	any	DT
randomwalker-info-585	222	32	possible	possible	JJ
randomwalker-info-585	222	33	strategy	strategy	NN
randomwalker-info-585	222	34	.	.	.
randomwalker-info-585	223	1	These	these	DT
randomwalker-info-585	223	2	learning	learn	VBG
randomwalker-info-585	223	3	algorithms	algorithm	NNS
randomwalker-info-585	223	4	all	all	DT
randomwalker-info-585	223	5	maintain	maintain	VBP
randomwalker-info-585	223	6	a	a	DT
randomwalker-info-585	223	7	weight	weight	NN
randomwalker-info-585	223	8	for	for	IN
randomwalker-info-585	223	9	every	every	DT
randomwalker-info-585	223	10	strategy	strategy	NN
randomwalker-info-585	223	11	,	,	,
randomwalker-info-585	223	12	and	and	CC
randomwalker-info-585	223	13	adjust	adjust	VB
randomwalker-info-585	223	14	the	the	DT
randomwalker-info-585	223	15	weights	weight	NNS
randomwalker-info-585	223	16	of	of	IN
randomwalker-info-585	223	17	the	the	DT
randomwalker-info-585	223	18	strategies	strategy	NNS
randomwalker-info-585	223	19	from	from	IN
randomwalker-info-585	223	20	game	game	NN
randomwalker-info-585	223	21	to	to	IN
randomwalker-info-585	223	22	game	game	NN
randomwalker-info-585	223	23	depending	depend	VBG
randomwalker-info-585	223	24	on	on	IN
randomwalker-info-585	223	25	how	how	WRB
randomwalker-info-585	223	26	well	well	RB
randomwalker-info-585	223	27	they	-PRON-	PRP
randomwalker-info-585	223	28	’re	be	VBZ
randomwalker-info-585	223	29	doing	do	VBG
randomwalker-info-585	223	30	.	.	.
randomwalker-info-585	224	1	Our	-PRON-	PRP$
randomwalker-info-585	224	2	simulator	simulator	NN
randomwalker-info-585	224	3	offers	offer	VBZ
randomwalker-info-585	224	4	two	two	CD
randomwalker-info-585	224	5	alternatives	alternative	NNS
randomwalker-info-585	224	6	for	for	IN
randomwalker-info-585	224	7	these	these	DT
randomwalker-info-585	224	8	update	update	NN
randomwalker-info-585	224	9	rules	rule	NNS
randomwalker-info-585	224	10	.	.	.
randomwalker-info-585	225	1	The	the	DT
randomwalker-info-585	225	2	first	first	JJ
randomwalker-info-585	225	3	al-	al-	JJ
randomwalker-info-585	225	4	ternative	ternative	NN
randomwalker-info-585	225	5	is	be	VBZ
randomwalker-info-585	225	6	an	an	DT
randomwalker-info-585	225	7	exact	exact	JJ
randomwalker-info-585	225	8	implementation	implementation	NN
randomwalker-info-585	225	9	of	of	IN
randomwalker-info-585	225	10	the	the	DT
randomwalker-info-585	225	11	EXP3	EXP3	NNP
randomwalker-info-585	225	12	algorithm	algorithm	NN
randomwalker-info-585	225	13	for	for	IN
randomwalker-info-585	225	14	learning	learn	VBG
randomwalker-info-585	225	15	with	with	IN
randomwalker-info-585	225	16	adversarial	adversarial	JJ
randomwalker-info-585	225	17	bandits	bandit	NNS
randomwalker-info-585	225	18	[	[	-LRB-
randomwalker-info-585	225	19	5	5	CD
randomwalker-info-585	225	20	,	,	,
randomwalker-info-585	225	21	6	6	CD
randomwalker-info-585	225	22	]	]	-RRB-
randomwalker-info-585	225	23	.	.	.
randomwalker-info-585	226	1	This	this	DT
randomwalker-info-585	226	2	update	update	NN
randomwalker-info-585	226	3	rule	rule	NN
randomwalker-info-585	226	4	provides	provide	VBZ
randomwalker-info-585	226	5	a	a	DT
randomwalker-info-585	226	6	theoretical	theoretical	JJ
randomwalker-info-585	226	7	guarantee	guarantee	NN
randomwalker-info-585	226	8	on	on	IN
randomwalker-info-585	226	9	the	the	DT
randomwalker-info-585	226	10	regret	regret	NN
randomwalker-info-585	226	11	of	of	IN
randomwalker-info-585	226	12	each	each	DT
randomwalker-info-585	226	13	miner	miner	NN
randomwalker-info-585	226	14	as	as	IN
randomwalker-info-585	226	15	a	a	DT
randomwalker-info-585	226	16	function	function	NN
randomwalker-info-585	226	17	of	of	IN
randomwalker-info-585	226	18	the	the	DT
randomwalker-info-585	226	19	number	number	NN
randomwalker-info-585	226	20	of	of	IN
randomwalker-info-585	226	21	games	game	NNS
randomwalker-info-585	226	22	played	play	VBN
randomwalker-info-585	226	23	and	and	CC
randomwalker-info-585	226	24	a	a	DT
randomwalker-info-585	226	25	tunable	tunable	JJ
randomwalker-info-585	226	26	parameter	parameter	NN
randomwalker-info-585	226	27	in	in	IN
randomwalker-info-585	226	28	the	the	DT
randomwalker-info-585	226	29	update	update	NN
randomwalker-info-585	226	30	rule	rule	NN
randomwalker-info-585	226	31	,	,	,
randomwalker-info-585	226	32	�	�	NNP
randomwalker-info-585	226	33	.	.	.
randomwalker-info-585	227	1	The	the	DT
randomwalker-info-585	227	2	second	second	JJ
randomwalker-info-585	227	3	alternative	alternative	NN
randomwalker-info-585	227	4	is	be	VBZ
randomwalker-info-585	227	5	based	base	VBN
randomwalker-info-585	227	6	on	on	IN
randomwalker-info-585	227	7	the	the	DT
randomwalker-info-585	227	8	multiplicative	multiplicative	JJ
randomwalker-info-585	227	9	weights	weight	NNS
randomwalker-info-585	227	10	update	update	NN
randomwalker-info-585	227	11	rule	rule	NN
randomwalker-info-585	227	12	(	(	-LRB-
randomwalker-info-585	227	13	MWU	MWU	NNP
randomwalker-info-585	227	14	)	)	-RRB-
randomwalker-info-585	227	15	for	for	IN
randomwalker-info-585	227	16	learning	learn	VBG
randomwalker-info-585	227	17	with	with	IN
randomwalker-info-585	227	18	experts	expert	NNS
randomwalker-info-585	227	19	[	[	-LRB-
randomwalker-info-585	227	20	4	4	CD
randomwalker-info-585	227	21	,	,	,
randomwalker-info-585	227	22	15	15	CD
randomwalker-info-585	227	23	]	]	-RRB-
randomwalker-info-585	227	24	.	.	.
randomwalker-info-585	228	1	We	-PRON-	PRP
randomwalker-info-585	228	2	find	find	VBP
randomwalker-info-585	228	3	that	that	IN
randomwalker-info-585	228	4	MWU	MWU	NNP
randomwalker-info-585	228	5	is	be	VBZ
randomwalker-info-585	228	6	com-	com-	NN
randomwalker-info-585	228	7	putationally	putationally	RB
randomwalker-info-585	228	8	expensive	expensive	JJ
randomwalker-info-585	228	9	,	,	,
randomwalker-info-585	228	10	so	so	RB
randomwalker-info-585	228	11	we	-PRON-	PRP
randomwalker-info-585	228	12	use	use	VBP
randomwalker-info-585	228	13	a	a	DT
randomwalker-info-585	228	14	less	less	RBR
randomwalker-info-585	228	15	expensive	expensive	JJ
randomwalker-info-585	228	16	proxy	proxy	NN
randomwalker-info-585	228	17	in-	in-	NN
randomwalker-info-585	228	18	stead	stead	NN
randomwalker-info-585	228	19	.	.	.
randomwalker-info-585	229	1	That	that	DT
randomwalker-info-585	229	2	means	mean	VBZ
randomwalker-info-585	229	3	there	there	EX
randomwalker-info-585	229	4	is	be	VBZ
randomwalker-info-585	229	5	no	no	DT
randomwalker-info-585	229	6	theoretical	theoretical	JJ
randomwalker-info-585	229	7	guarantee	guarantee	NN
randomwalker-info-585	229	8	on	on	IN
randomwalker-info-585	229	9	the	the	DT
randomwalker-info-585	229	10	regret	regret	NN
randomwalker-info-585	229	11	bounds	bound	NNS
randomwalker-info-585	229	12	.	.	.
randomwalker-info-585	230	1	But	but	CC
randomwalker-info-585	230	2	in	in	IN
randomwalker-info-585	230	3	practice	practice	NN
randomwalker-info-585	230	4	this	this	DT
randomwalker-info-585	230	5	update	update	NN
randomwalker-info-585	230	6	rule	rule	NN
randomwalker-info-585	230	7	is	be	VBZ
randomwalker-info-585	230	8	signifi-	signifi-	JJ
randomwalker-info-585	230	9	cantly	cantly	RB
randomwalker-info-585	230	10	faster	fast	RBR
randomwalker-info-585	230	11	and	and	CC
randomwalker-info-585	230	12	does	do	VBZ
randomwalker-info-585	230	13	converge	converge	VB
randomwalker-info-585	230	14	quickly	quickly	RB
randomwalker-info-585	230	15	to	to	IN
randomwalker-info-585	230	16	coarse	coarse	RB
randomwalker-info-585	230	17	correlated	correlate	VBN
randomwalker-info-585	230	18	equilibrium	equilibrium	NN
randomwalker-info-585	230	19	.	.	.
randomwalker-info-585	231	1	For	for	IN
randomwalker-info-585	231	2	a	a	DT
randomwalker-info-585	231	3	further	further	JJ
randomwalker-info-585	231	4	discussion	discussion	NN
randomwalker-info-585	231	5	of	of	IN
randomwalker-info-585	231	6	these	these	DT
randomwalker-info-585	231	7	update	update	NN
randomwalker-info-585	231	8	rules	rule	NNS
randomwalker-info-585	231	9	,	,	,
randomwalker-info-585	231	10	see	see	VB
randomwalker-info-585	231	11	Appendix	Appendix	NNP
randomwalker-info-585	231	12	B.	B.	NNP
randomwalker-info-585	232	1	All	all	DT
randomwalker-info-585	232	2	of	of	IN
randomwalker-info-585	232	3	the	the	DT
randomwalker-info-585	232	4	figures	figure	NNS
randomwalker-info-585	232	5	included	include	VBN
randomwalker-info-585	232	6	in	in	IN
randomwalker-info-585	232	7	this	this	DT
randomwalker-info-585	232	8	paper	paper	NN
randomwalker-info-585	232	9	were	be	VBD
randomwalker-info-585	232	10	generated	generate	VBN
randomwalker-info-585	232	11	from	from	IN
randomwalker-info-585	232	12	simulations	simulation	NNS
randomwalker-info-585	232	13	using	use	VBG
randomwalker-info-585	232	14	EXP3	EXP3	NNP
randomwalker-info-585	232	15	,	,	,
randomwalker-info-585	232	16	so	so	RB
randomwalker-info-585	232	17	they	-PRON-	PRP
randomwalker-info-585	232	18	come	come	VBP
randomwalker-info-585	232	19	with	with	IN
randomwalker-info-585	232	20	a	a	DT
randomwalker-info-585	232	21	theo-	theo-	JJ
randomwalker-info-585	232	22	retical	retical	JJ
randomwalker-info-585	232	23	guarantee	guarantee	NN
randomwalker-info-585	232	24	that	that	IN
randomwalker-info-585	232	25	all	all	DT
randomwalker-info-585	232	26	miners	miner	NNS
randomwalker-info-585	232	27	in	in	IN
randomwalker-info-585	232	28	the	the	DT
randomwalker-info-585	232	29	simulation	simulation	NN
randomwalker-info-585	232	30	have	have	VBP
randomwalker-info-585	232	31	no	no	DT
randomwalker-info-585	232	32	regret	regret	NN
randomwalker-info-585	232	33	.	.	.
randomwalker-info-585	233	1	4.3	4.3	LS
randomwalker-info-585	233	2	Versatility	versatility	NN
randomwalker-info-585	233	3	Our	-PRON-	PRP$
randomwalker-info-585	233	4	simulator	simulator	NN
randomwalker-info-585	233	5	has	have	VBZ
randomwalker-info-585	233	6	many	many	JJ
randomwalker-info-585	233	7	configurable	configurable	JJ
randomwalker-info-585	233	8	parameters	parameter	NNS
randomwalker-info-585	233	9	:	:	:
randomwalker-info-585	233	10	Strategies	strategy	NNS
randomwalker-info-585	233	11	.	.	.
randomwalker-info-585	234	1	Just	just	RB
randomwalker-info-585	234	2	to	to	TO
randomwalker-info-585	234	3	reiterate	reiterate	VB
randomwalker-info-585	234	4	:	:	:
randomwalker-info-585	234	5	every	every	DT
randomwalker-info-585	234	6	miner	miner	NN
randomwalker-info-585	234	7	in	in	IN
randomwalker-info-585	234	8	our	-PRON-	PRP$
randomwalker-info-585	234	9	simulator	simulator	NN
randomwalker-info-585	234	10	is	be	VBZ
randomwalker-info-585	234	11	assigned	assign	VBN
randomwalker-info-585	234	12	a	a	DT
randomwalker-info-585	234	13	time	time	NN
randomwalker-info-585	234	14	-	-	HYPH
randomwalker-info-585	234	15	driven	drive	VBN
randomwalker-info-585	234	16	strategy	strategy	NN
randomwalker-info-585	234	17	that	that	WDT
randomwalker-info-585	234	18	chooses	choose	VBZ
randomwalker-info-585	234	19	which	which	WDT
randomwalker-info-585	234	20	block	block	NN
randomwalker-info-585	234	21	to	to	TO
randomwalker-info-585	234	22	extend	extend	VB
randomwalker-info-585	234	23	,	,	,
randomwalker-info-585	234	24	how	how	WRB
randomwalker-info-585	234	25	many	many	JJ
randomwalker-info-585	234	26	transactions	transaction	NNS
randomwalker-info-585	234	27	to	to	TO
randomwalker-info-585	234	28	include	include	VB
randomwalker-info-585	234	29	,	,	,
randomwalker-info-585	234	30	and	and	CC
randomwalker-info-585	234	31	whether	whether	IN
randomwalker-info-585	234	32	to	to	TO
randomwalker-info-585	234	33	publish	publish	VB
randomwalker-info-585	234	34	any	any	DT
randomwalker-info-585	234	35	found	find	VBN
randomwalker-info-585	234	36	blocks	block	NNS
randomwalker-info-585	234	37	.	.	.
randomwalker-info-585	235	1	Any	any	DT
randomwalker-info-585	235	2	strategy	strategy	NN
randomwalker-info-585	235	3	that	that	WDT
randomwalker-info-585	235	4	fits	fit	VBZ
randomwalker-info-585	235	5	this	this	DT
randomwalker-info-585	235	6	framework	framework	NN
randomwalker-info-585	235	7	can	can	MD
randomwalker-info-585	235	8	be	be	VB
randomwalker-info-585	235	9	implemented	implement	VBN
randomwalker-info-585	235	10	in	in	IN
randomwalker-info-585	235	11	the	the	DT
randomwalker-info-585	235	12	simulator	simulator	NN
randomwalker-info-585	235	13	.	.	.
randomwalker-info-585	236	1	To	to	TO
randomwalker-info-585	236	2	design	design	VB
randomwalker-info-585	236	3	a	a	DT
randomwalker-info-585	236	4	new	new	JJ
randomwalker-info-585	236	5	strategy	strategy	NN
randomwalker-info-585	236	6	,	,	,
randomwalker-info-585	236	7	a	a	DT
randomwalker-info-585	236	8	user	user	NN
randomwalker-info-585	236	9	would	would	MD
randomwalker-info-585	236	10	create	create	VB
randomwalker-info-585	236	11	a	a	DT
randomwalker-info-585	236	12	new	new	JJ
randomwalker-info-585	236	13	function	function	NN
randomwalker-info-585	236	14	that	that	WDT
randomwalker-info-585	236	15	takes	take	VBZ
randomwalker-info-585	236	16	as	as	IN
randomwalker-info-585	236	17	input	input	NN
randomwalker-info-585	236	18	the	the	DT
randomwalker-info-585	236	19	current	current	JJ
randomwalker-info-585	236	20	public	public	JJ
randomwalker-info-585	236	21	state	state	NN
randomwalker-info-585	236	22	of	of	IN
randomwalker-info-585	236	23	Bitcoin	Bitcoin	NNP
randomwalker-info-585	236	24	network	network	NN
randomwalker-info-585	236	25	(	(	-LRB-
randomwalker-info-585	236	26	the	the	DT
randomwalker-info-585	236	27	blockchain	blockchain	JJ
randomwalker-info-585	236	28	and	and	CC
randomwalker-info-585	236	29	available	available	JJ
randomwalker-info-585	236	30	transaction	transaction	NN
randomwalker-info-585	236	31	fees	fee	NNS
randomwalker-info-585	236	32	)	)	-RRB-
randomwalker-info-585	236	33	,	,	,
randomwalker-info-585	236	34	and	and	CC
randomwalker-info-585	236	35	the	the	DT
randomwalker-info-585	236	36	miner	miner	NN
randomwalker-info-585	236	37	who	who	WP
randomwalker-info-585	236	38	is	be	VBZ
randomwalker-info-585	236	39	using	use	VBG
randomwalker-info-585	236	40	the	the	DT
randomwalker-info-585	236	41	strategy	strategy	NN
randomwalker-info-585	236	42	.	.	.
randomwalker-info-585	237	1	The	the	DT
randomwalker-info-585	237	2	function	function	NN
randomwalker-info-585	237	3	would	would	MD
randomwalker-info-585	237	4	then	then	RB
randomwalker-info-585	237	5	use	use	VB
randomwalker-info-585	237	6	this	this	DT
randomwalker-info-585	237	7	information	information	NN
randomwalker-info-585	237	8	to	to	TO
randomwalker-info-585	237	9	determine	determine	VB
randomwalker-info-585	237	10	which	which	WDT
randomwalker-info-585	237	11	block	block	NN
randomwalker-info-585	237	12	to	to	TO
randomwalker-info-585	237	13	extend	extend	VB
randomwalker-info-585	237	14	,	,	,
randomwalker-info-585	237	15	and	and	CC
randomwalker-info-585	237	16	how	how	WRB
randomwalker-info-585	237	17	many	many	JJ
randomwalker-info-585	237	18	of	of	IN
randomwalker-info-585	237	19	the	the	DT
randomwalker-info-585	237	20	transaction	transaction	NN
randomwalker-info-585	237	21	fees	fee	NNS
randomwalker-info-585	237	22	to	to	TO
randomwalker-info-585	237	23	include	include	VB
randomwalker-info-585	237	24	in	in	IN
randomwalker-info-585	237	25	the	the	DT
randomwalker-info-585	237	26	next	next	JJ
randomwalker-info-585	237	27	block	block	NN
randomwalker-info-585	237	28	.	.	.
randomwalker-info-585	238	1	Finally	finally	RB
randomwalker-info-585	238	2	,	,	,
randomwalker-info-585	238	3	the	the	DT
randomwalker-info-585	238	4	user	user	NN
randomwalker-info-585	238	5	would	would	MD
randomwalker-info-585	238	6	go	go	VB
randomwalker-info-585	238	7	to	to	IN
randomwalker-info-585	238	8	the	the	DT
randomwalker-info-585	238	9	publication	publication	NN
randomwalker-info-585	238	10	rules	rule	NNS
randomwalker-info-585	238	11	and	and	CC
randomwalker-info-585	238	12	add	add	VB
randomwalker-info-585	238	13	a	a	DT
randomwalker-info-585	238	14	rule	rule	NN
randomwalker-info-585	238	15	for	for	IN
randomwalker-info-585	238	16	how	how	WRB
randomwalker-info-585	238	17	the	the	DT
randomwalker-info-585	238	18	strategy	strategy	NN
randomwalker-info-585	238	19	should	should	MD
randomwalker-info-585	238	20	choose	choose	VB
randomwalker-info-585	238	21	whether	whether	IN
randomwalker-info-585	238	22	or	or	CC
randomwalker-info-585	238	23	not	not	RB
randomwalker-info-585	238	24	to	to	TO
randomwalker-info-585	238	25	publish	publish	VB
randomwalker-info-585	238	26	any	any	DT
randomwalker-info-585	238	27	found	find	VBN
randomwalker-info-585	238	28	blocks	block	NNS
randomwalker-info-585	238	29	.	.	.
randomwalker-info-585	239	1	Hash	Hash	NNP
randomwalker-info-585	239	2	Power	Power	NNP
randomwalker-info-585	239	3	.	.	.
randomwalker-info-585	240	1	Every	every	DT
randomwalker-info-585	240	2	miner	miner	NN
randomwalker-info-585	240	3	m	m	NN
randomwalker-info-585	240	4	is	be	VBZ
randomwalker-info-585	240	5	assigned	assign	VBN
randomwalker-info-585	240	6	a	a	DT
randomwalker-info-585	240	7	hash	hash	NN
randomwalker-info-585	240	8	power	power	NN
randomwalker-info-585	240	9	αm	αm	XX
randomwalker-info-585	240	10	.	.	.
randomwalker-info-585	241	1	Any	any	DT
randomwalker-info-585	241	2	number	number	NN
randomwalker-info-585	241	3	of	of	IN
randomwalker-info-585	241	4	miners	miner	NNS
randomwalker-info-585	241	5	,	,	,
randomwalker-info-585	241	6	and	and	CC
randomwalker-info-585	241	7	any	any	DT
randomwalker-info-585	241	8	αm	αm	XX
randomwalker-info-585	241	9	such	such	JJ
randomwalker-info-585	241	10	that	that	IN
randomwalker-info-585	241	11	∑	∑	.
randomwalker-info-585	241	12	m	m	NNP
randomwalker-info-585	241	13	αm	αm	XX
randomwalker-info-585	241	14	=	=	SYM
randomwalker-info-585	241	15	1	1	CD
randomwalker-info-585	241	16	can	can	MD
randomwalker-info-585	241	17	be	be	VB
randomwalker-info-585	241	18	supported	support	VBN
randomwalker-info-585	241	19	.	.	.
randomwalker-info-585	242	1	Round	round	JJ
randomwalker-info-585	242	2	Duration	Duration	NNP
randomwalker-info-585	242	3	.	.	.
randomwalker-info-585	243	1	The	the	DT
randomwalker-info-585	243	2	size	size	NN
randomwalker-info-585	243	3	of	of	IN
randomwalker-info-585	243	4	a	a	DT
randomwalker-info-585	243	5	round	round	NN
randomwalker-info-585	243	6	can	can	MD
randomwalker-info-585	243	7	be	be	VB
randomwalker-info-585	243	8	set	set	VBN
randomwalker-info-585	243	9	so	so	IN
randomwalker-info-585	243	10	the	the	DT
randomwalker-info-585	243	11	network	network	NN
randomwalker-info-585	243	12	finds	find	VBZ
randomwalker-info-585	243	13	a	a	DT
randomwalker-info-585	243	14	block	block	NN
randomwalker-info-585	243	15	every	every	DT
randomwalker-info-585	243	16	r	r	NN
randomwalker-info-585	243	17	rounds	round	NNS
randomwalker-info-585	243	18	in	in	IN
randomwalker-info-585	243	19	expectation	expectation	NN
randomwalker-info-585	243	20	,	,	,
randomwalker-info-585	243	21	for	for	IN
randomwalker-info-585	243	22	any	any	DT
randomwalker-info-585	243	23	r	r	NN
randomwalker-info-585	243	24	>	>	NN
randomwalker-info-585	243	25	0	0	CD
randomwalker-info-585	243	26	.	.	.
randomwalker-info-585	244	1	Rewards	reward	NNS
randomwalker-info-585	244	2	.	.	.
randomwalker-info-585	245	1	At	at	IN
randomwalker-info-585	245	2	the	the	DT
randomwalker-info-585	245	3	end	end	NN
randomwalker-info-585	245	4	of	of	IN
randomwalker-info-585	245	5	each	each	DT
randomwalker-info-585	245	6	game	game	NN
randomwalker-info-585	245	7	,	,	,
randomwalker-info-585	245	8	miners	miner	NNS
randomwalker-info-585	245	9	are	be	VBP
randomwalker-info-585	245	10	rewarded	reward	VBN
randomwalker-info-585	245	11	based	base	VBN
randomwalker-info-585	245	12	on	on	IN
randomwalker-info-585	245	13	their	-PRON-	PRP$
randomwalker-info-585	245	14	blocks	block	NNS
randomwalker-info-585	245	15	within	within	IN
randomwalker-info-585	245	16	the	the	DT
randomwalker-info-585	245	17	longest	long	JJS
randomwalker-info-585	245	18	chain	chain	NN
randomwalker-info-585	245	19	.	.	.
randomwalker-info-585	246	1	The	the	DT
randomwalker-info-585	246	2	reward	reward	NN
randomwalker-info-585	246	3	they	-PRON-	PRP
randomwalker-info-585	246	4	receive	receive	VBP
randomwalker-info-585	246	5	is	be	VBZ
randomwalker-info-585	246	6	b	b	NN
randomwalker-info-585	246	7	per	per	IN
randomwalker-info-585	246	8	block	block	NN
randomwalker-info-585	246	9	(	(	-LRB-
randomwalker-info-585	246	10	fixed	fix	VBN
randomwalker-info-585	246	11	reward	reward	NN
randomwalker-info-585	246	12	)	)	-RRB-
randomwalker-info-585	246	13	,	,	,
randomwalker-info-585	246	14	plus	plus	CC
randomwalker-info-585	246	15	any	any	DT
randomwalker-info-585	246	16	trans-	trans-	JJ
randomwalker-info-585	246	17	action	action	NN
randomwalker-info-585	246	18	fees	fee	NNS
randomwalker-info-585	246	19	.	.	.
randomwalker-info-585	247	1	a	a	DT
randomwalker-info-585	247	2	transaction	transaction	NN
randomwalker-info-585	247	3	fees	fee	NNS
randomwalker-info-585	247	4	accrue	accrue	VBP
randomwalker-info-585	247	5	in	in	IN
randomwalker-info-585	247	6	the	the	DT
randomwalker-info-585	247	7	system	system	NN
randomwalker-info-585	247	8	every	every	DT
randomwalker-info-585	247	9	round	round	NN
randomwalker-info-585	247	10	.	.	.
randomwalker-info-585	248	1	Both	both	DT
randomwalker-info-585	248	2	of	of	IN
randomwalker-info-585	248	3	these	these	DT
randomwalker-info-585	248	4	parameters	parameter	NNS
randomwalker-info-585	248	5	are	be	VBP
randomwalker-info-585	248	6	configurable	configurable	JJ
randomwalker-info-585	248	7	.	.	.
randomwalker-info-585	249	1	Costs	cost	NNS
randomwalker-info-585	249	2	.	.	.
randomwalker-info-585	250	1	There	there	EX
randomwalker-info-585	250	2	is	be	VBZ
randomwalker-info-585	250	3	a	a	DT
randomwalker-info-585	250	4	configurable	configurable	JJ
randomwalker-info-585	250	5	parameter	parameter	NN
randomwalker-info-585	250	6	cm	cm	VBZ
randomwalker-info-585	250	7	for	for	IN
randomwalker-info-585	250	8	every	every	DT
randomwalker-info-585	250	9	miner	miner	NN
randomwalker-info-585	250	10	m	m	NN
randomwalker-info-585	250	11	that	that	WDT
randomwalker-info-585	250	12	denotes	denote	VBZ
randomwalker-info-585	250	13	the	the	DT
randomwalker-info-585	250	14	cost	cost	NN
randomwalker-info-585	250	15	(	(	-LRB-
randomwalker-info-585	250	16	i.e.	i.e.	FW
randomwalker-info-585	251	1	in	in	IN
randomwalker-info-585	251	2	electricity	electricity	NN
randomwalker-info-585	251	3	)	)	-RRB-
randomwalker-info-585	251	4	for	for	IN
randomwalker-info-585	251	5	miner	miner	NN
randomwalker-info-585	251	6	m	m	NNP
randomwalker-info-585	251	7	to	to	IN
randomwalker-info-585	251	8	mine	-PRON-	PRP
randomwalker-info-585	251	9	.	.	.
randomwalker-info-585	252	1	For	for	IN
randomwalker-info-585	252	2	our	-PRON-	PRP$
randomwalker-info-585	252	3	simulations	simulation	NNS
randomwalker-info-585	252	4	,	,	,
randomwalker-info-585	252	5	we	-PRON-	PRP
randomwalker-info-585	252	6	always	always	RB
randomwalker-info-585	252	7	set	set	VBP
randomwalker-info-585	252	8	cm	cm	NNS
randomwalker-info-585	252	9	=	=	NFP
randomwalker-info-585	252	10	0	0	NFP
randomwalker-info-585	252	11	because	because	IN
randomwalker-info-585	252	12	we	-PRON-	PRP
randomwalker-info-585	252	13	are	be	VBP
randomwalker-info-585	252	14	n’t	not	RB
randomwalker-info-585	252	15	looking	look	VBG
randomwalker-info-585	252	16	at	at	IN
randomwalker-info-585	252	17	this	this	DT
randomwalker-info-585	252	18	aspect	aspect	NN
randomwalker-info-585	252	19	of	of	IN
randomwalker-info-585	252	20	mining	mining	NN
randomwalker-info-585	252	21	.	.	.
randomwalker-info-585	253	1	Latency	latency	NN
randomwalker-info-585	253	2	.	.	.
randomwalker-info-585	254	1	If	if	IN
randomwalker-info-585	254	2	desired	desire	VBN
randomwalker-info-585	254	3	,	,	,
randomwalker-info-585	254	4	latency	latency	NN
randomwalker-info-585	254	5	can	can	MD
randomwalker-info-585	254	6	be	be	VB
randomwalker-info-585	254	7	introduced	introduce	VBN
randomwalker-info-585	254	8	to	to	IN
randomwalker-info-585	254	9	the	the	DT
randomwalker-info-585	254	10	simu-	simu-	NN
randomwalker-info-585	254	11	lation	lation	NN
randomwalker-info-585	254	12	.	.	.
randomwalker-info-585	255	1	There	there	EX
randomwalker-info-585	255	2	is	be	VBZ
randomwalker-info-585	255	3	a	a	DT
randomwalker-info-585	255	4	configurable	configurable	JJ
randomwalker-info-585	255	5	parameter	parameter	NN
randomwalker-info-585	255	6	λ	λ	NN
randomwalker-info-585	255	7	such	such	JJ
randomwalker-info-585	255	8	that	that	IN
randomwalker-info-585	255	9	when	when	WRB
randomwalker-info-585	255	10	blocks	block	NNS
randomwalker-info-585	255	11	are	be	VBP
randomwalker-info-585	255	12	published	publish	VBN
randomwalker-info-585	255	13	,	,	,
randomwalker-info-585	255	14	it	-PRON-	PRP
randomwalker-info-585	255	15	takes	take	VBZ
randomwalker-info-585	255	16	λ	λ	PRP
randomwalker-info-585	255	17	rounds	round	NNS
randomwalker-info-585	255	18	before	before	IN
randomwalker-info-585	255	19	other	other	JJ
randomwalker-info-585	255	20	miners	miner	NNS
randomwalker-info-585	255	21	are	be	VBP
randomwalker-info-585	255	22	aware	aware	JJ
randomwalker-info-585	255	23	of	of	IN
randomwalker-info-585	255	24	this	this	DT
randomwalker-info-585	255	25	blocks	blocks	NNP
randomwalker-info-585	255	26	existence	existence	NN
randomwalker-info-585	255	27	.	.	.
randomwalker-info-585	256	1	Latency	latency	NN
randomwalker-info-585	256	2	in	in	IN
randomwalker-info-585	256	3	hearing	hear	VBG
randomwalker-info-585	256	4	about	about	IN
randomwalker-info-585	256	5	transactions	transaction	NNS
randomwalker-info-585	256	6	can	can	MD
randomwalker-info-585	256	7	also	also	RB
randomwalker-info-585	256	8	be	be	VB
randomwalker-info-585	256	9	implemented	implement	VBN
randomwalker-info-585	256	10	—	—	:
randomwalker-info-585	256	11	it	-PRON-	PRP
randomwalker-info-585	256	12	is	be	VBZ
randomwalker-info-585	256	13	currently	currently	RB
randomwalker-info-585	256	14	easi-	easi-	JJ
randomwalker-info-585	256	15	est	est	NNP
randomwalker-info-585	256	16	to	to	TO
randomwalker-info-585	256	17	do	do	VB
randomwalker-info-585	256	18	this	this	DT
randomwalker-info-585	256	19	by	by	IN
randomwalker-info-585	256	20	modifying	modify	VBG
randomwalker-info-585	256	21	strategies	strategy	NNS
randomwalker-info-585	256	22	to	to	TO
randomwalker-info-585	256	23	randomly	randomly	VB
randomwalker-info-585	256	24	“	"	``
randomwalker-info-585	256	25	pretend	pretend	VB
randomwalker-info-585	256	26	”	"	''
randomwalker-info-585	256	27	they	-PRON-	PRP
randomwalker-info-585	256	28	have	have	VBP
randomwalker-info-585	256	29	n’t	not	RB
randomwalker-info-585	256	30	heard	hear	VBN
randomwalker-info-585	256	31	of	of	IN
randomwalker-info-585	256	32	some	some	DT
randomwalker-info-585	256	33	transactions	transaction	NNS
randomwalker-info-585	256	34	.	.	.
randomwalker-info-585	257	1	Learning	learn	VBG
randomwalker-info-585	257	2	parameter	parameter	NN
randomwalker-info-585	257	3	.	.	.
randomwalker-info-585	258	1	Our	-PRON-	PRP$
randomwalker-info-585	258	2	learning	learning	NN
randomwalker-info-585	258	3	rules	rule	NNS
randomwalker-info-585	258	4	are	be	VBP
randomwalker-info-585	258	5	parameter-	parameter-	RB
randomwalker-info-585	258	6	ized	ize	VBN
randomwalker-info-585	258	7	by	by	IN
randomwalker-info-585	258	8	an	an	DT
randomwalker-info-585	258	9	�	�	NNP
randomwalker-info-585	258	10	∈	∈	IN
randomwalker-info-585	258	11	[	[	-LRB-
randomwalker-info-585	258	12	0	0	CD
randomwalker-info-585	258	13	,	,	,
randomwalker-info-585	258	14	1/2	1/2	CD
randomwalker-info-585	258	15	]	]	-RRB-
randomwalker-info-585	258	16	.	.	.
randomwalker-info-585	259	1	For	for	IN
randomwalker-info-585	259	2	EXP3	EXP3	NNP
randomwalker-info-585	259	3	,	,	,
randomwalker-info-585	259	4	it	-PRON-	PRP
randomwalker-info-585	259	5	is	be	VBZ
randomwalker-info-585	259	6	customary	customary	JJ
randomwalker-info-585	259	7	to	to	TO
randomwalker-info-585	259	8	set	set	VB
randomwalker-info-585	259	9	�	�	NNP
randomwalker-info-585	259	10	≈	≈	IN
randomwalker-info-585	259	11	√	√	NNP
randomwalker-info-585	259	12	n	n	CC
randomwalker-info-585	259	13	ln	ln	NNP
randomwalker-info-585	259	14	n	n	NN
randomwalker-info-585	259	15	/	/	SYM
randomwalker-info-585	259	16	T	T	NNP
randomwalker-info-585	259	17	,	,	,
randomwalker-info-585	259	18	where	where	WRB
randomwalker-info-585	259	19	n	n	PRP
randomwalker-info-585	259	20	is	be	VBZ
randomwalker-info-585	259	21	the	the	DT
randomwalker-info-585	259	22	number	number	NN
randomwalker-info-585	259	23	of	of	IN
randomwalker-info-585	259	24	strategies	strategy	NNS
randomwalker-info-585	259	25	consid-	consid-	VBP
randomwalker-info-585	259	26	ered	ered	JJ
randomwalker-info-585	259	27	and	and	CC
randomwalker-info-585	259	28	T	T	NNP
randomwalker-info-585	259	29	is	be	VBZ
randomwalker-info-585	259	30	the	the	DT
randomwalker-info-585	259	31	number	number	NN
randomwalker-info-585	259	32	of	of	IN
randomwalker-info-585	259	33	games	game	NNS
randomwalker-info-585	259	34	played	play	VBN
randomwalker-info-585	259	35	.	.	.
randomwalker-info-585	260	1	For	for	IN
randomwalker-info-585	260	2	MWU	MWU	NNP
randomwalker-info-585	260	3	(	(	-LRB-
randomwalker-info-585	260	4	and	and	CC
randomwalker-info-585	260	5	our	-PRON-	PRP$
randomwalker-info-585	260	6	“	"	``
randomwalker-info-585	260	7	MWU	mwu	NN
randomwalker-info-585	260	8	-	-	HYPH
randomwalker-info-585	260	9	like	like	JJ
randomwalker-info-585	260	10	”	"	''
randomwalker-info-585	260	11	update	update	NN
randomwalker-info-585	260	12	rule	rule	NN
randomwalker-info-585	260	13	)	)	-RRB-
randomwalker-info-585	260	14	,	,	,
randomwalker-info-585	260	15	it	-PRON-	PRP
randomwalker-info-585	260	16	is	be	VBZ
randomwalker-info-585	260	17	customary	customary	JJ
randomwalker-info-585	260	18	to	to	TO
randomwalker-info-585	260	19	set	set	VB
randomwalker-info-585	260	20	�	�	NNP
randomwalker-info-585	260	21	≈√	≈√	PRP
randomwalker-info-585	260	22	ln	ln	UH
randomwalker-info-585	260	23	n	n	NN
randomwalker-info-585	260	24	/	/	SYM
randomwalker-info-585	260	25	T.	t.	NN
randomwalker-info-585	261	1	Larger	large	JJR
randomwalker-info-585	261	2	�	�	NNP
randomwalker-info-585	261	3	encourages	encourage	VBZ
randomwalker-info-585	261	4	beliefs	belief	NNS
randomwalker-info-585	261	5	(	(	-LRB-
randomwalker-info-585	261	6	about	about	IN
randomwalker-info-585	261	7	the	the	DT
randomwalker-info-585	261	8	strength	strength	NN
randomwalker-info-585	261	9	of	of	IN
randomwalker-info-585	261	10	strategies	strategy	NNS
randomwalker-info-585	261	11	)	)	-RRB-
randomwalker-info-585	261	12	to	to	TO
randomwalker-info-585	261	13	be	be	VB
randomwalker-info-585	261	14	updated	update	VBN
randomwalker-info-585	261	15	rapidly	rapidly	RB
randomwalker-info-585	261	16	in	in	IN
randomwalker-info-585	261	17	response	response	NN
randomwalker-info-585	261	18	to	to	IN
randomwalker-info-585	261	19	recent	recent	JJ
randomwalker-info-585	261	20	games	game	NNS
randomwalker-info-585	261	21	.	.	.
randomwalker-info-585	262	1	Smaller	small	JJR
randomwalker-info-585	262	2	�	�	NNP
randomwalker-info-585	262	3	encourages	encourage	VBZ
randomwalker-info-585	262	4	waiting	wait	VBG
randomwalker-info-585	262	5	for	for	IN
randomwalker-info-585	262	6	more	more	JJR
randomwalker-info-585	262	7	evidence	evidence	NN
randomwalker-info-585	262	8	be-	be-	XX
randomwalker-info-585	262	9	fore	fore	IN
randomwalker-info-585	262	10	updating	update	VBG
randomwalker-info-585	262	11	beliefs	belief	NNS
randomwalker-info-585	262	12	.	.	.
randomwalker-info-585	263	1	Atomic	atomic	JJ
randomwalker-info-585	263	2	versus	versus	IN
randomwalker-info-585	263	3	Non	non	JJ
randomwalker-info-585	263	4	-	-	JJ
randomwalker-info-585	263	5	Atomic	atomic	JJ
randomwalker-info-585	263	6	Miners	Miners	NNPS
randomwalker-info-585	263	7	.	.	.
randomwalker-info-585	264	1	We	-PRON-	PRP
randomwalker-info-585	264	2	say	say	VBP
randomwalker-info-585	264	3	miners	miner	NNS
randomwalker-info-585	264	4	are	be	VBP
randomwalker-info-585	264	5	atomic	atomic	JJ
randomwalker-info-585	264	6	if	if	IN
randomwalker-info-585	264	7	there	there	EX
randomwalker-info-585	264	8	are	be	VBP
randomwalker-info-585	264	9	finitely	finitely	RB
randomwalker-info-585	264	10	many	many	JJ
randomwalker-info-585	264	11	of	of	IN
randomwalker-info-585	264	12	them	-PRON-	PRP
randomwalker-info-585	264	13	,	,	,
randomwalker-info-585	264	14	and	and	CC
randomwalker-info-585	264	15	each	each	DT
randomwalker-info-585	264	16	has	have	VBZ
randomwalker-info-585	264	17	a	a	DT
randomwalker-info-585	264	18	finite	finite	JJ
randomwalker-info-585	264	19	fraction	fraction	NN
randomwalker-info-585	264	20	of	of	IN
randomwalker-info-585	264	21	the	the	DT
randomwalker-info-585	264	22	total	total	JJ
randomwalker-info-585	264	23	hash	hash	NN
randomwalker-info-585	264	24	power	power	NN
randomwalker-info-585	264	25	.	.	.
randomwalker-info-585	265	1	Such	such	JJ
randomwalker-info-585	265	2	miners	miner	NNS
randomwalker-info-585	265	3	may	may	MD
randomwalker-info-585	265	4	have	have	VB
randomwalker-info-585	265	5	an	an	DT
randomwalker-info-585	265	6	interest	interest	NN
randomwalker-info-585	265	7	in	in	IN
randomwalker-info-585	265	8	sacrificing	sacrifice	VBG
randomwalker-info-585	265	9	immediate	immediate	JJ
randomwalker-info-585	265	10	gains	gain	NNS
randomwalker-info-585	265	11	related	relate	VBN
randomwalker-info-585	265	12	to	to	IN
randomwalker-info-585	265	13	a	a	DT
randomwalker-info-585	265	14	block	block	NN
randomwalker-info-585	265	15	mined	mine	VBN
randomwalker-info-585	265	16	now	now	RB
randomwalker-info-585	265	17	in	in	IN
randomwalker-info-585	265	18	order	order	NN
randomwalker-info-585	265	19	to	to	TO
randomwalker-info-585	265	20	achieve	achieve	VB
randomwalker-info-585	265	21	greater	great	JJR
randomwalker-info-585	265	22	gains	gain	NNS
randomwalker-info-585	265	23	for	for	IN
randomwalker-info-585	265	24	blocks	block	NNS
randomwalker-info-585	265	25	mined	mine	VBN
randomwalker-info-585	265	26	in	in	IN
randomwalker-info-585	265	27	the	the	DT
randomwalker-info-585	265	28	future	future	NN
randomwalker-info-585	265	29	.	.	.
randomwalker-info-585	266	1	Non	non	JJ
randomwalker-info-585	266	2	-	-	JJ
randomwalker-info-585	266	3	atomic	atomic	JJ
randomwalker-info-585	266	4	miners	miner	NNS
randomwalker-info-585	266	5	are	be	VBP
randomwalker-info-585	266	6	infinitesimally	infinitesimally	RB
randomwalker-info-585	266	7	small	small	JJ
randomwalker-info-585	266	8	,	,	,
randomwalker-info-585	266	9	but	but	CC
randomwalker-info-585	266	10	there	there	EX
randomwalker-info-585	266	11	are	be	VBP
randomwalker-info-585	266	12	infinitely	infinitely	RB
randomwalker-info-585	266	13	many	many	JJ
randomwalker-info-585	266	14	of	of	IN
randomwalker-info-585	266	15	them	-PRON-	PRP
randomwalker-info-585	266	16	.	.	.
randomwalker-info-585	267	1	When	when	WRB
randomwalker-info-585	267	2	such	such	JJ
randomwalker-info-585	267	3	miners	miner	NNS
randomwalker-info-585	267	4	find	find	VBP
randomwalker-info-585	267	5	a	a	DT
randomwalker-info-585	267	6	block	block	NN
randomwalker-info-585	267	7	,	,	,
randomwalker-info-585	267	8	they	-PRON-	PRP
randomwalker-info-585	267	9	are	be	VBP
randomwalker-info-585	267	10	only	only	RB
randomwalker-info-585	267	11	interested	interested	JJ
randomwalker-info-585	267	12	in	in	IN
randomwalker-info-585	267	13	maximizing	maximize	VBG
randomwalker-info-585	267	14	their	-PRON-	PRP$
randomwalker-info-585	267	15	gains	gain	NNS
randomwalker-info-585	267	16	related	relate	VBN
randomwalker-info-585	267	17	to	to	IN
randomwalker-info-585	267	18	that	that	DT
randomwalker-info-585	267	19	block	block	NN
randomwalker-info-585	267	20	(	(	-LRB-
randomwalker-info-585	267	21	because	because	IN
randomwalker-info-585	267	22	they	-PRON-	PRP
randomwalker-info-585	267	23	will	will	MD
randomwalker-info-585	267	24	never	never	RB
randomwalker-info-585	267	25	find	find	VB
randomwalker-info-585	267	26	another	another	DT
randomwalker-info-585	267	27	block	block	NN
randomwalker-info-585	267	28	in	in	IN
randomwalker-info-585	267	29	the	the	DT
randomwalker-info-585	267	30	future	future	NN
randomwalker-info-585	267	31	)	)	-RRB-
randomwalker-info-585	267	32	.	.	.
randomwalker-info-585	268	1	Obviously	obviously	RB
randomwalker-info-585	268	2	our	-PRON-	PRP$
randomwalker-info-585	268	3	simulation	simulation	NN
randomwalker-info-585	268	4	can	can	MD
randomwalker-info-585	268	5	not	not	RB
randomwalker-info-585	268	6	create	create	VB
randomwalker-info-585	268	7	infinitely	infinitely	RB
randomwalker-info-585	268	8	many	many	JJ
randomwalker-info-585	268	9	miners	miner	NNS
randomwalker-info-585	268	10	,	,	,
randomwalker-info-585	268	11	but	but	CC
randomwalker-info-585	268	12	we	-PRON-	PRP
randomwalker-info-585	268	13	can	can	MD
randomwalker-info-585	268	14	functionally	functionally	RB
randomwalker-info-585	268	15	simulate	simulate	VB
randomwalker-info-585	268	16	them	-PRON-	PRP
randomwalker-info-585	268	17	.	.	.
randomwalker-info-585	269	1	To	to	TO
randomwalker-info-585	269	2	simulate	simulate	VB
randomwalker-info-585	269	3	that	that	IN
randomwalker-info-585	269	4	an	an	DT
randomwalker-info-585	269	5	α	α	NNP
randomwalker-info-585	269	6	fraction	fraction	NN
randomwalker-info-585	269	7	of	of	IN
randomwalker-info-585	269	8	non	non	JJ
randomwalker-info-585	269	9	-	-	JJ
randomwalker-info-585	269	10	atomic	atomic	JJ
randomwalker-info-585	269	11	miners	miner	NNS
randomwalker-info-585	269	12	are	be	VBP
randomwalker-info-585	269	13	using	use	VBG
randomwalker-info-585	269	14	strategy	strategy	NN
randomwalker-info-585	269	15	s	s	JJ
randomwalker-info-585	269	16	,	,	,
randomwalker-info-585	269	17	we	-PRON-	PRP
randomwalker-info-585	269	18	instead	instead	RB
randomwalker-info-585	269	19	create	create	VBP
randomwalker-info-585	269	20	a	a	DT
randomwalker-info-585	269	21	single	single	JJ
randomwalker-info-585	269	22	atomic	atomic	JJ
randomwalker-info-585	269	23	miner	miner	NN
randomwalker-info-585	269	24	with	with	IN
randomwalker-info-585	269	25	an	an	DT
randomwalker-info-585	269	26	α	α	NNP
randomwalker-info-585	269	27	fraction	fraction	NN
randomwalker-info-585	269	28	of	of	IN
randomwalker-info-585	269	29	the	the	DT
randomwalker-info-585	269	30	hash	hash	NN
randomwalker-info-585	269	31	power	power	NN
randomwalker-info-585	269	32	,	,	,
randomwalker-info-585	269	33	and	and	CC
randomwalker-info-585	269	34	ensure	ensure	VB
randomwalker-info-585	269	35	that	that	IN
randomwalker-info-585	269	36	all	all	DT
randomwalker-info-585	269	37	of	of	IN
randomwalker-info-585	269	38	this	this	DT
randomwalker-info-585	269	39	miner	miner	NN
randomwalker-info-585	269	40	’s	’s	POS
randomwalker-info-585	269	41	strategic	strategic	JJ
randomwalker-info-585	269	42	decisions	decision	NNS
randomwalker-info-585	269	43	take	take	VBP
randomwalker-info-585	269	44	as	as	IN
randomwalker-info-585	269	45	input	input	NN
randomwalker-info-585	269	46	only	only	RB
randomwalker-info-585	269	47	the	the	DT
randomwalker-info-585	269	48	public	public	JJ
randomwalker-info-585	269	49	information	information	NN
randomwalker-info-585	269	50	available	available	JJ
randomwalker-info-585	269	51	to	to	IN
randomwalker-info-585	269	52	the	the	DT
randomwalker-info-585	269	53	entire	entire	JJ
randomwalker-info-585	269	54	network	network	NN
randomwalker-info-585	269	55	,	,	,
randomwalker-info-585	269	56	and	and	CC
randomwalker-info-585	269	57	does	do	VBZ
randomwalker-info-585	269	58	not	not	RB
randomwalker-info-585	269	59	treat	treat	VB
randomwalker-info-585	269	60	“	"	``
randomwalker-info-585	269	61	their	-PRON-	PRP$
randomwalker-info-585	269	62	own	own	JJ
randomwalker-info-585	269	63	”	"	''
randomwalker-info-585	269	64	blocks	block	VBZ
randomwalker-info-585	269	65	any	any	DT
randomwalker-info-585	269	66	differently	differently	RB
randomwalker-info-585	269	67	than	than	IN
randomwalker-info-585	269	68	generic	generic	JJ
randomwalker-info-585	269	69	blocks	block	NNS
randomwalker-info-585	269	70	.	.	.
randomwalker-info-585	270	1	Of	of	RB
randomwalker-info-585	270	2	course	course	RB
randomwalker-info-585	270	3	,	,	,
randomwalker-info-585	270	4	the	the	DT
randomwalker-info-585	270	5	real	real	JJ
randomwalker-info-585	270	6	world	world	NN
randomwalker-info-585	270	7	is	be	VBZ
randomwalker-info-585	270	8	atomic	atomic	JJ
randomwalker-info-585	270	9	.	.	.
randomwalker-info-585	271	1	But	but	CC
randomwalker-info-585	271	2	it	-PRON-	PRP
randomwalker-info-585	271	3	is	be	VBZ
randomwalker-info-585	271	4	extremely	extremely	RB
randomwalker-info-585	271	5	helpful	helpful	JJ
randomwalker-info-585	271	6	to	to	TO
randomwalker-info-585	271	7	compare	compare	VB
randomwalker-info-585	271	8	simulation	simulation	NN
randomwalker-info-585	271	9	results	result	NNS
randomwalker-info-585	271	10	between	between	IN
randomwalker-info-585	271	11	the	the	DT
randomwalker-info-585	271	12	two	two	CD
randomwalker-info-585	271	13	mod-	mod-	NN
randomwalker-info-585	271	14	els	el	VBZ
randomwalker-info-585	271	15	to	to	TO
randomwalker-info-585	271	16	isolate	isolate	VB
randomwalker-info-585	271	17	behavior	behavior	NN
randomwalker-info-585	271	18	that	that	WDT
randomwalker-info-585	271	19	arises	arise	VBZ
randomwalker-info-585	271	20	only	only	RB
randomwalker-info-585	271	21	when	when	WRB
randomwalker-info-585	271	22	miners	miner	NNS
randomwalker-info-585	271	23	are	be	VBP
randomwalker-info-585	271	24	atomic	atomic	JJ
randomwalker-info-585	271	25	(	(	-LRB-
randomwalker-info-585	271	26	example	example	NN
randomwalker-info-585	271	27	:	:	:
randomwalker-info-585	271	28	selfish	selfish	JJ
randomwalker-info-585	271	29	mining	mining	NN
randomwalker-info-585	271	30	)	)	-RRB-
randomwalker-info-585	271	31	,	,	,
randomwalker-info-585	271	32	as	as	RB
randomwalker-info-585	271	33	intuitively	intuitively	RB
randomwalker-info-585	271	34	this	this	DT
randomwalker-info-585	271	35	behav-	behav-	JJ
randomwalker-info-585	271	36	ior	ior	NNP
randomwalker-info-585	271	37	“	"	``
randomwalker-info-585	271	38	gets	get	VBZ
randomwalker-info-585	271	39	worse	bad	JJR
randomwalker-info-585	271	40	”	"	''
randomwalker-info-585	271	41	with	with	IN
randomwalker-info-585	271	42	big	big	JJ
randomwalker-info-585	271	43	miners	miner	NNS
randomwalker-info-585	271	44	(	(	-LRB-
randomwalker-info-585	271	45	as	as	IN
randomwalker-info-585	271	46	with	with	IN
randomwalker-info-585	271	47	selfish	selfish	JJ
randomwalker-info-585	271	48	mining	mining	NN
randomwalker-info-585	271	49	)	)	-RRB-
randomwalker-info-585	271	50	.	.	.
randomwalker-info-585	272	1	4.4	4.4	CD
randomwalker-info-585	272	2	Implementation	implementation	NN
randomwalker-info-585	272	3	and	and	CC
randomwalker-info-585	272	4	performance	performance	NN
randomwalker-info-585	272	5	.	.	.
randomwalker-info-585	273	1	The	the	DT
randomwalker-info-585	273	2	simulator	simulator	NN
randomwalker-info-585	273	3	is	be	VBZ
randomwalker-info-585	273	4	written	write	VBN
randomwalker-info-585	273	5	in	in	IN
randomwalker-info-585	273	6	C++	C++	NNP
randomwalker-info-585	273	7	,	,	,
randomwalker-info-585	273	8	and	and	CC
randomwalker-info-585	273	9	has	have	VBZ
randomwalker-info-585	273	10	a	a	DT
randomwalker-info-585	273	11	running	run	VBG
randomwalker-info-585	273	12	time	time	NN
randomwalker-info-585	273	13	proportional	proportional	JJ
randomwalker-info-585	273	14	to	to	IN
randomwalker-info-585	273	15	the	the	DT
randomwalker-info-585	273	16	product	product	NN
randomwalker-info-585	273	17	of	of	IN
randomwalker-info-585	273	18	the	the	DT
randomwalker-info-585	273	19	number	number	NN
randomwalker-info-585	273	20	of	of	IN
randomwalker-info-585	273	21	games	game	NNS
randomwalker-info-585	273	22	,	,	,
randomwalker-info-585	273	23	the	the	DT
randomwalker-info-585	273	24	number	number	NN
randomwalker-info-585	273	25	of	of	IN
randomwalker-info-585	273	26	rounds	round	NNS
randomwalker-info-585	273	27	per	per	IN
randomwalker-info-585	273	28	game	game	NN
randomwalker-info-585	273	29	,	,	,
randomwalker-info-585	273	30	and	and	CC
randomwalker-info-585	273	31	the	the	DT
randomwalker-info-585	273	32	number	number	NN
randomwalker-info-585	273	33	of	of	IN
randomwalker-info-585	273	34	miners	miner	NNS
randomwalker-info-585	273	35	.	.	.
randomwalker-info-585	274	1	We	-PRON-	PRP
randomwalker-info-585	274	2	find	find	VBP
randomwalker-info-585	274	3	that	that	IN
randomwalker-info-585	274	4	for	for	IN
randomwalker-info-585	274	5	accurate	accurate	JJ
randomwalker-info-585	274	6	results	result	NNS
randomwalker-info-585	274	7	,	,	,
randomwalker-info-585	274	8	the	the	DT
randomwalker-info-585	274	9	games	game	NNS
randomwalker-info-585	274	10	need	need	VBP
randomwalker-info-585	274	11	to	to	TO
randomwalker-info-585	274	12	include	include	VB
randomwalker-info-585	274	13	enough	enough	JJ
randomwalker-info-585	274	14	rounds	round	NNS
randomwalker-info-585	274	15	so	so	IN
randomwalker-info-585	274	16	that	that	IN
randomwalker-info-585	274	17	that	that	DT
randomwalker-info-585	274	18	for	for	IN
randomwalker-info-585	274	19	every	every	DT
randomwalker-info-585	274	20	strategy	strategy	NN
randomwalker-info-585	274	21	,	,	,
randomwalker-info-585	274	22	the	the	DT
randomwalker-info-585	274	23	miners	miner	NNS
randomwalker-info-585	274	24	using	use	VBG
randomwalker-info-585	274	25	it	-PRON-	PRP
randomwalker-info-585	274	26	together	together	RB
randomwalker-info-585	274	27	find	find	VBP
randomwalker-info-585	274	28	tens	ten	NNS
randomwalker-info-585	274	29	of	of	IN
randomwalker-info-585	274	30	blocks	block	NNS
randomwalker-info-585	274	31	.	.	.
randomwalker-info-585	275	1	We	-PRON-	PRP
randomwalker-info-585	275	2	also	also	RB
randomwalker-info-585	275	3	find	find	VBP
randomwalker-info-585	275	4	that	that	IN
randomwalker-info-585	275	5	it	-PRON-	PRP
randomwalker-info-585	275	6	takes	take	VBZ
randomwalker-info-585	275	7	on	on	RP
randomwalker-info-585	275	8	the	the	DT
randomwalker-info-585	275	9	order	order	NN
randomwalker-info-585	275	10	of	of	IN
randomwalker-info-585	275	11	a	a	DT
randomwalker-info-585	275	12	few	few	JJ
randomwalker-info-585	275	13	hundred	hundred	CD
randomwalker-info-585	275	14	thousand	thousand	CD
randomwalker-info-585	275	15	games	game	NNS
randomwalker-info-585	275	16	for	for	IN
randomwalker-info-585	275	17	our	-PRON-	PRP$
randomwalker-info-585	275	18	learning	learn	VBG
randomwalker-info-585	275	19	algorithms	algorithm	NNS
randomwalker-info-585	275	20	to	to	TO
randomwalker-info-585	275	21	converge	converge	VB
randomwalker-info-585	275	22	to	to	IN
randomwalker-info-585	275	23	an	an	DT
randomwalker-info-585	275	24	equilibrium	equilibrium	NN
randomwalker-info-585	275	25	.	.	.
randomwalker-info-585	276	1	On	on	IN
randomwalker-info-585	276	2	a	a	DT
randomwalker-info-585	276	3	commodity	commodity	NN
randomwalker-info-585	276	4	laptop	laptop	NN
randomwalker-info-585	276	5	with	with	IN
randomwalker-info-585	276	6	a	a	DT
randomwalker-info-585	276	7	2.7	2.7	CD
randomwalker-info-585	276	8	GHz	GHz	NNS
randomwalker-info-585	276	9	Intel	Intel	NNP
randomwalker-info-585	276	10	Core	Core	NNP
randomwalker-info-585	276	11	i5	i5	NNP
randomwalker-info-585	276	12	proces-	proces-	NN
randomwalker-info-585	276	13	sor	sor	NN
randomwalker-info-585	276	14	,	,	,
randomwalker-info-585	276	15	running	run	VBG
randomwalker-info-585	276	16	a	a	DT
randomwalker-info-585	276	17	simulation	simulation	NN
randomwalker-info-585	276	18	of	of	IN
randomwalker-info-585	276	19	1000	1000	CD
randomwalker-info-585	276	20	games	game	NNS
randomwalker-info-585	276	21	with	with	IN
randomwalker-info-585	276	22	200	200	CD
randomwalker-info-585	276	23	miners	miner	NNS
randomwalker-info-585	276	24	,	,	,
randomwalker-info-585	276	25	an	an	DT
randomwalker-info-585	276	26	average	average	JJ
randomwalker-info-585	276	27	interarrival	interarrival	JJ
randomwalker-info-585	276	28	time	time	NN
randomwalker-info-585	276	29	of	of	IN
randomwalker-info-585	276	30	600	600	CD
randomwalker-info-585	276	31	rounds	round	NNS
randomwalker-info-585	276	32	,	,	,
randomwalker-info-585	276	33	and	and	CC
randomwalker-info-585	276	34	a	a	DT
randomwalker-info-585	276	35	total	total	NN
randomwalker-info-585	276	36	of	of	IN
randomwalker-info-585	276	37	6,000,000	6,000,000	CD
randomwalker-info-585	276	38	rounds	round	NNS
randomwalker-info-585	276	39	(	(	-LRB-
randomwalker-info-585	276	40	≈10,000	≈10,000	CD
randomwalker-info-585	276	41	blocks	block	NNS
randomwalker-info-585	276	42	will	will	MD
randomwalker-info-585	276	43	be	be	VB
randomwalker-info-585	276	44	created	create	VBN
randomwalker-info-585	276	45	)	)	-RRB-
randomwalker-info-585	276	46	,	,	,
randomwalker-info-585	276	47	takes	take	VBZ
randomwalker-info-585	276	48	ap-	ap-	RB
randomwalker-info-585	276	49	proximately	proximately	RB
randomwalker-info-585	276	50	22	22	CD
randomwalker-info-585	276	51	seconds	second	NNS
randomwalker-info-585	276	52	.	.	.
randomwalker-info-585	277	1	Limitations	limitation	NNS
randomwalker-info-585	277	2	.	.	.
randomwalker-info-585	278	1	A	a	DT
randomwalker-info-585	278	2	current	current	JJ
randomwalker-info-585	278	3	limitation	limitation	NN
randomwalker-info-585	278	4	of	of	IN
randomwalker-info-585	278	5	the	the	DT
randomwalker-info-585	278	6	simulator	simulator	NN
randomwalker-info-585	278	7	is	be	VBZ
randomwalker-info-585	278	8	that	that	IN
randomwalker-info-585	278	9	the	the	DT
randomwalker-info-585	278	10	transaction	transaction	NN
randomwalker-info-585	278	11	fees	fee	NNS
randomwalker-info-585	278	12	can	can	MD
randomwalker-info-585	278	13	only	only	RB
randomwalker-info-585	278	14	be	be	VB
randomwalker-info-585	278	15	modeled	model	VBN
randomwalker-info-585	278	16	as	as	IN
randomwalker-info-585	278	17	coming	come	VBG
randomwalker-info-585	278	18	in	in	RB
randomwalker-info-585	278	19	at	at	IN
randomwalker-info-585	278	20	a	a	DT
randomwalker-info-585	278	21	uniform	uniform	JJ
randomwalker-info-585	278	22	rate	rate	NN
randomwalker-info-585	278	23	in	in	IN
randomwalker-info-585	278	24	time	time	NN
randomwalker-info-585	278	25	.	.	.
randomwalker-info-585	279	1	Additionally	additionally	RB
randomwalker-info-585	279	2	,	,	,
randomwalker-info-585	279	3	the	the	DT
randomwalker-info-585	279	4	simulator	simulator	NN
randomwalker-info-585	279	5	is	be	VBZ
randomwalker-info-585	279	6	not	not	RB
randomwalker-info-585	279	7	capable	capable	JJ
randomwalker-info-585	279	8	of	of	IN
randomwalker-info-585	279	9	modeling	model	VBG
randomwalker-info-585	279	10	mining	mining	NN
randomwalker-info-585	279	11	pool	pool	NN
randomwalker-info-585	279	12	dynamics	dynamic	NNS
randomwalker-info-585	279	13	beyond	beyond	IN
randomwalker-info-585	279	14	treating	treat	VBG
randomwalker-info-585	279	15	them	-PRON-	PRP
randomwalker-info-585	279	16	as	as	IN
randomwalker-info-585	279	17	a	a	DT
randomwalker-info-585	279	18	single	single	JJ
randomwalker-info-585	279	19	miner	miner	NN
randomwalker-info-585	279	20	with	with	IN
randomwalker-info-585	279	21	hash	hash	NN
randomwalker-info-585	279	22	power	power	NN
randomwalker-info-585	279	23	equal	equal	JJ
randomwalker-info-585	279	24	to	to	IN
randomwalker-info-585	279	25	that	that	DT
randomwalker-info-585	279	26	of	of	IN
randomwalker-info-585	279	27	the	the	DT
randomwalker-info-585	279	28	pool	pool	NN
randomwalker-info-585	279	29	.	.	.
randomwalker-info-585	280	1	This	this	DT
randomwalker-info-585	280	2	does	do	VBZ
randomwalker-info-585	280	3	n’t	not	RB
randomwalker-info-585	280	4	allow	allow	VB
randomwalker-info-585	280	5	for	for	IN
randomwalker-info-585	280	6	consideration	consideration	NN
randomwalker-info-585	280	7	of	of	IN
randomwalker-info-585	280	8	attacks	attack	NNS
randomwalker-info-585	280	9	such	such	JJ
randomwalker-info-585	280	10	as	as	IN
randomwalker-info-585	280	11	those	those	DT
randomwalker-info-585	280	12	presented	present	VBN
randomwalker-info-585	280	13	in	in	IN
randomwalker-info-585	280	14	[	[	-LRB-
randomwalker-info-585	280	15	8	8	CD
randomwalker-info-585	280	16	]	]	-RRB-
randomwalker-info-585	280	17	.	.	.
randomwalker-info-585	281	1	5	5	CD
randomwalker-info-585	281	2	.	.	.
randomwalker-info-585	282	1	NEW	new	JJ
randomwalker-info-585	282	2	DEVIANT	DEVIANT	NNP
randomwalker-info-585	282	3	MINING	mining	NN
randomwalker-info-585	282	4	BEHAVIOR	BEHAVIOR	NNP
randomwalker-info-585	282	5	In	in	IN
randomwalker-info-585	282	6	this	this	DT
randomwalker-info-585	282	7	section	section	NN
randomwalker-info-585	282	8	,	,	,
randomwalker-info-585	282	9	we	-PRON-	PRP
randomwalker-info-585	282	10	examine	examine	VBP
randomwalker-info-585	282	11	what	what	WP
randomwalker-info-585	282	12	deviant	deviant	NN
randomwalker-info-585	282	13	mining	mining	NN
randomwalker-info-585	282	14	behavior	behavior	NN
randomwalker-info-585	282	15	might	may	MD
randomwalker-info-585	282	16	unfold	unfold	VB
randomwalker-info-585	282	17	in	in	IN
randomwalker-info-585	282	18	the	the	DT
randomwalker-info-585	282	19	transaction	transaction	NN
randomwalker-info-585	282	20	fees	fee	NNS
randomwalker-info-585	282	21	model	model	NN
randomwalker-info-585	282	22	that	that	WDT
randomwalker-info-585	282	23	does	do	VBZ
randomwalker-info-585	282	24	n’t	not	RB
randomwalker-info-585	282	25	arise	arise	VB
randomwalker-info-585	282	26	in	in	IN
randomwalker-info-585	282	27	the	the	DT
randomwalker-info-585	282	28	block	block	NN
randomwalker-info-585	282	29	-	-	HYPH
randomwalker-info-585	282	30	reward	reward	NN
randomwalker-info-585	282	31	model	model	NN
randomwalker-info-585	282	32	.	.	.
randomwalker-info-585	283	1	Specifically	specifically	RB
randomwalker-info-585	283	2	,	,	,
randomwalker-info-585	283	3	we	-PRON-	PRP
randomwalker-info-585	283	4	argue	argue	VBP
randomwalker-info-585	283	5	that	that	DT
randomwalker-info-585	283	6	:	:	:
randomwalker-info-585	283	7	•	•	VB
randomwalker-info-585	283	8	It	-PRON-	PRP
randomwalker-info-585	283	9	is	be	VBZ
randomwalker-info-585	283	10	reasonable	reasonable	JJ
randomwalker-info-585	283	11	to	to	TO
randomwalker-info-585	283	12	expect	expect	VB
randomwalker-info-585	283	13	self	self	NN
randomwalker-info-585	283	14	-	-	HYPH
randomwalker-info-585	283	15	interested	interested	JJ
randomwalker-info-585	283	16	miners	miner	NNS
randomwalker-info-585	283	17	to	to	TO
randomwalker-info-585	283	18	be-	be-	RB
randomwalker-info-585	283	19	come	come	VB
randomwalker-info-585	283	20	PettyCompliant	PettyCompliant	NNP
randomwalker-info-585	283	21	instead	instead	RB
randomwalker-info-585	283	22	of	of	IN
randomwalker-info-585	283	23	DefaultCompli-	defaultcompli-	NN
randomwalker-info-585	283	24	ant	ant	NN
randomwalker-info-585	283	25	once	once	RB
randomwalker-info-585	283	26	transaction	transaction	NN
randomwalker-info-585	283	27	fees	fee	NNS
randomwalker-info-585	283	28	take	take	VBP
randomwalker-info-585	283	29	over	over	RP
randomwalker-info-585	283	30	.	.	.
randomwalker-info-585	284	1	•	•	VB
randomwalker-info-585	284	2	The	the	DT
randomwalker-info-585	284	3	existence	existence	NN
randomwalker-info-585	284	4	of	of	IN
randomwalker-info-585	284	5	PettyCompliant	PettyCompliant	NNP
randomwalker-info-585	284	6	miners	miner	NNS
randomwalker-info-585	284	7	in	in	IN
randomwalker-info-585	284	8	the	the	DT
randomwalker-info-585	284	9	net-	net-	NN
randomwalker-info-585	284	10	work	work	NN
randomwalker-info-585	284	11	opens	open	VBZ
randomwalker-info-585	284	12	the	the	DT
randomwalker-info-585	284	13	field	field	NN
randomwalker-info-585	284	14	for	for	IN
randomwalker-info-585	284	15	a	a	DT
randomwalker-info-585	284	16	range	range	NN
randomwalker-info-585	284	17	of	of	IN
randomwalker-info-585	284	18	aggressive	aggressive	JJ
randomwalker-info-585	284	19	strategies	strategy	NNS
randomwalker-info-585	284	20	with	with	IN
randomwalker-info-585	284	21	detrimental	detrimental	JJ
randomwalker-info-585	284	22	effects	effect	NNS
randomwalker-info-585	284	23	to	to	IN
randomwalker-info-585	284	24	Bitcoin	Bitcoin	NNP
randomwalker-info-585	284	25	’s	’s	POS
randomwalker-info-585	284	26	stability	stability	NN
randomwalker-info-585	284	27	.	.	.
randomwalker-info-585	285	1	5.1	5.1	CD
randomwalker-info-585	285	2	Phase	Phase	NNP
randomwalker-info-585	285	3	One	one	CD
randomwalker-info-585	285	4	:	:	:
randomwalker-info-585	285	5	Petty	petty	JJ
randomwalker-info-585	285	6	compliant	compliant	JJ
randomwalker-info-585	285	7	Observation	observation	NN
randomwalker-info-585	285	8	:	:	:
randomwalker-info-585	285	9	The	the	DT
randomwalker-info-585	285	10	default	default	NN
randomwalker-info-585	285	11	client	client	NN
randomwalker-info-585	285	12	behavior	behavior	NN
randomwalker-info-585	285	13	of	of	IN
randomwalker-info-585	285	14	min-	min-	NNP
randomwalker-info-585	285	15	ing	ing	NNP
randomwalker-info-585	285	16	on	on	IN
randomwalker-info-585	285	17	the	the	DT
randomwalker-info-585	285	18	oldest	old	JJS
randomwalker-info-585	285	19	block	block	NN
randomwalker-info-585	285	20	is	be	VBZ
randomwalker-info-585	285	21	not	not	RB
randomwalker-info-585	285	22	optimal	optimal	JJ
randomwalker-info-585	285	23	.	.	.
randomwalker-info-585	286	1	Miners	miner	NNS
randomwalker-info-585	286	2	can	can	MD
randomwalker-info-585	286	3	do	do	VB
randomwalker-info-585	286	4	strictly	strictly	RB
randomwalker-info-585	286	5	better	better	RB
randomwalker-info-585	286	6	by	by	IN
randomwalker-info-585	286	7	mining	mine	VBG
randomwalker-info-585	286	8	on	on	IN
randomwalker-info-585	286	9	the	the	DT
randomwalker-info-585	286	10	block	block	NN
randomwalker-info-585	286	11	that	that	WDT
randomwalker-info-585	286	12	leaves	leave	VBZ
randomwalker-info-585	286	13	the	the	DT
randomwalker-info-585	286	14	most	most	JJS
randomwalker-info-585	286	15	transactions	transaction	NNS
randomwalker-info-585	286	16	fees	fee	NNS
randomwalker-info-585	286	17	unclaimed	unclaimed	JJ
randomwalker-info-585	286	18	.	.	.
randomwalker-info-585	287	1	Consider	consider	VB
randomwalker-info-585	287	2	the	the	DT
randomwalker-info-585	287	3	case	case	NN
randomwalker-info-585	287	4	where	where	WRB
randomwalker-info-585	287	5	there	there	EX
randomwalker-info-585	287	6	is	be	VBZ
randomwalker-info-585	287	7	a	a	DT
randomwalker-info-585	287	8	fork	fork	NN
randomwalker-info-585	287	9	:	:	:
randomwalker-info-585	287	10	two	two	CD
randomwalker-info-585	287	11	blocks	block	NNS
randomwalker-info-585	287	12	are	be	VBP
randomwalker-info-585	287	13	tied	tie	VBN
randomwalker-info-585	287	14	for	for	IN
randomwalker-info-585	287	15	longest	long	JJS
randomwalker-info-585	287	16	chain	chain	NN
randomwalker-info-585	287	17	.	.	.
randomwalker-info-585	288	1	The	the	DT
randomwalker-info-585	288	2	traditional	traditional	JJ
randomwalker-info-585	288	3	behavior	behavior	NN
randomwalker-info-585	288	4	,	,	,
randomwalker-info-585	288	5	and	and	CC
randomwalker-info-585	288	6	the	the	DT
randomwalker-info-585	288	7	one	one	CD
randomwalker-info-585	288	8	programmed	program	VBD
randomwalker-info-585	288	9	into	into	IN
randomwalker-info-585	288	10	the	the	DT
randomwalker-info-585	288	11	default	default	NN
randomwalker-info-585	288	12	client,4	client,4	NNP
randomwalker-info-585	288	13	would	would	MD
randomwalker-info-585	288	14	have	have	VB
randomwalker-info-585	288	15	the	the	DT
randomwalker-info-585	288	16	miner	miner	NN
randomwalker-info-585	288	17	select	select	VB
randomwalker-info-585	288	18	the	the	DT
randomwalker-info-585	288	19	older	old	JJR
randomwalker-info-585	288	20	of	of	IN
randomwalker-info-585	288	21	the	the	DT
randomwalker-info-585	288	22	two	two	CD
randomwalker-info-585	288	23	potential	potential	JJ
randomwalker-info-585	288	24	block	block	NN
randomwalker-info-585	288	25	heads	head	NNS
randomwalker-info-585	288	26	.	.	.
randomwalker-info-585	289	1	However	however	RB
randomwalker-info-585	289	2	,	,	,
randomwalker-info-585	289	3	there	there	EX
randomwalker-info-585	289	4	is	be	VBZ
randomwalker-info-585	289	5	really	really	RB
randomwalker-info-585	289	6	no	no	DT
randomwalker-info-585	289	7	cost	cost	NN
randomwalker-info-585	289	8	for	for	IN
randomwalker-info-585	289	9	that	that	DT
randomwalker-info-585	289	10	miner	miner	NN
randomwalker-info-585	289	11	instead	instead	RB
randomwalker-info-585	289	12	to	to	TO
randomwalker-info-585	289	13	tie	tie	VB
randomwalker-info-585	289	14	-	-	HYPH
randomwalker-info-585	289	15	break	break	NN
randomwalker-info-585	289	16	arbitrarily	arbitrarily	RB
randomwalker-info-585	289	17	.	.	.
randomwalker-info-585	290	1	In	in	IN
randomwalker-info-585	290	2	particular	particular	JJ
randomwalker-info-585	290	3	,	,	,
randomwalker-info-585	290	4	if	if	IN
randomwalker-info-585	290	5	the	the	DT
randomwalker-info-585	290	6	miner	miner	NN
randomwalker-info-585	290	7	is	be	VBZ
randomwalker-info-585	290	8	planning	plan	VBG
randomwalker-info-585	290	9	to	to	IN
randomwalker-info-585	290	10	in-	in-	RB
randomwalker-info-585	290	11	clude	clude	VB
randomwalker-info-585	290	12	all	all	DT
randomwalker-info-585	290	13	unclaimed	unclaimed	JJ
randomwalker-info-585	290	14	transactions	transaction	NNS
randomwalker-info-585	290	15	in	in	IN
randomwalker-info-585	290	16	their	-PRON-	PRP$
randomwalker-info-585	290	17	block	block	NN
randomwalker-info-585	290	18	,	,	,
randomwalker-info-585	290	19	it	-PRON-	PRP
randomwalker-info-585	290	20	would	would	MD
randomwalker-info-585	290	21	be	be	VB
randomwalker-info-585	290	22	in	in	IN
randomwalker-info-585	290	23	that	that	DT
randomwalker-info-585	290	24	miner	miner	NN
randomwalker-info-585	290	25	’s	’s	POS
randomwalker-info-585	290	26	interest	interest	NN
randomwalker-info-585	290	27	not	not	RB
randomwalker-info-585	290	28	to	to	TO
randomwalker-info-585	290	29	mine	-PRON-	PRP
randomwalker-info-585	290	30	on	on	IN
randomwalker-info-585	290	31	the	the	DT
randomwalker-info-585	290	32	oldest	old	JJS
randomwalker-info-585	290	33	block	block	NN
randomwalker-info-585	290	34	,	,	,
randomwalker-info-585	290	35	but	but	CC
randomwalker-info-585	290	36	instead	instead	RB
randomwalker-info-585	290	37	the	the	DT
randomwalker-info-585	290	38	block	block	NN
randomwalker-info-585	290	39	that	that	WDT
randomwalker-info-585	290	40	leaves	leave	VBZ
randomwalker-info-585	290	41	the	the	DT
randomwalker-info-585	290	42	most	most	RBS
randomwalker-info-585	290	43	remaining	remaining	JJ
randomwalker-info-585	290	44	fees	fee	NNS
randomwalker-info-585	290	45	.	.	.
randomwalker-info-585	291	1	Therefore	therefore	RB
randomwalker-info-585	291	2	,	,	,
randomwalker-info-585	291	3	a	a	DT
randomwalker-info-585	291	4	strategic	strategic	JJ
randomwalker-info-585	291	5	miner	miner	NN
randomwalker-info-585	291	6	would	would	MD
randomwalker-info-585	291	7	want	want	VB
randomwalker-info-585	291	8	to	to	TO
randomwalker-info-585	291	9	mine	mine	VB
randomwalker-info-585	291	10	on	on	IN
randomwalker-info-585	291	11	MostmH	MostmH	NNS
randomwalker-info-585	291	12	instead	instead	RB
randomwalker-info-585	291	13	of	of	IN
randomwalker-info-585	291	14	OldestmH	OldestmH	NNS
randomwalker-info-585	291	15	.	.	.
randomwalker-info-585	292	1	We	-PRON-	PRP
randomwalker-info-585	292	2	call	call	VBP
randomwalker-info-585	292	3	this	this	DT
randomwalker-info-585	292	4	strategy	strategy	NN
randomwalker-info-585	292	5	petty	petty	JJ
randomwalker-info-585	292	6	compliant	compliant	JJ
randomwalker-info-585	292	7	,	,	,
randomwalker-info-585	292	8	4Note	4note	JJ
randomwalker-info-585	292	9	:	:	:
randomwalker-info-585	292	10	this	this	DT
randomwalker-info-585	292	11	is	be	VBZ
randomwalker-info-585	292	12	not	not	RB
randomwalker-info-585	292	13	a	a	DT
randomwalker-info-585	292	14	self	self	NN
randomwalker-info-585	292	15	-	-	HYPH
randomwalker-info-585	292	16	enforcing	enforce	VBG
randomwalker-info-585	292	17	part	part	NN
randomwalker-info-585	292	18	of	of	IN
randomwalker-info-585	292	19	the	the	DT
randomwalker-info-585	292	20	protocol	protocol	NN
randomwalker-info-585	292	21	.	.	.
randomwalker-info-585	293	1	It	-PRON-	PRP
randomwalker-info-585	293	2	’s	’	VBZ
randomwalker-info-585	293	3	purely	purely	RB
randomwalker-info-585	293	4	client	client	NN
randomwalker-info-585	293	5	-	-	HYPH
randomwalker-info-585	293	6	side	side	NN
randomwalker-info-585	293	7	behavior	behavior	NN
randomwalker-info-585	293	8	.	.	.
randomwalker-info-585	294	1	as	as	IN
randomwalker-info-585	294	2	it	-PRON-	PRP
randomwalker-info-585	294	3	is	be	VBZ
randomwalker-info-585	294	4	still	still	RB
randomwalker-info-585	294	5	mining	mine	VBG
randomwalker-info-585	294	6	on	on	IN
randomwalker-info-585	294	7	a	a	DT
randomwalker-info-585	294	8	longest	long	JJS
randomwalker-info-585	294	9	chain	chain	NN
randomwalker-info-585	294	10	,	,	,
randomwalker-info-585	294	11	including	include	VBG
randomwalker-info-585	294	12	all	all	DT
randomwalker-info-585	294	13	available	available	JJ
randomwalker-info-585	294	14	transactions	transaction	NNS
randomwalker-info-585	294	15	,	,	,
randomwalker-info-585	294	16	and	and	CC
randomwalker-info-585	294	17	publishing	publish	VBG
randomwalker-info-585	294	18	all	all	DT
randomwalker-info-585	294	19	blocks	block	NNS
randomwalker-info-585	294	20	that	that	WDT
randomwalker-info-585	294	21	are	be	VBP
randomwalker-info-585	294	22	found	find	VBN
randomwalker-info-585	294	23	(	(	-LRB-
randomwalker-info-585	294	24	like	like	IN
randomwalker-info-585	294	25	a	a	DT
randomwalker-info-585	294	26	default	default	NN
randomwalker-info-585	294	27	compliant	compliant	JJ
randomwalker-info-585	294	28	miner	miner	NN
randomwalker-info-585	294	29	)	)	-RRB-
randomwalker-info-585	294	30	.	.	.
randomwalker-info-585	295	1	It	-PRON-	PRP
randomwalker-info-585	295	2	is	be	VBZ
randomwalker-info-585	295	3	just	just	RB
randomwalker-info-585	295	4	tie	tie	NN
randomwalker-info-585	295	5	-	-	HYPH
randomwalker-info-585	295	6	breaking	breaking	NN
randomwalker-info-585	295	7	between	between	IN
randomwalker-info-585	295	8	longest	long	JJS
randomwalker-info-585	295	9	chains	chain	NNS
randomwalker-info-585	295	10	in	in	IN
randomwalker-info-585	295	11	a	a	DT
randomwalker-info-585	295	12	“	"	``
randomwalker-info-585	295	13	petty	petty	JJ
randomwalker-info-585	295	14	”	"	''
randomwalker-info-585	295	15	way	way	NN
randomwalker-info-585	295	16	to	to	TO
randomwalker-info-585	295	17	achieve	achieve	VB
randomwalker-info-585	295	18	greater	great	JJR
randomwalker-info-585	295	19	revenue	revenue	NN
randomwalker-info-585	295	20	.	.	.
randomwalker-info-585	296	1	PettyCompliant	pettycompliant	NN
randomwalker-info-585	296	2	:	:	:
randomwalker-info-585	296	3	Mine	-PRON-	PRP
randomwalker-info-585	296	4	like	like	IN
randomwalker-info-585	296	5	a	a	DT
randomwalker-info-585	296	6	default	default	NN
randomwalker-info-585	296	7	compliant	compliant	JJ
randomwalker-info-585	296	8	miner	miner	NN
randomwalker-info-585	296	9	,	,	,
randomwalker-info-585	296	10	except	except	IN
randomwalker-info-585	296	11	when	when	WRB
randomwalker-info-585	296	12	choos-	choos-	NNP
randomwalker-info-585	296	13	ing	ing	NNP
randomwalker-info-585	296	14	between	between	IN
randomwalker-info-585	296	15	two	two	CD
randomwalker-info-585	296	16	sides	side	NNS
randomwalker-info-585	296	17	in	in	IN
randomwalker-info-585	296	18	a	a	DT
randomwalker-info-585	296	19	fork	fork	NN
randomwalker-info-585	296	20	;	;	:
randomwalker-info-585	296	21	mine	mine	NN
randomwalker-info-585	296	22	on	on	IN
randomwalker-info-585	296	23	the	the	DT
randomwalker-info-585	296	24	block	block	NN
randomwalker-info-585	296	25	that	that	WDT
randomwalker-info-585	296	26	has	have	VBZ
randomwalker-info-585	296	27	claimed	claim	VBN
randomwalker-info-585	296	28	the	the	DT
randomwalker-info-585	296	29	fewest	few	JJS
randomwalker-info-585	296	30	transaction	transaction	NN
randomwalker-info-585	296	31	fees	fee	NNS
randomwalker-info-585	296	32	.	.	.
randomwalker-info-585	297	1	Which	which	WDT
randomwalker-info-585	297	2	Block	Block	NNP
randomwalker-info-585	297	3	:	:	:
randomwalker-info-585	297	4	Mining(m	mining(m	LS
randomwalker-info-585	297	5	)	)	-RRB-
randomwalker-info-585	297	6	=	=	NFP
randomwalker-info-585	297	7	MostmH	MostmH	NNS
randomwalker-info-585	297	8	.	.	.
randomwalker-info-585	298	1	How	how	WRB
randomwalker-info-585	298	2	much	much	JJ
randomwalker-info-585	298	3	:	:	:
randomwalker-info-585	298	4	include	include	VBP
randomwalker-info-585	298	5	Rem(Mining(m	Rem(Mining(m	NNP
randomwalker-info-585	298	6	)	)	-RRB-
randomwalker-info-585	298	7	)	)	-RRB-
randomwalker-info-585	298	8	.	.	.
randomwalker-info-585	299	1	Publish(B	Publish(B	VBN
randomwalker-info-585	299	2	)	)	-RRB-
randomwalker-info-585	299	3	?	?	.
randomwalker-info-585	300	1	yes	yes	UH
randomwalker-info-585	300	2	.	.	.
randomwalker-info-585	301	1	If	if	IN
randomwalker-info-585	301	2	forks	fork	NNS
randomwalker-info-585	301	3	ever	ever	RB
randomwalker-info-585	301	4	exist	exist	VBP
randomwalker-info-585	301	5	,	,	,
randomwalker-info-585	301	6	then	then	RB
randomwalker-info-585	301	7	PettyCompliant	PettyCompliant	NNP
randomwalker-info-585	301	8	strictly	strictly	RB
randomwalker-info-585	301	9	outper-	outper-	JJ
randomwalker-info-585	301	10	forms	form	NNS
randomwalker-info-585	301	11	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	301	12	.	.	.
randomwalker-info-585	302	1	The	the	DT
randomwalker-info-585	302	2	two	two	CD
randomwalker-info-585	302	3	are	be	VBP
randomwalker-info-585	302	4	identical	identical	JJ
randomwalker-info-585	302	5	except	except	IN
randomwalker-info-585	302	6	for	for	IN
randomwalker-info-585	302	7	the	the	DT
randomwalker-info-585	302	8	case	case	NN
randomwalker-info-585	302	9	where	where	WRB
randomwalker-info-585	302	10	the	the	DT
randomwalker-info-585	302	11	miner	miner	NN
randomwalker-info-585	302	12	is	be	VBZ
randomwalker-info-585	302	13	required	require	VBN
randomwalker-info-585	302	14	to	to	TO
randomwalker-info-585	302	15	choose	choose	VB
randomwalker-info-585	302	16	between	between	IN
randomwalker-info-585	302	17	two	two	CD
randomwalker-info-585	302	18	equal	equal	JJ
randomwalker-info-585	302	19	height	height	NN
randomwalker-info-585	302	20	blocks	block	NNS
randomwalker-info-585	302	21	to	to	IN
randomwalker-info-585	302	22	mine	-PRON-	PRP
randomwalker-info-585	302	23	on	on	RP
randomwalker-info-585	302	24	.	.	.
randomwalker-info-585	303	1	In	in	IN
randomwalker-info-585	303	2	this	this	DT
randomwalker-info-585	303	3	case	case	NN
randomwalker-info-585	303	4	PettyCompli-	pettycompli-	NN
randomwalker-info-585	303	5	ant	ant	NN
randomwalker-info-585	303	6	always	always	RB
randomwalker-info-585	303	7	makes	make	VBZ
randomwalker-info-585	303	8	the	the	DT
randomwalker-info-585	303	9	decision	decision	NN
randomwalker-info-585	303	10	to	to	TO
randomwalker-info-585	303	11	mine	-PRON-	PRP
randomwalker-info-585	303	12	in	in	IN
randomwalker-info-585	303	13	a	a	DT
randomwalker-info-585	303	14	location	location	NN
randomwalker-info-585	303	15	that	that	WDT
randomwalker-info-585	303	16	maximizes	maximize	VBZ
randomwalker-info-585	303	17	their	-PRON-	PRP$
randomwalker-info-585	303	18	rewards	reward	NNS
randomwalker-info-585	303	19	,	,	,
randomwalker-info-585	303	20	and	and	CC
randomwalker-info-585	303	21	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	303	22	might	may	MD
randomwalker-info-585	303	23	not	not	RB
randomwalker-info-585	303	24	.	.	.
randomwalker-info-585	304	1	In	in	IN
randomwalker-info-585	304	2	our	-PRON-	PRP$
randomwalker-info-585	304	3	mining	mining	NN
randomwalker-info-585	304	4	strategy	strategy	NN
randomwalker-info-585	304	5	simulator	simulator	NN
randomwalker-info-585	304	6	,	,	,
randomwalker-info-585	304	7	we	-PRON-	PRP
randomwalker-info-585	304	8	compare	compare	VBP
randomwalker-info-585	304	9	De-	de-	UH
randomwalker-info-585	304	10	faultCompliant	faultcompliant	NN
randomwalker-info-585	304	11	to	to	IN
randomwalker-info-585	304	12	PettyCompliant	PettyCompliant	NNP
randomwalker-info-585	304	13	and	and	CC
randomwalker-info-585	304	14	do	do	VB
randomwalker-info-585	304	15	in	in	IN
randomwalker-info-585	304	16	fact	fact	NN
randomwalker-info-585	304	17	see	see	VB
randomwalker-info-585	304	18	that	that	IN
randomwalker-info-585	304	19	PettyCompliant	PettyCompliant	NNP
randomwalker-info-585	304	20	outperforms	outperform	VBZ
randomwalker-info-585	304	21	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	304	22	,	,	,
randomwalker-info-585	304	23	regardless	regardless	RB
randomwalker-info-585	304	24	of	of	IN
randomwalker-info-585	304	25	the	the	DT
randomwalker-info-585	304	26	breakdown	breakdown	NN
randomwalker-info-585	304	27	of	of	IN
randomwalker-info-585	304	28	other	other	JJ
randomwalker-info-585	304	29	miners	miner	NNS
randomwalker-info-585	304	30	in	in	IN
randomwalker-info-585	304	31	any	any	DT
randomwalker-info-585	304	32	simula-	simula-	NN
randomwalker-info-585	304	33	tion	tion	NN
randomwalker-info-585	304	34	where	where	WRB
randomwalker-info-585	304	35	there	there	EX
randomwalker-info-585	304	36	is	be	VBZ
randomwalker-info-585	304	37	enough	enough	JJ
randomwalker-info-585	304	38	latency	latency	NN
randomwalker-info-585	304	39	(	(	-LRB-
randomwalker-info-585	304	40	in	in	IN
randomwalker-info-585	304	41	learning	learning	NN
randomwalker-info-585	304	42	of	of	IN
randomwalker-info-585	304	43	both	both	DT
randomwalker-info-585	304	44	new	new	JJ
randomwalker-info-585	304	45	blocks	block	NNS
randomwalker-info-585	304	46	and	and	CC
randomwalker-info-585	304	47	transactions	transaction	NNS
randomwalker-info-585	304	48	)	)	-RRB-
randomwalker-info-585	304	49	that	that	IN
randomwalker-info-585	304	50	forks	fork	NNS
randomwalker-info-585	304	51	naturally	naturally	RB
randomwalker-info-585	304	52	occur	occur	VBP
randomwalker-info-585	304	53	.	.	.
randomwalker-info-585	305	1	Note	note	VB
randomwalker-info-585	305	2	that	that	IN
randomwalker-info-585	305	3	the	the	DT
randomwalker-info-585	305	4	existence	existence	NN
randomwalker-info-585	305	5	of	of	IN
randomwalker-info-585	305	6	petty	petty	JJ
randomwalker-info-585	305	7	compliant	compliant	JJ
randomwalker-info-585	305	8	miners	miner	NNS
randomwalker-info-585	305	9	is	be	VBZ
randomwalker-info-585	305	10	not	not	RB
randomwalker-info-585	305	11	necessarily	necessarily	RB
randomwalker-info-585	305	12	harmful	harmful	JJ
randomwalker-info-585	305	13	by	by	IN
randomwalker-info-585	305	14	itself	-PRON-	PRP
randomwalker-info-585	305	15	:	:	:
randomwalker-info-585	305	16	so	so	CC
randomwalker-info-585	305	17	what	what	WP
randomwalker-info-585	305	18	if	if	IN
randomwalker-info-585	305	19	miners	miner	NNS
randomwalker-info-585	305	20	are	be	VBP
randomwalker-info-585	305	21	tie-	tie-	RB
randomwalker-info-585	305	22	breaking	break	VBG
randomwalker-info-585	305	23	differently	differently	RB
randomwalker-info-585	305	24	in	in	IN
randomwalker-info-585	305	25	the	the	DT
randomwalker-info-585	305	26	rare	rare	JJ
randomwalker-info-585	305	27	event	event	NN
randomwalker-info-585	305	28	that	that	WDT
randomwalker-info-585	305	29	forks	fork	NNS
randomwalker-info-585	305	30	naturally	naturally	RB
randomwalker-info-585	305	31	occur	occur	VBP
randomwalker-info-585	305	32	?	?	.
randomwalker-info-585	306	1	The	the	DT
randomwalker-info-585	306	2	problem	problem	NN
randomwalker-info-585	306	3	arises	arise	VBZ
randomwalker-info-585	306	4	when	when	WRB
randomwalker-info-585	306	5	other	other	JJ
randomwalker-info-585	306	6	strategic	strategic	JJ
randomwalker-info-585	306	7	miners	miner	NNS
randomwalker-info-585	306	8	no-	no-	RB
randomwalker-info-585	306	9	tice	tice	RB
randomwalker-info-585	306	10	the	the	DT
randomwalker-info-585	306	11	existence	existence	NN
randomwalker-info-585	306	12	of	of	IN
randomwalker-info-585	306	13	petty	petty	JJ
randomwalker-info-585	306	14	compliant	compliant	JJ
randomwalker-info-585	306	15	miners	miner	NNS
randomwalker-info-585	306	16	and	and	CC
randomwalker-info-585	306	17	choose	choose	VB
randomwalker-info-585	306	18	to	to	TO
randomwalker-info-585	306	19	exploit	exploit	VB
randomwalker-info-585	306	20	this	this	DT
randomwalker-info-585	306	21	with	with	IN
randomwalker-info-585	306	22	more	more	RBR
randomwalker-info-585	306	23	aggressive	aggressive	JJ
randomwalker-info-585	306	24	tactics	tactic	NNS
randomwalker-info-585	306	25	.	.	.
randomwalker-info-585	307	1	We	-PRON-	PRP
randomwalker-info-585	307	2	’ll	will	MD
randomwalker-info-585	307	3	see	see	VB
randomwalker-info-585	307	4	some	some	DT
randomwalker-info-585	307	5	examples	example	NNS
randomwalker-info-585	307	6	of	of	IN
randomwalker-info-585	307	7	this	this	DT
randomwalker-info-585	307	8	in	in	IN
randomwalker-info-585	307	9	the	the	DT
randomwalker-info-585	307	10	remainder	remainder	NN
randomwalker-info-585	307	11	of	of	IN
randomwalker-info-585	307	12	this	this	DT
randomwalker-info-585	307	13	section	section	NN
randomwalker-info-585	307	14	.	.	.
randomwalker-info-585	308	1	The	the	DT
randomwalker-info-585	308	2	ex-	ex-	JJ
randomwalker-info-585	308	3	istence	istence	NN
randomwalker-info-585	308	4	of	of	IN
randomwalker-info-585	308	5	PettyCompliant	PettyCompliant	NNP
randomwalker-info-585	308	6	miners	miner	NNS
randomwalker-info-585	308	7	impact	impact	VB
randomwalker-info-585	308	8	other	other	JJ
randomwalker-info-585	308	9	deviant	deviant	NN
randomwalker-info-585	308	10	strategies	strategy	NNS
randomwalker-info-585	308	11	in	in	IN
randomwalker-info-585	308	12	surprising	surprising	JJ
randomwalker-info-585	308	13	ways	way	NNS
randomwalker-info-585	308	14	too	too	RB
randomwalker-info-585	308	15	.	.	.
randomwalker-info-585	309	1	For	for	IN
randomwalker-info-585	309	2	example	example	NN
randomwalker-info-585	309	3	,	,	,
randomwalker-info-585	309	4	a	a	DT
randomwalker-info-585	309	5	selfish	selfish	JJ
randomwalker-info-585	309	6	miner	miner	NN
randomwalker-info-585	309	7	(	(	-LRB-
randomwalker-info-585	309	8	discussed	discuss	VBN
randomwalker-info-585	309	9	more	more	RBR
randomwalker-info-585	309	10	in	in	IN
randomwalker-info-585	309	11	Section	Section	NNP
randomwalker-info-585	309	12	6	6	CD
randomwalker-info-585	309	13	)	)	-RRB-
randomwalker-info-585	309	14	,	,	,
randomwalker-info-585	309	15	performs	perform	VBZ
randomwalker-info-585	309	16	better	better	RB
randomwalker-info-585	309	17	against	against	IN
randomwalker-info-585	309	18	PettyCompliant	PettyCompliant	NNP
randomwalker-info-585	309	19	miners	miner	NNS
randomwalker-info-585	309	20	than	than	IN
randomwalker-info-585	309	21	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	309	22	.	.	.
randomwalker-info-585	310	1	5.2	5.2	CD
randomwalker-info-585	310	2	Phase	phase	NN
randomwalker-info-585	310	3	Two	two	CD
randomwalker-info-585	310	4	:	:	:
randomwalker-info-585	310	5	Lazy	lazy	JJ
randomwalker-info-585	310	6	Undercutting	undercut	VBG
randomwalker-info-585	310	7	Observation	observation	NN
randomwalker-info-585	310	8	:	:	:
randomwalker-info-585	310	9	Once	once	IN
randomwalker-info-585	310	10	some	some	DT
randomwalker-info-585	310	11	fraction	fraction	NN
randomwalker-info-585	310	12	of	of	IN
randomwalker-info-585	310	13	miners	miner	NNS
randomwalker-info-585	310	14	is	be	VBZ
randomwalker-info-585	310	15	petty	petty	JJ
randomwalker-info-585	310	16	compliant	compliant	JJ
randomwalker-info-585	310	17	,	,	,
randomwalker-info-585	310	18	other	other	JJ
randomwalker-info-585	310	19	miners	miner	NNS
randomwalker-info-585	310	20	may	may	MD
randomwalker-info-585	310	21	profit	profit	VB
randomwalker-info-585	310	22	by	by	IN
randomwalker-info-585	310	23	in-	in-	JJ
randomwalker-info-585	310	24	tentionally	tentionally	RB
randomwalker-info-585	310	25	forking	fork	VBG
randomwalker-info-585	310	26	the	the	DT
randomwalker-info-585	310	27	chain	chain	NN
randomwalker-info-585	310	28	.	.	.
randomwalker-info-585	311	1	The	the	DT
randomwalker-info-585	311	2	key	key	JJ
randomwalker-info-585	311	3	insight	insight	NN
randomwalker-info-585	311	4	for	for	IN
randomwalker-info-585	311	5	more	more	RBR
randomwalker-info-585	311	6	aggressive	aggressive	JJ
randomwalker-info-585	311	7	strategies	strategy	NNS
randomwalker-info-585	311	8	is	be	VBZ
randomwalker-info-585	311	9	that	that	IN
randomwalker-info-585	311	10	a	a	DT
randomwalker-info-585	311	11	deviant	deviant	NN
randomwalker-info-585	311	12	miner	miner	NN
randomwalker-info-585	311	13	can	can	MD
randomwalker-info-585	311	14	incentivize	incentivize	VB
randomwalker-info-585	311	15	petty	petty	JJ
randomwalker-info-585	311	16	compliant	compliant	JJ
randomwalker-info-585	311	17	miners	miner	NNS
randomwalker-info-585	311	18	to	to	TO
randomwalker-info-585	311	19	ex-	ex-	RB
randomwalker-info-585	311	20	tend	tend	VB
randomwalker-info-585	311	21	their	-PRON-	PRP$
randomwalker-info-585	311	22	block	block	NN
randomwalker-info-585	311	23	,	,	,
randomwalker-info-585	311	24	even	even	RB
randomwalker-info-585	311	25	if	if	IN
randomwalker-info-585	311	26	an	an	DT
randomwalker-info-585	311	27	older	old	JJR
randomwalker-info-585	311	28	block	block	NN
randomwalker-info-585	311	29	of	of	IN
randomwalker-info-585	311	30	the	the	DT
randomwalker-info-585	311	31	same	same	JJ
randomwalker-info-585	311	32	height	height	NN
randomwalker-info-585	311	33	was	be	VBD
randomwalker-info-585	311	34	discovered	discover	VBN
randomwalker-info-585	311	35	several	several	JJ
randomwalker-info-585	311	36	minutes	minute	NNS
randomwalker-info-585	311	37	earlier	early	RBR
randomwalker-info-585	311	38	,	,	,
randomwalker-info-585	311	39	for	for	IN
randomwalker-info-585	311	40	instance	instance	NN
randomwalker-info-585	311	41	,	,	,
randomwalker-info-585	311	42	by	by	IN
randomwalker-info-585	311	43	ex-	ex-	XX
randomwalker-info-585	311	44	tending	tend	VBG
randomwalker-info-585	311	45	that	that	DT
randomwalker-info-585	311	46	block	block	NN
randomwalker-info-585	311	47	’s	’s	POS
randomwalker-info-585	311	48	direct	direct	JJ
randomwalker-info-585	311	49	predecessor	predecessor	NN
randomwalker-info-585	311	50	and	and	CC
randomwalker-info-585	311	51	including	include	VBG
randomwalker-info-585	311	52	slightly	slightly	RB
randomwalker-info-585	311	53	fewer	few	JJR
randomwalker-info-585	311	54	transaction	transaction	NN
randomwalker-info-585	311	55	fees	fee	NNS
randomwalker-info-585	311	56	.	.	.
randomwalker-info-585	312	1	If	if	IN
randomwalker-info-585	312	2	the	the	DT
randomwalker-info-585	312	3	current	current	JJ
randomwalker-info-585	312	4	unauthorized	unauthorized	JJ
randomwalker-info-585	312	5	transac-	transac-	NN
randomwalker-info-585	312	6	tion	tion	NN
randomwalker-info-585	312	7	fees	fee	NNS
randomwalker-info-585	312	8	are	be	VBP
randomwalker-info-585	312	9	substantially	substantially	RB
randomwalker-info-585	312	10	fewer	few	JJR
randomwalker-info-585	312	11	than	than	IN
randomwalker-info-585	312	12	those	those	DT
randomwalker-info-585	312	13	included	include	VBN
randomwalker-info-585	312	14	by	by	IN
randomwalker-info-585	312	15	the	the	DT
randomwalker-info-585	312	16	current	current	JJ
randomwalker-info-585	312	17	MostH	MostH	NNP
randomwalker-info-585	312	18	,	,	,
randomwalker-info-585	312	19	then	then	RB
randomwalker-info-585	312	20	maybe	maybe	RB
randomwalker-info-585	312	21	it	-PRON-	PRP
randomwalker-info-585	312	22	is	be	VBZ
randomwalker-info-585	312	23	in	in	IN
randomwalker-info-585	312	24	a	a	DT
randomwalker-info-585	312	25	miner	miner	NN
randomwalker-info-585	312	26	’s	’s	POS
randomwalker-info-585	312	27	interest	interest	NN
randomwalker-info-585	312	28	to	to	TO
randomwalker-info-585	312	29	try	try	VB
randomwalker-info-585	312	30	and	and	CC
randomwalker-info-585	312	31	replace	replace	VB
randomwalker-info-585	312	32	MostH	MostH	NNP
randomwalker-info-585	312	33	with	with	IN
randomwalker-info-585	312	34	a	a	DT
randomwalker-info-585	312	35	new	new	JJ
randomwalker-info-585	312	36	block	block	NN
randomwalker-info-585	312	37	of	of	IN
randomwalker-info-585	312	38	height	height	NN
randomwalker-info-585	312	39	H	h	NN
randomwalker-info-585	312	40	,	,	,
randomwalker-info-585	312	41	instead	instead	RB
randomwalker-info-585	312	42	of	of	IN
randomwalker-info-585	312	43	continuing	continue	VBG
randomwalker-info-585	312	44	on	on	IN
randomwalker-info-585	312	45	top	top	NN
randomwalker-info-585	312	46	of	of	IN
randomwalker-info-585	312	47	it	-PRON-	PRP
randomwalker-info-585	312	48	.	.	.
randomwalker-info-585	313	1	We	-PRON-	PRP
randomwalker-info-585	313	2	call	call	VBP
randomwalker-info-585	313	3	this	this	DT
randomwalker-info-585	313	4	undercutting	undercutting	NN
randomwalker-info-585	313	5	.	.	.
randomwalker-info-585	314	1	So	so	RB
randomwalker-info-585	314	2	what	what	WP
randomwalker-info-585	314	3	might	may	MD
randomwalker-info-585	314	4	a	a	DT
randomwalker-info-585	314	5	strategic	strategic	JJ
randomwalker-info-585	314	6	miner	miner	NN
randomwalker-info-585	314	7	do	do	VB
randomwalker-info-585	314	8	to	to	TO
randomwalker-info-585	314	9	take	take	VB
randomwalker-info-585	314	10	advantage	advantage	NN
randomwalker-info-585	314	11	of	of	IN
randomwalker-info-585	314	12	this	this	DT
randomwalker-info-585	314	13	?	?	.
randomwalker-info-585	315	1	They	-PRON-	PRP
randomwalker-info-585	315	2	might	may	MD
randomwalker-info-585	315	3	first	first	RB
randomwalker-info-585	315	4	compare	compare	VB
randomwalker-info-585	315	5	between	between	IN
randomwalker-info-585	315	6	the	the	DT
randomwalker-info-585	315	7	maximum	maximum	JJ
randomwalker-info-585	315	8	rewards	reward	NNS
randomwalker-info-585	315	9	they	-PRON-	PRP
randomwalker-info-585	315	10	could	could	MD
randomwalker-info-585	315	11	get	get	VB
randomwalker-info-585	315	12	by	by	IN
randomwalker-info-585	315	13	continuing	continue	VBG
randomwalker-info-585	315	14	versus	versus	IN
randomwalker-info-585	315	15	undercutting	undercutting	NN
randomwalker-info-585	315	16	(	(	-LRB-
randomwalker-info-585	315	17	while	while	IN
randomwalker-info-585	315	18	still	still	RB
randomwalker-info-585	315	19	becoming	become	VBG
randomwalker-info-585	315	20	the	the	DT
randomwalker-info-585	315	21	new	new	JJ
randomwalker-info-585	315	22	MostH	MostH	NNP
randomwalker-info-585	315	23	)	)	-RRB-
randomwalker-info-585	315	24	,	,	,
randomwalker-info-585	315	25	and	and	CC
randomwalker-info-585	315	26	mine	mine	NN
randomwalker-info-585	315	27	on	on	IN
randomwalker-info-585	315	28	top	top	NN
randomwalker-info-585	315	29	of	of	IN
randomwalker-info-585	315	30	whichever	whichever	WDT
randomwalker-info-585	315	31	block	block	NN
randomwalker-info-585	315	32	yields	yield	NNS
randomwalker-info-585	315	33	greater	great	JJR
randomwalker-info-585	315	34	rewards	reward	NNS
randomwalker-info-585	315	35	.	.	.
randomwalker-info-585	316	1	Then	then	RB
randomwalker-info-585	316	2	,	,	,
randomwalker-info-585	316	3	to	to	TO
randomwalker-info-585	316	4	protect	protect	VB
randomwalker-info-585	316	5	themselves	-PRON-	PRP
randomwalker-info-585	316	6	with	with	IN
randomwalker-info-585	316	7	certainty	certainty	NN
randomwalker-info-585	316	8	against	against	IN
randomwalker-info-585	316	9	future	future	JJ
randomwalker-info-585	316	10	undercutters	undercutter	NNS
randomwalker-info-585	316	11	using	use	VBG
randomwalker-info-585	316	12	the	the	DT
randomwalker-info-585	316	13	same	same	JJ
randomwalker-info-585	316	14	rule	rule	NN
randomwalker-info-585	316	15	,	,	,
randomwalker-info-585	316	16	they	-PRON-	PRP
randomwalker-info-585	316	17	could	could	MD
randomwalker-info-585	316	18	take	take	VB
randomwalker-info-585	316	19	half	half	NN
randomwalker-info-585	316	20	of	of	IN
randomwalker-info-585	316	21	the	the	DT
randomwalker-info-585	316	22	remaining	remain	VBG
randomwalker-info-585	316	23	transac-	transac-	NN
randomwalker-info-585	316	24	tions	tion	NNS
randomwalker-info-585	316	25	.	.	.
randomwalker-info-585	317	1	Because	because	IN
randomwalker-info-585	317	2	of	of	IN
randomwalker-info-585	317	3	the	the	DT
randomwalker-info-585	317	4	somewhat	somewhat	RB
randomwalker-info-585	317	5	lax	lax	JJ
randomwalker-info-585	317	6	reasoning	reasoning	NN
randomwalker-info-585	317	7	used	use	VBN
randomwalker-info-585	317	8	to	to	TO
randomwalker-info-585	317	9	choose	choose	VB
randomwalker-info-585	317	10	these	these	DT
randomwalker-info-585	317	11	parameters	parameter	NNS
randomwalker-info-585	317	12	,	,	,
randomwalker-info-585	317	13	we	-PRON-	PRP
randomwalker-info-585	317	14	call	call	VBP
randomwalker-info-585	317	15	this	this	DT
randomwalker-info-585	317	16	strategy	strategy	NN
randomwalker-info-585	317	17	LazyFork	LazyFork	NNP
randomwalker-info-585	317	18	.	.	.
randomwalker-info-585	318	1	While	while	IN
randomwalker-info-585	318	2	the	the	DT
randomwalker-info-585	318	3	existence	existence	NN
randomwalker-info-585	318	4	of	of	IN
randomwalker-info-585	318	5	PettyCompliant	PettyCompliant	NNP
randomwalker-info-585	318	6	miners	miner	NNS
randomwalker-info-585	318	7	them-	them-	NN
randomwalker-info-585	318	8	selves	self	NNS
randomwalker-info-585	318	9	is	be	VBZ
randomwalker-info-585	318	10	relatively	relatively	RB
randomwalker-info-585	318	11	benign	benign	JJ
randomwalker-info-585	318	12	,	,	,
randomwalker-info-585	318	13	the	the	DT
randomwalker-info-585	318	14	existence	existence	NN
randomwalker-info-585	318	15	of	of	IN
randomwalker-info-585	318	16	LazyFork	LazyFork	NNP
randomwalker-info-585	318	17	min-	min-	JJ
randomwalker-info-585	318	18	ers	er	NNS
randomwalker-info-585	318	19	would	would	MD
randomwalker-info-585	318	20	be	be	VB
randomwalker-info-585	318	21	bad	bad	JJ
randomwalker-info-585	318	22	:	:	:
randomwalker-info-585	318	23	they	-PRON-	PRP
randomwalker-info-585	318	24	frequently	frequently	RB
randomwalker-info-585	318	25	decide	decide	VBP
randomwalker-info-585	318	26	to	to	TO
randomwalker-info-585	318	27	intentionally	intentionally	RB
randomwalker-info-585	318	28	orphan	orphan	VB
randomwalker-info-585	318	29	blocks	block	NNS
randomwalker-info-585	318	30	in	in	IN
randomwalker-info-585	318	31	order	order	NN
randomwalker-info-585	318	32	to	to	TO
randomwalker-info-585	318	33	achieve	achieve	VB
randomwalker-info-585	318	34	greater	great	JJR
randomwalker-info-585	318	35	rewards	reward	NNS
randomwalker-info-585	318	36	.	.	.
randomwalker-info-585	319	1	In	in	IN
randomwalker-info-585	319	2	addi-	addi-	JJ
randomwalker-info-585	319	3	tion	tion	NN
randomwalker-info-585	319	4	to	to	IN
randomwalker-info-585	319	5	creating	create	VBG
randomwalker-info-585	319	6	uncertainty	uncertainty	NN
randomwalker-info-585	319	7	about	about	IN
randomwalker-info-585	319	8	when	when	WRB
randomwalker-info-585	319	9	blocks	block	NNS
randomwalker-info-585	319	10	are	be	VBP
randomwalker-info-585	319	11	“	"	``
randomwalker-info-585	319	12	safely	safely	RB
randomwalker-info-585	319	13	”	"	''
randomwalker-info-585	319	14	in	in	IN
randomwalker-info-585	319	15	the	the	DT
randomwalker-info-585	319	16	eventual	eventual	JJ
randomwalker-info-585	319	17	longest	long	JJS
randomwalker-info-585	319	18	chain	chain	NN
randomwalker-info-585	319	19	,	,	,
randomwalker-info-585	319	20	this	this	DT
randomwalker-info-585	319	21	decreases	decrease	VBZ
randomwalker-info-585	319	22	the	the	DT
randomwalker-info-585	319	23	effective	effective	JJ
randomwalker-info-585	319	24	hash	hash	NN
randomwalker-info-585	319	25	power	power	NN
randomwalker-info-585	319	26	of	of	IN
randomwalker-info-585	319	27	the	the	DT
randomwalker-info-585	319	28	network	network	NN
randomwalker-info-585	319	29	and	and	CC
randomwalker-info-585	319	30	makes	make	VBZ
randomwalker-info-585	319	31	Bitcoin	Bitcoin	NNP
randomwalker-info-585	319	32	more	more	RBR
randomwalker-info-585	319	33	prone	prone	JJ
randomwalker-info-585	319	34	to	to	TO
randomwalker-info-585	319	35	double	double	VB
randomwalker-info-585	319	36	spend	spend	NN
randomwalker-info-585	319	37	attacks	attack	NNS
randomwalker-info-585	319	38	.	.	.
randomwalker-info-585	320	1	For	for	IN
randomwalker-info-585	320	2	cleanliness	cleanliness	NN
randomwalker-info-585	320	3	in	in	IN
randomwalker-info-585	320	4	formally	formally	RB
randomwalker-info-585	320	5	defining	define	VBG
randomwalker-info-585	320	6	LazyFork	LazyFork	NNP
randomwalker-info-585	320	7	and	and	CC
randomwalker-info-585	320	8	other	other	JJ
randomwalker-info-585	320	9	undercutting	undercutting	NN
randomwalker-info-585	320	10	strategies	strategy	NNS
randomwalker-info-585	320	11	,	,	,
randomwalker-info-585	320	12	we	-PRON-	PRP
randomwalker-info-585	320	13	introduce	introduce	VBP
randomwalker-info-585	320	14	the	the	DT
randomwalker-info-585	320	15	notation	notation	NN
randomwalker-info-585	320	16	Gapi	Gapi	NNP
randomwalker-info-585	320	17	=	=	SYM
randomwalker-info-585	320	18	Rem(Mosti−1	Rem(Mosti−1	NNP
randomwalker-info-585	320	19	)	)	-RRB-
randomwalker-info-585	320	20	−	−	NNP
randomwalker-info-585	320	21	Rem(Mosti	Rem(Mosti	NNP
randomwalker-info-585	320	22	)	)	-RRB-
randomwalker-info-585	320	23	,	,	,
randomwalker-info-585	320	24	the	the	DT
randomwalker-info-585	320	25	maximum	maximum	JJ
randomwalker-info-585	320	26	transaction	transaction	NN
randomwalker-info-585	320	27	fees	fee	VBZ
randomwalker-info-585	320	28	that	that	IN
randomwalker-info-585	320	29	a	a	DT
randomwalker-info-585	320	30	miner	miner	NN
randomwalker-info-585	320	31	could	could	MD
randomwalker-info-585	320	32	include	include	VB
randomwalker-info-585	320	33	while	while	IN
randomwalker-info-585	320	34	mining	mine	VBG
randomwalker-info-585	320	35	on	on	IN
randomwalker-info-585	320	36	top	top	NN
randomwalker-info-585	320	37	of	of	IN
randomwalker-info-585	320	38	Mosti−1	mosti−1	NN
randomwalker-info-585	320	39	to	to	TO
randomwalker-info-585	320	40	become	become	VB
randomwalker-info-585	320	41	the	the	DT
randomwalker-info-585	320	42	new	new	JJ
randomwalker-info-585	320	43	Mosti	Mosti	NNP
randomwalker-info-585	320	44	.	.	.
randomwalker-info-585	321	1	LazyFork	LazyFork	NNP
randomwalker-info-585	321	2	:	:	:
randomwalker-info-585	321	3	Forks	fork	NNS
randomwalker-info-585	321	4	the	the	DT
randomwalker-info-585	321	5	blockchain	blockchain	NN
randomwalker-info-585	321	6	if	if	IN
randomwalker-info-585	321	7	the	the	DT
randomwalker-info-585	321	8	head	head	NN
randomwalker-info-585	321	9	block	block	NN
randomwalker-info-585	321	10	is	be	VBZ
randomwalker-info-585	321	11	more	more	RBR
randomwalker-info-585	321	12	valuable	valuable	JJ
randomwalker-info-585	321	13	than	than	IN
randomwalker-info-585	321	14	the	the	DT
randomwalker-info-585	321	15	unclaimed	unclaimed	JJ
randomwalker-info-585	321	16	transaction	transaction	NN
randomwalker-info-585	321	17	fees	fee	NNS
randomwalker-info-585	321	18	it	-PRON-	PRP
randomwalker-info-585	321	19	leaves	leave	VBZ
randomwalker-info-585	321	20	behind	behind	RB
randomwalker-info-585	321	21	.	.	.
randomwalker-info-585	322	1	Only	only	RB
randomwalker-info-585	322	2	takes	take	VBZ
randomwalker-info-585	322	3	half	half	NN
randomwalker-info-585	322	4	of	of	IN
randomwalker-info-585	322	5	the	the	DT
randomwalker-info-585	322	6	possible	possible	JJ
randomwalker-info-585	322	7	transaction	transaction	NN
randomwalker-info-585	322	8	fees	fee	NNS
randomwalker-info-585	322	9	to	to	TO
randomwalker-info-585	322	10	prevent	prevent	VB
randomwalker-info-585	322	11	other	other	JJ
randomwalker-info-585	322	12	lazy	lazy	JJ
randomwalker-info-585	322	13	forkers	forker	NNS
randomwalker-info-585	322	14	from	from	IN
randomwalker-info-585	322	15	forking	fork	VBG
randomwalker-info-585	322	16	their	-PRON-	PRP$
randomwalker-info-585	322	17	block	block	NN
randomwalker-info-585	322	18	.	.	.
randomwalker-info-585	323	1	Which	which	WDT
randomwalker-info-585	323	2	Block	Block	NNP
randomwalker-info-585	323	3	:	:	:
randomwalker-info-585	323	4	if	if	IN
randomwalker-info-585	323	5	Owner(MostmH	Owner(MostmH	NNS
randomwalker-info-585	323	6	)	)	-RRB-
randomwalker-info-585	323	7	=	=	NFP
randomwalker-info-585	323	8	m	m	NNP
randomwalker-info-585	323	9	or	or	CC
randomwalker-info-585	323	10	Rem(Most	Rem(Most	NNP
randomwalker-info-585	323	11	m	m	NNP
randomwalker-info-585	323	12	H	h	NN
randomwalker-info-585	323	13	)	)	-RRB-
randomwalker-info-585	323	14	≥	≥	UH
randomwalker-info-585	323	15	GapH	GapH	NNP
randomwalker-info-585	323	16	Mining(m	mining(m	CD
randomwalker-info-585	323	17	)	)	-RRB-
randomwalker-info-585	323	18	=	=	NFP
randomwalker-info-585	323	19	MostmH	MostmH	NNS
randomwalker-info-585	323	20	.	.	.
randomwalker-info-585	324	1	else	else	RB
randomwalker-info-585	324	2	Mining(m	Mining(m	NNP
randomwalker-info-585	324	3	)	)	-RRB-
randomwalker-info-585	324	4	=	=	NFP
randomwalker-info-585	324	5	MostmH−1	MostmH−1	NNP
randomwalker-info-585	324	6	.	.	.
randomwalker-info-585	325	1	How	how	WRB
randomwalker-info-585	325	2	much	much	JJ
randomwalker-info-585	325	3	:	:	:
randomwalker-info-585	325	4	include	include	VB
randomwalker-info-585	325	5	Rem(Mining(m))/2	rem(mining(m))/2	CD
randomwalker-info-585	325	6	.	.	.
randomwalker-info-585	326	1	Publish(B	Publish(B	VBN
randomwalker-info-585	326	2	)	)	-RRB-
randomwalker-info-585	326	3	?	?	.
randomwalker-info-585	327	1	:	:	:
randomwalker-info-585	327	2	yes	yes	UH
randomwalker-info-585	327	3	.	.	.
randomwalker-info-585	328	1	5.3	5.3	CD
randomwalker-info-585	328	2	Phase	phase	NN
randomwalker-info-585	328	3	Three	three	CD
randomwalker-info-585	328	4	:	:	:
randomwalker-info-585	328	5	Aggressive	aggressive	JJ
randomwalker-info-585	328	6	Undercutting	undercutting	NN
randomwalker-info-585	328	7	Simulation	Simulation	NNP
randomwalker-info-585	328	8	result	result	NN
randomwalker-info-585	328	9	:	:	:
randomwalker-info-585	328	10	increasingly	increasingly	RB
randomwalker-info-585	328	11	aggressive	aggressive	JJ
randomwalker-info-585	328	12	under-	under-	NN
randomwalker-info-585	328	13	cutting	cut	VBG
randomwalker-info-585	328	14	behavior	behavior	NN
randomwalker-info-585	328	15	evolves	evolve	NNS
randomwalker-info-585	328	16	when	when	WRB
randomwalker-info-585	328	17	miners	miner	NNS
randomwalker-info-585	328	18	strategize	strategize	VBP
randomwalker-info-585	328	19	.	.	.
randomwalker-info-585	329	1	Once	once	IN
randomwalker-info-585	329	2	miners	miner	NNS
randomwalker-info-585	329	3	consider	consider	VBP
randomwalker-info-585	329	4	undercutting	undercut	VBG
randomwalker-info-585	329	5	,	,	,
randomwalker-info-585	329	6	they	-PRON-	PRP
randomwalker-info-585	329	7	may	may	MD
randomwalker-info-585	329	8	also	also	RB
randomwalker-info-585	329	9	try	try	VB
randomwalker-info-585	329	10	to	to	TO
randomwalker-info-585	329	11	aggressively	aggressively	RB
randomwalker-info-585	329	12	optimize	optimize	VB
randomwalker-info-585	329	13	the	the	DT
randomwalker-info-585	329	14	tradeoff	tradeoff	NN
randomwalker-info-585	329	15	between	between	IN
randomwalker-info-585	329	16	maximizing	maximize	VBG
randomwalker-info-585	329	17	the	the	DT
randomwalker-info-585	329	18	transaction	transaction	NN
randomwalker-info-585	329	19	fees	fee	NNS
randomwalker-info-585	329	20	included	include	VBN
randomwalker-info-585	329	21	in	in	IN
randomwalker-info-585	329	22	blocks	block	NNS
randomwalker-info-585	329	23	they	-PRON-	PRP
randomwalker-info-585	329	24	mine	mine	VBP
randomwalker-info-585	329	25	and	and	CC
randomwalker-info-585	329	26	minimizing	minimize	VBG
randomwalker-info-585	329	27	the	the	DT
randomwalker-info-585	329	28	chance	chance	NN
randomwalker-info-585	329	29	that	that	IN
randomwalker-info-585	329	30	their	-PRON-	PRP$
randomwalker-info-585	329	31	block	block	NN
randomwalker-info-585	329	32	will	will	MD
randomwalker-info-585	329	33	be	be	VB
randomwalker-info-585	329	34	undercut	undercut	JJ
randomwalker-info-585	329	35	by	by	IN
randomwalker-info-585	329	36	other	other	JJ
randomwalker-info-585	329	37	miners	miner	NNS
randomwalker-info-585	329	38	in	in	IN
randomwalker-info-585	329	39	the	the	DT
randomwalker-info-585	329	40	system	system	NN
randomwalker-info-585	329	41	(	(	-LRB-
randomwalker-info-585	329	42	as	as	IN
randomwalker-info-585	329	43	opposed	oppose	VBN
randomwalker-info-585	329	44	to	to	IN
randomwalker-info-585	329	45	using	use	VBG
randomwalker-info-585	329	46	the	the	DT
randomwalker-info-585	329	47	less	less	RBR
randomwalker-info-585	329	48	-	-	HYPH
randomwalker-info-585	329	49	principled	principle	VBN
randomwalker-info-585	329	50	reason-	reason-	NN
randomwalker-info-585	329	51	ing	ing	NN
randomwalker-info-585	329	52	of	of	IN
randomwalker-info-585	329	53	LazyFork	LazyFork	NNP
randomwalker-info-585	329	54	)	)	-RRB-
randomwalker-info-585	329	55	.	.	.
randomwalker-info-585	330	1	We	-PRON-	PRP
randomwalker-info-585	330	2	define	define	VBP
randomwalker-info-585	330	3	these	these	DT
randomwalker-info-585	330	4	strategies	strategy	NNS
randomwalker-info-585	330	5	so	so	IN
randomwalker-info-585	330	6	that	that	IN
randomwalker-info-585	330	7	when	when	WRB
randomwalker-info-585	330	8	they	-PRON-	PRP
randomwalker-info-585	330	9	are	be	VBP
randomwalker-info-585	330	10	presented	present	VBN
randomwalker-info-585	330	11	with	with	IN
randomwalker-info-585	330	12	Rem(Mining(m	Rem(Mining(m	NNP
randomwalker-info-585	330	13	)	)	-RRB-
randomwalker-info-585	330	14	)	)	-RRB-
randomwalker-info-585	330	15	=	=	NFP
randomwalker-info-585	330	16	x	x	LS
randomwalker-info-585	330	17	,	,	,
randomwalker-info-585	330	18	they	-PRON-	PRP
randomwalker-info-585	330	19	will	will	MD
randomwalker-info-585	330	20	authorize	authorize	VB
randomwalker-info-585	330	21	f(x	f(x	ADD
randomwalker-info-585	330	22	)	)	-RRB-
randomwalker-info-585	330	23	transactions	transaction	NNS
randomwalker-info-585	330	24	,	,	,
randomwalker-info-585	330	25	for	for	IN
randomwalker-info-585	330	26	some	some	DT
randomwalker-info-585	330	27	f	f	NN
randomwalker-info-585	330	28	(	(	-LRB-
randomwalker-info-585	330	29	·	·	NFP
randomwalker-info-585	330	30	)	)	-RRB-
randomwalker-info-585	330	31	with	with	IN
randomwalker-info-585	330	32	f(x	f(x	NNP
randomwalker-info-585	330	33	)	)	-RRB-
randomwalker-info-585	330	34	∈	∈	IN
randomwalker-info-585	330	35	[	[	-LRB-
randomwalker-info-585	330	36	0,x	0,x	CD
randomwalker-info-585	330	37	]	]	-RRB-
randomwalker-info-585	330	38	for	for	IN
randomwalker-info-585	330	39	all	all	DT
randomwalker-info-585	330	40	x	x	NN
randomwalker-info-585	330	41	,	,	,
randomwalker-info-585	330	42	and	and	CC
randomwalker-info-585	330	43	call	call	VB
randomwalker-info-585	330	44	them	-PRON-	PRP
randomwalker-info-585	330	45	forkers	forker	NNS
randomwalker-info-585	330	46	.	.	.
randomwalker-info-585	331	1	While	while	IN
randomwalker-info-585	331	2	in	in	IN
randomwalker-info-585	331	3	principle	principle	NN
randomwalker-info-585	331	4	,	,	,
randomwalker-info-585	331	5	forkers	forker	NNS
randomwalker-info-585	331	6	could	could	MD
randomwalker-info-585	331	7	consider	consider	VB
randomwalker-info-585	331	8	going	go	VBG
randomwalker-info-585	331	9	back	back	RB
randomwalker-info-585	331	10	sev-	sev-	JJ
randomwalker-info-585	331	11	eral	eral	JJ
randomwalker-info-585	331	12	blocks	block	NNS
randomwalker-info-585	331	13	to	to	IN
randomwalker-info-585	331	14	undercut	undercut	VB
randomwalker-info-585	331	15	,	,	,
randomwalker-info-585	331	16	the	the	DT
randomwalker-info-585	331	17	strategies	strategy	NNS
randomwalker-info-585	331	18	we	-PRON-	PRP
randomwalker-info-585	331	19	study	study	VBP
randomwalker-info-585	331	20	only	only	RB
randomwalker-info-585	331	21	consider	consider	VBP
randomwalker-info-585	331	22	mining	mine	VBG
randomwalker-info-585	331	23	on	on	IN
randomwalker-info-585	331	24	top	top	NN
randomwalker-info-585	331	25	of	of	IN
randomwalker-info-585	331	26	a	a	DT
randomwalker-info-585	331	27	block	block	NN
randomwalker-info-585	331	28	of	of	IN
randomwalker-info-585	331	29	height	height	NN
randomwalker-info-585	331	30	H	h	NN
randomwalker-info-585	331	31	or	or	CC
randomwalker-info-585	331	32	H	h	NN
randomwalker-info-585	331	33	−	−	NNP
randomwalker-info-585	331	34	1	1	CD
randomwalker-info-585	331	35	.	.	.
randomwalker-info-585	332	1	Certainly	certainly	RB
randomwalker-info-585	332	2	,	,	,
randomwalker-info-585	332	3	it	-PRON-	PRP
randomwalker-info-585	332	4	would	would	MD
randomwalker-info-585	332	5	be	be	VB
randomwalker-info-585	332	6	an	an	DT
randomwalker-info-585	332	7	interesting	interesting	JJ
randomwalker-info-585	332	8	direction	direction	NN
randomwalker-info-585	332	9	for	for	IN
randomwalker-info-585	332	10	future	future	JJ
randomwalker-info-585	332	11	work	work	NN
randomwalker-info-585	332	12	to	to	TO
randomwalker-info-585	332	13	see	see	VB
randomwalker-info-585	332	14	if	if	IN
randomwalker-info-585	332	15	any	any	DT
randomwalker-info-585	332	16	additional	additional	JJ
randomwalker-info-585	332	17	gains	gain	NNS
randomwalker-info-585	332	18	can	can	MD
randomwalker-info-585	332	19	be	be	VB
randomwalker-info-585	332	20	achieved	achieve	VBN
randomwalker-info-585	332	21	by	by	IN
randomwalker-info-585	332	22	considering	consider	VBG
randomwalker-info-585	332	23	blocks	block	NNS
randomwalker-info-585	332	24	of	of	IN
randomwalker-info-585	332	25	height	height	NN
randomwalker-info-585	332	26	H	h	NN
randomwalker-info-585	332	27	−	−	NNP
randomwalker-info-585	332	28	2	2	CD
randomwalker-info-585	332	29	or	or	CC
randomwalker-info-585	332	30	less	less	JJR
randomwalker-info-585	332	31	,	,	,
randomwalker-info-585	332	32	but	but	CC
randomwalker-info-585	332	33	already	already	RB
randomwalker-info-585	332	34	we	-PRON-	PRP
randomwalker-info-585	332	35	uncover	uncover	VBP
randomwalker-info-585	332	36	interesting	interesting	JJ
randomwalker-info-585	332	37	behavior	behavior	NN
randomwalker-info-585	332	38	when	when	WRB
randomwalker-info-585	332	39	forkers	forker	NNS
randomwalker-info-585	332	40	go	go	VBP
randomwalker-info-585	332	41	back	back	RB
randomwalker-info-585	332	42	just	just	RB
randomwalker-info-585	332	43	a	a	DT
randomwalker-info-585	332	44	single	single	JJ
randomwalker-info-585	332	45	block	block	NN
randomwalker-info-585	332	46	.	.	.
randomwalker-info-585	333	1	A	a	DT
randomwalker-info-585	333	2	function	function	NN
randomwalker-info-585	333	3	forking	fork	VBG
randomwalker-info-585	333	4	miner	miner	NN
randomwalker-info-585	333	5	looks	look	VBZ
randomwalker-info-585	333	6	at	at	IN
randomwalker-info-585	333	7	potential	potential	JJ
randomwalker-info-585	333	8	blocks	block	NNS
randomwalker-info-585	333	9	at	at	IN
randomwalker-info-585	333	10	height	height	NN
randomwalker-info-585	333	11	H	h	NN
randomwalker-info-585	333	12	that	that	IN
randomwalker-info-585	333	13	they	-PRON-	PRP
randomwalker-info-585	333	14	could	could	MD
randomwalker-info-585	333	15	extend	extend	VB
randomwalker-info-585	333	16	,	,	,
randomwalker-info-585	333	17	and	and	CC
randomwalker-info-585	333	18	within	within	IN
randomwalker-info-585	333	19	this	this	DT
randomwalker-info-585	333	20	set	set	NN
randomwalker-info-585	333	21	considers	consider	NNS
randomwalker-info-585	333	22	ex-	ex-	XX
randomwalker-info-585	333	23	tending	tend	VBG
randomwalker-info-585	333	24	only	only	RB
randomwalker-info-585	333	25	MostmH	MostmH	NNS
randomwalker-info-585	333	26	,	,	,
randomwalker-info-585	333	27	since	since	IN
randomwalker-info-585	333	28	it	-PRON-	PRP
randomwalker-info-585	333	29	leaves	leave	VBZ
randomwalker-info-585	333	30	the	the	DT
randomwalker-info-585	333	31	most	most	RBS
randomwalker-info-585	333	32	remaining	remaining	JJ
randomwalker-info-585	333	33	transaction	transaction	NN
randomwalker-info-585	333	34	fees	fee	NNS
randomwalker-info-585	333	35	.	.	.
randomwalker-info-585	334	1	If	if	IN
randomwalker-info-585	334	2	a	a	DT
randomwalker-info-585	334	3	miner	miner	NN
randomwalker-info-585	334	4	indeed	indeed	RB
randomwalker-info-585	334	5	chooses	choose	VBZ
randomwalker-info-585	334	6	to	to	IN
randomwalker-info-585	334	7	mine	-PRON-	PRP
randomwalker-info-585	334	8	on	on	IN
randomwalker-info-585	334	9	top	top	NN
randomwalker-info-585	334	10	of	of	IN
randomwalker-info-585	334	11	MostmH	MostmH	NNS
randomwalker-info-585	334	12	,	,	,
randomwalker-info-585	334	13	we	-PRON-	PRP
randomwalker-info-585	334	14	call	call	VBP
randomwalker-info-585	334	15	this	this	DT
randomwalker-info-585	334	16	continuing	continuing	NN
randomwalker-info-585	334	17	.	.	.
randomwalker-info-585	335	1	They	-PRON-	PRP
randomwalker-info-585	335	2	also	also	RB
randomwalker-info-585	335	3	look	look	VBP
randomwalker-info-585	335	4	at	at	IN
randomwalker-info-585	335	5	poten-	poten-	NNP
randomwalker-info-585	335	6	tial	tial	JJ
randomwalker-info-585	335	7	blocks	block	NNS
randomwalker-info-585	335	8	of	of	IN
randomwalker-info-585	335	9	height	height	NN
randomwalker-info-585	335	10	H−1	h−1	CD
randomwalker-info-585	335	11	,	,	,
randomwalker-info-585	335	12	again	again	RB
randomwalker-info-585	335	13	considering	consider	VBG
randomwalker-info-585	335	14	only	only	RB
randomwalker-info-585	335	15	extending	extend	VBG
randomwalker-info-585	335	16	the	the	DT
randomwalker-info-585	335	17	block	block	NN
randomwalker-info-585	335	18	MostmH−1	MostmH−1	NNP
randomwalker-info-585	335	19	from	from	IN
randomwalker-info-585	335	20	this	this	DT
randomwalker-info-585	335	21	set	set	NN
randomwalker-info-585	335	22	.	.	.
randomwalker-info-585	336	1	If	if	IN
randomwalker-info-585	336	2	a	a	DT
randomwalker-info-585	336	3	miner	miner	NN
randomwalker-info-585	336	4	indeed	indeed	RB
randomwalker-info-585	336	5	chooses	choose	VBZ
randomwalker-info-585	336	6	to	to	IN
randomwalker-info-585	336	7	mine	-PRON-	PRP
randomwalker-info-585	336	8	on	on	IN
randomwalker-info-585	336	9	top	top	NN
randomwalker-info-585	336	10	of	of	IN
randomwalker-info-585	336	11	MostmH−1	MostmH−1	NNP
randomwalker-info-585	336	12	,	,	,
randomwalker-info-585	336	13	we	-PRON-	PRP
randomwalker-info-585	336	14	call	call	VBP
randomwalker-info-585	336	15	this	this	DT
randomwalker-info-585	336	16	undercutting	undercutting	NN
randomwalker-info-585	336	17	.	.	.
randomwalker-info-585	337	1	When	when	WRB
randomwalker-info-585	337	2	deciding	decide	VBG
randomwalker-info-585	337	3	whether	whether	IN
randomwalker-info-585	337	4	to	to	TO
randomwalker-info-585	337	5	continue	continue	VB
randomwalker-info-585	337	6	or	or	CC
randomwalker-info-585	337	7	undercut	undercut	VB
randomwalker-info-585	337	8	,	,	,
randomwalker-info-585	337	9	a	a	DT
randomwalker-info-585	337	10	forker	forker	NN
randomwalker-info-585	337	11	simply	simply	RB
randomwalker-info-585	337	12	observes	observe	VBZ
randomwalker-info-585	337	13	that	that	IN
randomwalker-info-585	337	14	they	-PRON-	PRP
randomwalker-info-585	337	15	will	will	MD
randomwalker-info-585	337	16	choose	choose	VB
randomwalker-info-585	337	17	to	to	TO
randomwalker-info-585	337	18	claim	claim	VB
randomwalker-info-585	337	19	f(Rem(MostmH	f(Rem(MostmH	.
randomwalker-info-585	337	20	)	)	-RRB-
randomwalker-info-585	337	21	)	)	-RRB-
randomwalker-info-585	337	22	by	by	IN
randomwalker-info-585	337	23	continuing	continue	VBG
randomwalker-info-585	337	24	,	,	,
randomwalker-info-585	337	25	versus	versus	IN
randomwalker-info-585	337	26	min{f(Rem(MostmH−1)),GapH	min{f(Rem(MostmH−1)),GapH	NNP
randomwalker-info-585	337	27	}	}	-RRB-
randomwalker-info-585	337	28	if	if	IN
randomwalker-info-585	337	29	they	-PRON-	PRP
randomwalker-info-585	337	30	undercut	undercut	VBP
randomwalker-info-585	337	31	(	(	-LRB-
randomwalker-info-585	337	32	the	the	DT
randomwalker-info-585	337	33	min	min	NN
randomwalker-info-585	337	34	is	be	VBZ
randomwalker-info-585	337	35	taken	take	VBN
randomwalker-info-585	337	36	because	because	IN
randomwalker-info-585	337	37	they	-PRON-	PRP
randomwalker-info-585	337	38	must	must	MD
randomwalker-info-585	337	39	actually	actually	RB
randomwalker-info-585	337	40	un-	un-	VB
randomwalker-info-585	337	41	dercut	dercut	NN
randomwalker-info-585	337	42	in	in	IN
randomwalker-info-585	337	43	order	order	NN
randomwalker-info-585	337	44	to	to	TO
randomwalker-info-585	337	45	incentivize	incentivize	VB
randomwalker-info-585	337	46	future	future	JJ
randomwalker-info-585	337	47	miners	miner	NNS
randomwalker-info-585	337	48	to	to	TO
randomwalker-info-585	337	49	select	select	VB
randomwalker-info-585	337	50	their	-PRON-	PRP$
randomwalker-info-585	337	51	Figure	figure	NN
randomwalker-info-585	337	52	3	3	CD
randomwalker-info-585	337	53	:	:	:
randomwalker-info-585	337	54	Normalized	normalized	JJ
randomwalker-info-585	337	55	weights	weight	NNS
randomwalker-info-585	337	56	of	of	IN
randomwalker-info-585	337	57	different	different	JJ
randomwalker-info-585	337	58	linear	linear	NN
randomwalker-info-585	337	59	co-	co-	VBD
randomwalker-info-585	337	60	efficient	efficient	JJ
randomwalker-info-585	337	61	function	function	NN
randomwalker-info-585	337	62	forking	fork	VBG
randomwalker-info-585	337	63	strategies	strategy	NNS
randomwalker-info-585	337	64	over	over	IN
randomwalker-info-585	337	65	a	a	DT
randomwalker-info-585	337	66	series	series	NN
randomwalker-info-585	337	67	of	of	IN
randomwalker-info-585	337	68	games	game	NNS
randomwalker-info-585	337	69	.	.	.
randomwalker-info-585	338	1	Strategies	strategy	NNS
randomwalker-info-585	338	2	that	that	WDT
randomwalker-info-585	338	3	are	be	VBP
randomwalker-info-585	338	4	slightly	slightly	RB
randomwalker-info-585	338	5	more	more	JJR
randomwalker-info-585	338	6	aggres-	aggres-	NN
randomwalker-info-585	338	7	sive	sive	JJ
randomwalker-info-585	338	8	than	than	IN
randomwalker-info-585	338	9	the	the	DT
randomwalker-info-585	338	10	most	most	RBS
randomwalker-info-585	338	11	common	common	JJ
randomwalker-info-585	338	12	strategy	strategy	NN
randomwalker-info-585	338	13	perform	perform	VBP
randomwalker-info-585	338	14	the	the	DT
randomwalker-info-585	338	15	best	good	JJS
randomwalker-info-585	338	16	and	and	CC
randomwalker-info-585	338	17	have	have	VBP
randomwalker-info-585	338	18	their	-PRON-	PRP$
randomwalker-info-585	338	19	normalized	normalize	VBN
randomwalker-info-585	338	20	weights	weight	NNS
randomwalker-info-585	338	21	increase	increase	NN
randomwalker-info-585	338	22	.	.	.
randomwalker-info-585	339	1	This	this	DT
randomwalker-info-585	339	2	simulation	simulation	NN
randomwalker-info-585	339	3	had	have	VBD
randomwalker-info-585	339	4	200	200	CD
randomwalker-info-585	339	5	miners	miner	NNS
randomwalker-info-585	339	6	,	,	,
randomwalker-info-585	339	7	9	9	CD
randomwalker-info-585	339	8	strategies	strategy	NNS
randomwalker-info-585	339	9	,	,	,
randomwalker-info-585	339	10	10,000	10,000	CD
randomwalker-info-585	339	11	blocks	block	NNS
randomwalker-info-585	339	12	per	per	IN
randomwalker-info-585	339	13	game	game	NN
randomwalker-info-585	339	14	and	and	CC
randomwalker-info-585	339	15	an	an	DT
randomwalker-info-585	339	16	�	�	NNP
randomwalker-info-585	339	17	value	value	NN
randomwalker-info-585	339	18	of	of	IN
randomwalker-info-585	339	19	.01	.01	NNP
randomwalker-info-585	339	20	.	.	.
randomwalker-info-585	339	21	block	block	NNP
randomwalker-info-585	339	22	)	)	-RRB-
randomwalker-info-585	339	23	.	.	.
randomwalker-info-585	340	1	So	so	RB
randomwalker-info-585	340	2	for	for	IN
randomwalker-info-585	340	3	a	a	DT
randomwalker-info-585	340	4	given	give	VBN
randomwalker-info-585	340	5	f	f	NN
randomwalker-info-585	340	6	,	,	,
randomwalker-info-585	340	7	we	-PRON-	PRP
randomwalker-info-585	340	8	can	can	MD
randomwalker-info-585	340	9	define	define	VB
randomwalker-info-585	340	10	:	:	:
randomwalker-info-585	340	11	Valcont(f	Valcont(f	NNP
randomwalker-info-585	340	12	)	)	-RRB-
randomwalker-info-585	340	13	=	=	NFP
randomwalker-info-585	340	14	f(Rem(Most	f(rem(most	NN
randomwalker-info-585	340	15	m	m	NN
randomwalker-info-585	340	16	H	h	NN
randomwalker-info-585	340	17	)	)	-RRB-
randomwalker-info-585	340	18	)	)	-RRB-
randomwalker-info-585	340	19	Valunder(f	Valunder(f	NNP
randomwalker-info-585	340	20	)	)	-RRB-
randomwalker-info-585	340	21	=	=	NFP
randomwalker-info-585	340	22	min{f(Rem(MostmH−1)),GapH	min{f(Rem(MostmH−1)),GapH	NNP
randomwalker-info-585	340	23	}	}	-RRB-
randomwalker-info-585	340	24	If	if	IN
randomwalker-info-585	340	25	Valcont(f	valcont(f	NN
randomwalker-info-585	340	26	)	)	-RRB-
randomwalker-info-585	340	27	>	>	XX
randomwalker-info-585	340	28	Valunder(f	Valunder(f	NNP
randomwalker-info-585	340	29	)	)	-RRB-
randomwalker-info-585	340	30	,	,	,
randomwalker-info-585	340	31	then	then	RB
randomwalker-info-585	340	32	more	more	JJR
randomwalker-info-585	340	33	rewards	reward	NNS
randomwalker-info-585	340	34	can	can	MD
randomwalker-info-585	340	35	be	be	VB
randomwalker-info-585	340	36	achieved	achieve	VBN
randomwalker-info-585	340	37	by	by	IN
randomwalker-info-585	340	38	continuing	continue	VBG
randomwalker-info-585	340	39	.	.	.
randomwalker-info-585	341	1	Otherwise	otherwise	RB
randomwalker-info-585	341	2	,	,	,
randomwalker-info-585	341	3	more	more	JJR
randomwalker-info-585	341	4	rewards	reward	NNS
randomwalker-info-585	341	5	can	can	MD
randomwalker-info-585	341	6	be	be	VB
randomwalker-info-585	341	7	achieved	achieve	VBN
randomwalker-info-585	341	8	through	through	IN
randomwalker-info-585	341	9	undercutting	undercutting	NN
randomwalker-info-585	341	10	.	.	.
randomwalker-info-585	342	1	Formally	formally	RB
randomwalker-info-585	342	2	,	,	,
randomwalker-info-585	342	3	for	for	IN
randomwalker-info-585	342	4	any	any	DT
randomwalker-info-585	342	5	function	function	NN
randomwalker-info-585	342	6	f	f	NN
randomwalker-info-585	342	7	(	(	-LRB-
randomwalker-info-585	342	8	·	·	NFP
randomwalker-info-585	342	9	)	)	-RRB-
randomwalker-info-585	342	10	,	,	,
randomwalker-info-585	342	11	this	this	DT
randomwalker-info-585	342	12	induces	induce	VBZ
randomwalker-info-585	342	13	the	the	DT
randomwalker-info-585	342	14	following	follow	VBG
randomwalker-info-585	342	15	formal	formal	JJ
randomwalker-info-585	342	16	strategy	strategy	NN
randomwalker-info-585	342	17	:	:	:
randomwalker-info-585	342	18	Function	function	NN
randomwalker-info-585	342	19	-	-	HYPH
randomwalker-info-585	342	20	Fork(f	Fork(f	NNP
randomwalker-info-585	342	21	)	)	-RRB-
randomwalker-info-585	342	22	:	:	:
randomwalker-info-585	342	23	Always	always	RB
randomwalker-info-585	342	24	takes	take	VBZ
randomwalker-info-585	342	25	a	a	DT
randomwalker-info-585	342	26	certain	certain	JJ
randomwalker-info-585	342	27	function	function	NN
randomwalker-info-585	342	28	,	,	,
randomwalker-info-585	342	29	f	f	NNP
randomwalker-info-585	342	30	(	(	-LRB-
randomwalker-info-585	342	31	·	·	NFP
randomwalker-info-585	342	32	)	)	-RRB-
randomwalker-info-585	342	33	,	,	,
randomwalker-info-585	342	34	of	of	IN
randomwalker-info-585	342	35	the	the	DT
randomwalker-info-585	342	36	possible	possible	JJ
randomwalker-info-585	342	37	transactions	transaction	NNS
randomwalker-info-585	342	38	it	-PRON-	PRP
randomwalker-info-585	342	39	could	could	MD
randomwalker-info-585	342	40	claim	claim	VB
randomwalker-info-585	342	41	.	.	.
randomwalker-info-585	343	1	Always	always	RB
randomwalker-info-585	343	2	mines	mine	NNS
randomwalker-info-585	343	3	in	in	IN
randomwalker-info-585	343	4	the	the	DT
randomwalker-info-585	343	5	location	location	NN
randomwalker-info-585	343	6	to	to	TO
randomwalker-info-585	343	7	maximize	maximize	VB
randomwalker-info-585	343	8	the	the	DT
randomwalker-info-585	343	9	size	size	NN
randomwalker-info-585	343	10	of	of	IN
randomwalker-info-585	343	11	the	the	DT
randomwalker-info-585	343	12	block	block	NN
randomwalker-info-585	343	13	they	-PRON-	PRP
randomwalker-info-585	343	14	would	would	MD
randomwalker-info-585	343	15	make	make	VB
randomwalker-info-585	343	16	,	,	,
randomwalker-info-585	343	17	with	with	IN
randomwalker-info-585	343	18	the	the	DT
randomwalker-info-585	343	19	constraint	constraint	NN
randomwalker-info-585	343	20	that	that	IN
randomwalker-info-585	343	21	if	if	IN
randomwalker-info-585	343	22	they	-PRON-	PRP
randomwalker-info-585	343	23	fork	fork	VBP
randomwalker-info-585	343	24	,	,	,
randomwalker-info-585	343	25	they	-PRON-	PRP
randomwalker-info-585	343	26	must	must	MD
randomwalker-info-585	343	27	undercut	undercut	VB
randomwalker-info-585	343	28	.	.	.
randomwalker-info-585	344	1	Which	which	WDT
randomwalker-info-585	344	2	Block	Block	NNP
randomwalker-info-585	344	3	:	:	:
randomwalker-info-585	344	4	if	if	IN
randomwalker-info-585	344	5	Owner(MostmH	Owner(MostmH	NNS
randomwalker-info-585	344	6	)	)	-RRB-
randomwalker-info-585	344	7	=	=	NFP
randomwalker-info-585	344	8	m	m	NN
randomwalker-info-585	344	9	or	or	CC
randomwalker-info-585	344	10	Valcont(f	Valcont(f	NNP
randomwalker-info-585	344	11	)	)	-RRB-
randomwalker-info-585	344	12	>	>	XX
randomwalker-info-585	344	13	Valunder(f	Valunder(f	NNP
randomwalker-info-585	344	14	)	)	-RRB-
randomwalker-info-585	344	15	Mining(m	Mining(m	NNP
randomwalker-info-585	344	16	)	)	-RRB-
randomwalker-info-585	344	17	=	=	NFP
randomwalker-info-585	344	18	MostmH	MostmH	NNS
randomwalker-info-585	344	19	.	.	.
randomwalker-info-585	345	1	else	else	RB
randomwalker-info-585	345	2	Mining(m	Mining(m	NNP
randomwalker-info-585	345	3	)	)	-RRB-
randomwalker-info-585	345	4	=	=	NFP
randomwalker-info-585	345	5	MostmH−1	MostmH−1	NNP
randomwalker-info-585	345	6	.	.	.
randomwalker-info-585	346	1	How	how	WRB
randomwalker-info-585	346	2	much	much	JJ
randomwalker-info-585	346	3	:	:	:
randomwalker-info-585	346	4	if	if	IN
randomwalker-info-585	346	5	Mining(m	mining(m	NN
randomwalker-info-585	346	6	)	)	-RRB-
randomwalker-info-585	346	7	=	=	NFP
randomwalker-info-585	346	8	MostmH	MostmH	NNS
randomwalker-info-585	346	9	include	include	VBP
randomwalker-info-585	346	10	Valcont(f	Valcont(f	NNP
randomwalker-info-585	346	11	)	)	-RRB-
randomwalker-info-585	346	12	.	.	.
randomwalker-info-585	347	1	else	else	RB
randomwalker-info-585	347	2	include	include	VBP
randomwalker-info-585	347	3	Valunder(f	Valunder(f	NNP
randomwalker-info-585	347	4	)	)	-RRB-
randomwalker-info-585	347	5	.	.	.
randomwalker-info-585	348	1	Publish(B	Publish(B	VBN
randomwalker-info-585	348	2	)	)	-RRB-
randomwalker-info-585	348	3	?	?	.
randomwalker-info-585	349	1	:	:	:
randomwalker-info-585	349	2	yes	yes	UH
randomwalker-info-585	349	3	.	.	.
randomwalker-info-585	350	1	Any	any	DT
randomwalker-info-585	350	2	reasonable	reasonable	JJ
randomwalker-info-585	350	3	choice	choice	NN
randomwalker-info-585	350	4	of	of	IN
randomwalker-info-585	350	5	f	f	NNP
randomwalker-info-585	350	6	(	(	-LRB-
randomwalker-info-585	350	7	·	·	NFP
randomwalker-info-585	350	8	)	)	-RRB-
randomwalker-info-585	350	9	will	will	MD
randomwalker-info-585	350	10	be	be	VB
randomwalker-info-585	350	11	monotonically	monotonically	RB
randomwalker-info-585	350	12	in-	in-	JJ
randomwalker-info-585	350	13	creasing	creasing	NN
randomwalker-info-585	350	14	,	,	,
randomwalker-info-585	350	15	which	which	WDT
randomwalker-info-585	350	16	means	mean	VBZ
randomwalker-info-585	350	17	that	that	IN
randomwalker-info-585	350	18	f(MostmH−1	f(mostmh−1	CD
randomwalker-info-585	350	19	)	)	-RRB-
randomwalker-info-585	350	20	will	will	MD
randomwalker-info-585	350	21	always	always	RB
randomwalker-info-585	350	22	be	be	VB
randomwalker-info-585	350	23	larger	large	JJR
randomwalker-info-585	350	24	than	than	IN
randomwalker-info-585	350	25	f(MostmH	f(MostmH	NNP
randomwalker-info-585	350	26	)	)	-RRB-
randomwalker-info-585	350	27	,	,	,
randomwalker-info-585	350	28	so	so	IN
randomwalker-info-585	350	29	the	the	DT
randomwalker-info-585	350	30	decision	decision	NN
randomwalker-info-585	350	31	on	on	IN
randomwalker-info-585	350	32	whether	whether	IN
randomwalker-info-585	350	33	to	to	TO
randomwalker-info-585	350	34	continue	continue	VB
randomwalker-info-585	350	35	or	or	CC
randomwalker-info-585	350	36	undercut	undercut	JJ
randomwalker-info-585	350	37	will	will	MD
randomwalker-info-585	350	38	come	come	VB
randomwalker-info-585	350	39	down	down	RP
randomwalker-info-585	350	40	to	to	IN
randomwalker-info-585	350	41	a	a	DT
randomwalker-info-585	350	42	comparison	comparison	NN
randomwalker-info-585	350	43	of	of	IN
randomwalker-info-585	350	44	f(MostmH	f(MostmH	NNP
randomwalker-info-585	350	45	)	)	-RRB-
randomwalker-info-585	350	46	ver-	ver-	NNP
randomwalker-info-585	350	47	sus	sus	NNP
randomwalker-info-585	350	48	GapH.	GapH.	.
randomwalker-info-585	351	1	One	one	CD
randomwalker-info-585	351	2	natural	natural	JJ
randomwalker-info-585	351	3	family	family	NN
randomwalker-info-585	351	4	of	of	IN
randomwalker-info-585	351	5	f	f	NNP
randomwalker-info-585	351	6	(	(	-LRB-
randomwalker-info-585	351	7	·	·	NFP
randomwalker-info-585	351	8	)	)	-RRB-
randomwalker-info-585	351	9	to	to	TO
randomwalker-info-585	351	10	consider	consider	VB
randomwalker-info-585	351	11	is	be	VBZ
randomwalker-info-585	351	12	linear	linear	JJ
randomwalker-info-585	351	13	functions	function	NNS
randomwalker-info-585	351	14	(	(	-LRB-
randomwalker-info-585	351	15	that	that	RB
randomwalker-info-585	351	16	is	is	RB
randomwalker-info-585	351	17	,	,	,
randomwalker-info-585	351	18	f(x	f(x	NNP
randomwalker-info-585	351	19	)	)	-RRB-
randomwalker-info-585	351	20	=	=	NFP
randomwalker-info-585	351	21	kx	kx	UH
randomwalker-info-585	351	22	for	for	IN
randomwalker-info-585	351	23	some	some	DT
randomwalker-info-585	351	24	k	k	NN
randomwalker-info-585	351	25	∈	∈	IN
randomwalker-info-585	351	26	[	[	-LRB-
randomwalker-info-585	351	27	0	0	CD
randomwalker-info-585	351	28	,	,	,
randomwalker-info-585	351	29	1	1	CD
randomwalker-info-585	351	30	]	]	-RRB-
randomwalker-info-585	351	31	)	)	-RRB-
randomwalker-info-585	351	32	.	.	.
randomwalker-info-585	352	1	If	if	IN
randomwalker-info-585	352	2	we	-PRON-	PRP
randomwalker-info-585	352	3	take	take	VBP
randomwalker-info-585	352	4	a	a	DT
randomwalker-info-585	352	5	group	group	NN
randomwalker-info-585	352	6	of	of	IN
randomwalker-info-585	352	7	Figure	Figure	NNP
randomwalker-info-585	352	8	4	4	CD
randomwalker-info-585	352	9	:	:	:
randomwalker-info-585	352	10	This	this	DT
randomwalker-info-585	352	11	is	be	VBZ
randomwalker-info-585	352	12	a	a	DT
randomwalker-info-585	352	13	simulation	simulation	NN
randomwalker-info-585	352	14	of	of	IN
randomwalker-info-585	352	15	8	8	CD
randomwalker-info-585	352	16	atomic	atomic	JJ
randomwalker-info-585	352	17	miners	miner	NNS
randomwalker-info-585	352	18	.	.	.
randomwalker-info-585	353	1	The	the	DT
randomwalker-info-585	353	2	simulation	simulation	NN
randomwalker-info-585	353	3	parameters	parameter	NNS
randomwalker-info-585	353	4	are	be	VBP
randomwalker-info-585	353	5	otherwise	otherwise	RB
randomwalker-info-585	353	6	configured	configure	VBN
randomwalker-info-585	353	7	the	the	DT
randomwalker-info-585	353	8	same	same	JJ
randomwalker-info-585	353	9	way	way	NN
randomwalker-info-585	353	10	as	as	IN
randomwalker-info-585	353	11	Figure	figure	NN
randomwalker-info-585	353	12	3	3	CD
randomwalker-info-585	353	13	.	.	.
randomwalker-info-585	354	1	We	-PRON-	PRP
randomwalker-info-585	354	2	see	see	VBP
randomwalker-info-585	354	3	that	that	IN
randomwalker-info-585	354	4	when	when	WRB
randomwalker-info-585	354	5	there	there	EX
randomwalker-info-585	354	6	are	be	VBP
randomwalker-info-585	354	7	a	a	DT
randomwalker-info-585	354	8	small	small	JJ
randomwalker-info-585	354	9	number	number	NN
randomwalker-info-585	354	10	of	of	IN
randomwalker-info-585	354	11	atomic	atomic	JJ
randomwalker-info-585	354	12	miners	miner	NNS
randomwalker-info-585	354	13	the	the	DT
randomwalker-info-585	354	14	more	more	JJR
randomwalker-info-585	354	15	ag-	ag-	NN
randomwalker-info-585	354	16	gressive	gressive	JJ
randomwalker-info-585	354	17	undercutters	undercutter	NNS
randomwalker-info-585	354	18	are	be	VBP
randomwalker-info-585	354	19	no	no	RB
randomwalker-info-585	354	20	longer	long	RBR
randomwalker-info-585	354	21	effective	effective	JJ
randomwalker-info-585	354	22	since	since	IN
randomwalker-info-585	354	23	they	-PRON-	PRP
randomwalker-info-585	354	24	are	be	VBP
randomwalker-info-585	354	25	beaten	beat	VBN
randomwalker-info-585	354	26	by	by	IN
randomwalker-info-585	354	27	more	more	RBR
randomwalker-info-585	354	28	gentle	gentle	JJ
randomwalker-info-585	354	29	forkers	forker	NNS
randomwalker-info-585	354	30	who	who	WP
randomwalker-info-585	354	31	are	be	VBP
randomwalker-info-585	354	32	lucky	lucky	JJ
randomwalker-info-585	354	33	enough	enough	RB
randomwalker-info-585	354	34	to	to	IN
randomwalker-info-585	354	35	mine	-PRON-	PRP
randomwalker-info-585	354	36	two	two	CD
randomwalker-info-585	354	37	blocks	block	NNS
randomwalker-info-585	354	38	in	in	IN
randomwalker-info-585	354	39	a	a	DT
randomwalker-info-585	354	40	row	row	NN
randomwalker-info-585	354	41	.	.	.
randomwalker-info-585	355	1	these	these	DT
randomwalker-info-585	355	2	strategies	strategy	NNS
randomwalker-info-585	355	3	,	,	,
randomwalker-info-585	355	4	and	and	CC
randomwalker-info-585	355	5	let	let	VB
randomwalker-info-585	355	6	non	non	JJ
randomwalker-info-585	355	7	-	-	JJ
randomwalker-info-585	355	8	atomic	atomic	JJ
randomwalker-info-585	355	9	strategic	strategic	JJ
randomwalker-info-585	355	10	miners	miner	NNS
randomwalker-info-585	355	11	learn	learn	VBP
randomwalker-info-585	355	12	over	over	IN
randomwalker-info-585	355	13	many	many	JJ
randomwalker-info-585	355	14	games	game	NNS
randomwalker-info-585	355	15	which	which	WDT
randomwalker-info-585	355	16	perform	perform	VBP
randomwalker-info-585	355	17	best	best	RB
randomwalker-info-585	355	18	,	,	,
randomwalker-info-585	355	19	we	-PRON-	PRP
randomwalker-info-585	355	20	get	get	VBP
randomwalker-info-585	355	21	the	the	DT
randomwalker-info-585	355	22	plot	plot	NN
randomwalker-info-585	355	23	in	in	IN
randomwalker-info-585	355	24	Figure	figure	NN
randomwalker-info-585	355	25	3	3	CD
randomwalker-info-585	355	26	.	.	.
randomwalker-info-585	356	1	What	what	WP
randomwalker-info-585	356	2	we	-PRON-	PRP
randomwalker-info-585	356	3	see	see	VBP
randomwalker-info-585	356	4	is	be	VBZ
randomwalker-info-585	356	5	the	the	DT
randomwalker-info-585	356	6	following	follow	VBG
randomwalker-info-585	356	7	:	:	:
randomwalker-info-585	356	8	when	when	WRB
randomwalker-info-585	356	9	the	the	DT
randomwalker-info-585	356	10	majority	majority	NN
randomwalker-info-585	356	11	of	of	IN
randomwalker-info-585	356	12	miners	miner	NNS
randomwalker-info-585	356	13	are	be	VBP
randomwalker-info-585	356	14	using	use	VBG
randomwalker-info-585	356	15	Function	function	NN
randomwalker-info-585	356	16	-	-	HYPH
randomwalker-info-585	356	17	Fork(kx	Fork(kx	NNP
randomwalker-info-585	356	18	)	)	-RRB-
randomwalker-info-585	356	19	,	,	,
randomwalker-info-585	356	20	the	the	DT
randomwalker-info-585	356	21	best	good	JJS
randomwalker-info-585	356	22	response	response	NN
randomwalker-info-585	356	23	is	be	VBZ
randomwalker-info-585	356	24	to	to	TO
randomwalker-info-585	356	25	use	use	VB
randomwalker-info-585	356	26	Function	Function	NNP
randomwalker-info-585	356	27	-	-	HYPH
randomwalker-info-585	356	28	Fork(k′x	Fork(k′x	NNP
randomwalker-info-585	356	29	)	)	-RRB-
randomwalker-info-585	356	30	,	,	,
randomwalker-info-585	356	31	for	for	IN
randomwalker-info-585	356	32	k′	k′	NNP
randomwalker-info-585	356	33	a	a	DT
randomwalker-info-585	356	34	little	little	JJ
randomwalker-info-585	356	35	smaller	small	JJR
randomwalker-info-585	356	36	than	than	IN
randomwalker-info-585	356	37	k	k	NN
randomwalker-info-585	356	38	,	,	,
randomwalker-info-585	356	39	(	(	-LRB-
randomwalker-info-585	356	40	i.e.	i.e.	FW
randomwalker-info-585	357	1	to	to	TO
randomwalker-info-585	357	2	undercut	undercut	VB
randomwalker-info-585	357	3	just	just	RB
randomwalker-info-585	357	4	a	a	DT
randomwalker-info-585	357	5	little	little	JJ
randomwalker-info-585	357	6	bit	bit	NN
randomwalker-info-585	357	7	more	more	RBR
randomwalker-info-585	357	8	aggressively	aggressively	RB
randomwalker-info-585	357	9	)	)	-RRB-
randomwalker-info-585	357	10	.	.	.
randomwalker-info-585	358	1	So	so	RB
randomwalker-info-585	358	2	eventually	eventually	RB
randomwalker-info-585	358	3	the	the	DT
randomwalker-info-585	358	4	smallest	small	JJS
randomwalker-info-585	358	5	coefficient	coefficient	NN
randomwalker-info-585	358	6	in	in	IN
randomwalker-info-585	358	7	our	-PRON-	PRP$
randomwalker-info-585	358	8	simulation	simulation	NN
randomwalker-info-585	358	9	becomes	become	VBZ
randomwalker-info-585	358	10	dominant	dominant	JJ
randomwalker-info-585	358	11	.	.	.
randomwalker-info-585	359	1	If	if	IN
randomwalker-info-585	359	2	we	-PRON-	PRP
randomwalker-info-585	359	3	instead	instead	RB
randomwalker-info-585	359	4	consider	consider	VBP
randomwalker-info-585	359	5	atomic	atomic	JJ
randomwalker-info-585	359	6	miners	miner	NNS
randomwalker-info-585	359	7	,	,	,
randomwalker-info-585	359	8	we	-PRON-	PRP
randomwalker-info-585	359	9	observe	observe	VBP
randomwalker-info-585	359	10	the	the	DT
randomwalker-info-585	359	11	be-	be-	JJ
randomwalker-info-585	359	12	havior	havior	NN
randomwalker-info-585	359	13	in	in	IN
randomwalker-info-585	359	14	Figure	Figure	NNP
randomwalker-info-585	359	15	4	4	CD
randomwalker-info-585	359	16	—	—	:
randomwalker-info-585	359	17	less	less	RBR
randomwalker-info-585	359	18	aggressive	aggressive	JJ
randomwalker-info-585	359	19	undercutters	undercutter	NNS
randomwalker-info-585	359	20	remain	remain	VBP
randomwalker-info-585	359	21	dominant	dominant	JJ
randomwalker-info-585	359	22	.	.	.
randomwalker-info-585	360	1	This	this	DT
randomwalker-info-585	360	2	is	be	VBZ
randomwalker-info-585	360	3	because	because	IN
randomwalker-info-585	360	4	even	even	RB
randomwalker-info-585	360	5	when	when	WRB
randomwalker-info-585	360	6	other	other	JJ
randomwalker-info-585	360	7	miners	miner	NNS
randomwalker-info-585	360	8	are	be	VBP
randomwalker-info-585	360	9	ag-	ag-	RB
randomwalker-info-585	360	10	gressively	gressively	RB
randomwalker-info-585	360	11	undercutting	undercut	VBG
randomwalker-info-585	360	12	,	,	,
randomwalker-info-585	360	13	each	each	DT
randomwalker-info-585	360	14	miner	miner	NN
randomwalker-info-585	360	15	still	still	RB
randomwalker-info-585	360	16	has	have	VBZ
randomwalker-info-585	360	17	a	a	DT
randomwalker-info-585	360	18	decent	decent	JJ
randomwalker-info-585	360	19	chance	chance	NN
randomwalker-info-585	360	20	to	to	TO
randomwalker-info-585	360	21	get	get	VB
randomwalker-info-585	360	22	their	-PRON-	PRP$
randomwalker-info-585	360	23	block	block	NN
randomwalker-info-585	360	24	accepted	accept	VBN
randomwalker-info-585	360	25	“	"	``
randomwalker-info-585	360	26	for	for	IN
randomwalker-info-585	360	27	free	free	JJ
randomwalker-info-585	360	28	,	,	,
randomwalker-info-585	360	29	”	"	''
randomwalker-info-585	360	30	by	by	IN
randomwalker-info-585	360	31	mining	mine	VBG
randomwalker-info-585	360	32	two	two	CD
randomwalker-info-585	360	33	blocks	block	NNS
randomwalker-info-585	360	34	in	in	IN
randomwalker-info-585	360	35	a	a	DT
randomwalker-info-585	360	36	row	row	NN
randomwalker-info-585	360	37	.	.	.
randomwalker-info-585	361	1	Note	note	VB
randomwalker-info-585	361	2	that	that	IN
randomwalker-info-585	361	3	simulation	simulation	NN
randomwalker-info-585	361	4	is	be	VBZ
randomwalker-info-585	361	5	vital	vital	JJ
randomwalker-info-585	361	6	to	to	IN
randomwalker-info-585	361	7	this	this	DT
randomwalker-info-585	361	8	understanding	understanding	NN
randomwalker-info-585	361	9	due	due	IN
randomwalker-info-585	361	10	to	to	IN
randomwalker-info-585	361	11	the	the	DT
randomwalker-info-585	361	12	large	large	JJ
randomwalker-info-585	361	13	number	number	NN
randomwalker-info-585	361	14	of	of	IN
randomwalker-info-585	361	15	parameters	parameter	NNS
randomwalker-info-585	361	16	to	to	TO
randomwalker-info-585	361	17	consider	consider	VB
randomwalker-info-585	361	18	.	.	.
randomwalker-info-585	362	1	5.4	5.4	CD
randomwalker-info-585	362	2	An	an	DT
randomwalker-info-585	362	3	Undercutting	Undercutting	NNP
randomwalker-info-585	362	4	Equilibrium	Equilibrium	NNP
randomwalker-info-585	362	5	Analytical	analytical	JJ
randomwalker-info-585	362	6	result	result	NN
randomwalker-info-585	362	7	:	:	:
randomwalker-info-585	362	8	An	an	DT
randomwalker-info-585	362	9	equilibrium	equilibrium	NN
randomwalker-info-585	362	10	exists	exist	VBZ
randomwalker-info-585	362	11	where	where	WRB
randomwalker-info-585	362	12	all	all	DT
randomwalker-info-585	362	13	miners	miner	NNS
randomwalker-info-585	362	14	use	use	VBP
randomwalker-info-585	362	15	the	the	DT
randomwalker-info-585	362	16	same	same	JJ
randomwalker-info-585	362	17	undercutting	undercutting	NN
randomwalker-info-585	362	18	strategy	strategy	NN
randomwalker-info-585	362	19	.	.	.
randomwalker-info-585	363	1	It	-PRON-	PRP
randomwalker-info-585	363	2	in-	in-	RB
randomwalker-info-585	363	3	duces	duce	VBZ
randomwalker-info-585	363	4	a	a	DT
randomwalker-info-585	363	5	growing	grow	VBG
randomwalker-info-585	363	6	backlog	backlog	NN
randomwalker-info-585	363	7	of	of	IN
randomwalker-info-585	363	8	transactions	transaction	NNS
randomwalker-info-585	363	9	.	.	.
randomwalker-info-585	364	1	Linear	linear	JJ
randomwalker-info-585	364	2	function	function	NN
randomwalker-info-585	364	3	-	-	HYPH
randomwalker-info-585	364	4	forking	forking	NN
randomwalker-info-585	364	5	is	be	VBZ
randomwalker-info-585	364	6	of	of	IN
randomwalker-info-585	364	7	course	course	NN
randomwalker-info-585	364	8	a	a	DT
randomwalker-info-585	364	9	natural	natural	JJ
randomwalker-info-585	364	10	class	class	NN
randomwalker-info-585	364	11	of	of	IN
randomwalker-info-585	364	12	strate-	strate-	NNS
randomwalker-info-585	364	13	gies	gy	NNS
randomwalker-info-585	364	14	to	to	TO
randomwalker-info-585	364	15	consider	consider	VB
randomwalker-info-585	364	16	,	,	,
randomwalker-info-585	364	17	but	but	CC
randomwalker-info-585	364	18	our	-PRON-	PRP$
randomwalker-info-585	364	19	simulations	simulation	NNS
randomwalker-info-585	364	20	in	in	IN
randomwalker-info-585	364	21	the	the	DT
randomwalker-info-585	364	22	previous	previous	JJ
randomwalker-info-585	364	23	section	section	NN
randomwalker-info-585	364	24	show	show	VBP
randomwalker-info-585	364	25	that	that	IN
randomwalker-info-585	364	26	long	long	JJ
randomwalker-info-585	364	27	-	-	HYPH
randomwalker-info-585	364	28	term	term	NN
randomwalker-info-585	364	29	behavior	behavior	NN
randomwalker-info-585	364	30	may	may	MD
randomwalker-info-585	364	31	be	be	VB
randomwalker-info-585	364	32	erratic	erratic	JJ
randomwalker-info-585	364	33	if	if	IN
randomwalker-info-585	364	34	miners	miner	NNS
randomwalker-info-585	364	35	only	only	RB
randomwalker-info-585	364	36	consider	consider	VBP
randomwalker-info-585	364	37	these	these	DT
randomwalker-info-585	364	38	strategies	strategy	NNS
randomwalker-info-585	364	39	.	.	.
randomwalker-info-585	365	1	Our	-PRON-	PRP$
randomwalker-info-585	365	2	goal	goal	NN
randomwalker-info-585	365	3	in	in	IN
randomwalker-info-585	365	4	this	this	DT
randomwalker-info-585	365	5	section	section	NN
randomwalker-info-585	365	6	is	be	VBZ
randomwalker-info-585	365	7	to	to	TO
randomwalker-info-585	365	8	un-	un-	VB
randomwalker-info-585	365	9	derstand	derstand	NN
randomwalker-info-585	365	10	what	what	WP
randomwalker-info-585	365	11	undercutting	undercut	VBG
randomwalker-info-585	365	12	behavior	behavior	NN
randomwalker-info-585	365	13	is	be	VBZ
randomwalker-info-585	365	14	stable	stable	JJ
randomwalker-info-585	365	15	.	.	.
randomwalker-info-585	366	1	Our	-PRON-	PRP$
randomwalker-info-585	366	2	approach	approach	NN
randomwalker-info-585	366	3	is	be	VBZ
randomwalker-info-585	366	4	to	to	TO
randomwalker-info-585	366	5	find	find	VB
randomwalker-info-585	366	6	a	a	DT
randomwalker-info-585	366	7	function	function	NN
randomwalker-info-585	366	8	f	f	NN
randomwalker-info-585	366	9	(	(	-LRB-
randomwalker-info-585	366	10	·	·	NFP
randomwalker-info-585	366	11	)	)	-RRB-
randomwalker-info-585	366	12	such	such	JJ
randomwalker-info-585	366	13	that	that	IN
randomwalker-info-585	366	14	Function-	Function-	NNP
randomwalker-info-585	366	15	Fork(f	Fork(f	NNS
randomwalker-info-585	366	16	)	)	-RRB-
randomwalker-info-585	366	17	is	be	VBZ
randomwalker-info-585	366	18	an	an	DT
randomwalker-info-585	366	19	equilibrium	equilibrium	NN
randomwalker-info-585	366	20	.	.	.
randomwalker-info-585	367	1	That	that	RB
randomwalker-info-585	367	2	is	is	RB
randomwalker-info-585	367	3	,	,	,
randomwalker-info-585	367	4	as	as	RB
randomwalker-info-585	367	5	long	long	RB
randomwalker-info-585	367	6	as	as	IN
randomwalker-info-585	367	7	every	every	DT
randomwalker-info-585	367	8	other	other	JJ
randomwalker-info-585	367	9	miner	miner	NN
randomwalker-info-585	367	10	is	be	VBZ
randomwalker-info-585	367	11	using	use	VBG
randomwalker-info-585	367	12	the	the	DT
randomwalker-info-585	367	13	strategy	strategy	NN
randomwalker-info-585	367	14	Function	function	NN
randomwalker-info-585	367	15	-	-	HYPH
randomwalker-info-585	367	16	Fork(f	Fork(f	NNP
randomwalker-info-585	367	17	)	)	-RRB-
randomwalker-info-585	367	18	,	,	,
randomwalker-info-585	367	19	it	-PRON-	PRP
randomwalker-info-585	367	20	is	be	VBZ
randomwalker-info-585	367	21	in	in	IN
randomwalker-info-585	367	22	your	-PRON-	PRP$
randomwalker-info-585	367	23	interest	interest	NN
randomwalker-info-585	367	24	to	to	TO
randomwalker-info-585	367	25	do	do	VB
randomwalker-info-585	367	26	so	so	RB
randomwalker-info-585	367	27	as	as	RB
randomwalker-info-585	367	28	well	well	RB
randomwalker-info-585	367	29	.	.	.
randomwalker-info-585	368	1	In	in	IN
randomwalker-info-585	368	2	other	other	JJ
randomwalker-info-585	368	3	words	word	NNS
randomwalker-info-585	368	4	,	,	,
randomwalker-info-585	368	5	we	-PRON-	PRP
randomwalker-info-585	368	6	would	would	MD
randomwalker-info-585	368	7	like	like	VB
randomwalker-info-585	368	8	to	to	TO
randomwalker-info-585	368	9	find	find	VB
randomwalker-info-585	368	10	an	an	DT
randomwalker-info-585	368	11	f	f	NN
randomwalker-info-585	368	12	such	such	JJ
randomwalker-info-585	368	13	that	that	IN
randomwalker-info-585	368	14	Function	Function	NNP
randomwalker-info-585	368	15	-	-	HYPH
randomwalker-info-585	368	16	fork(f	fork(f	NNP
randomwalker-info-585	368	17	)	)	-RRB-
randomwalker-info-585	368	18	is	be	VBZ
randomwalker-info-585	368	19	a	a	DT
randomwalker-info-585	368	20	best	good	JJS
randomwalker-info-585	368	21	-	-	HYPH
randomwalker-info-585	368	22	response	response	NN
randomwalker-info-585	368	23	to	to	IN
randomwalker-info-585	368	24	the	the	DT
randomwalker-info-585	368	25	case	case	NN
randomwalker-info-585	368	26	when	when	WRB
randomwalker-info-585	368	27	all	all	DT
randomwalker-info-585	368	28	other	other	JJ
randomwalker-info-585	368	29	miners	miner	NNS
randomwalker-info-585	368	30	themselves	-PRON-	PRP
randomwalker-info-585	368	31	use	use	VBP
randomwalker-info-585	368	32	Function-	Function-	NNP
randomwalker-info-585	368	33	fork(f	fork(f	NNP
randomwalker-info-585	368	34	)	)	-RRB-
randomwalker-info-585	368	35	.	.	.
randomwalker-info-585	369	1	We	-PRON-	PRP
randomwalker-info-585	369	2	provide	provide	VBP
randomwalker-info-585	369	3	now	now	RB
randomwalker-info-585	369	4	intuition	intuition	NN
randomwalker-info-585	369	5	for	for	IN
randomwalker-info-585	369	6	why	why	WRB
randomwalker-info-585	369	7	the	the	DT
randomwalker-info-585	369	8	f	f	NN
randomwalker-info-585	369	9	(	(	-LRB-
randomwalker-info-585	369	10	·	·	NFP
randomwalker-info-585	369	11	)	)	-RRB-
randomwalker-info-585	369	12	we	-PRON-	PRP
randomwalker-info-585	369	13	present	present	VBP
randomwalker-info-585	369	14	yields	yield	NNS
randomwalker-info-585	369	15	an	an	DT
randomwalker-info-585	369	16	equilibrium	equilibrium	NN
randomwalker-info-585	369	17	.	.	.
randomwalker-info-585	370	1	So	so	RB
randomwalker-info-585	370	2	what	what	WP
randomwalker-info-585	370	3	does	do	VBZ
randomwalker-info-585	370	4	it	-PRON-	PRP
randomwalker-info-585	370	5	mean	mean	VB
randomwalker-info-585	370	6	for	for	IN
randomwalker-info-585	370	7	a	a	DT
randomwalker-info-585	370	8	strategy	strategy	NN
randomwalker-info-585	370	9	to	to	TO
randomwalker-info-585	370	10	be	be	VB
randomwalker-info-585	370	11	a	a	DT
randomwalker-info-585	370	12	best	good	JJS
randomwalker-info-585	370	13	-	-	HYPH
randomwalker-info-585	370	14	response	response	NN
randomwalker-info-585	370	15	to	to	IN
randomwalker-info-585	370	16	other	other	JJ
randomwalker-info-585	370	17	miner	miner	NN
randomwalker-info-585	370	18	behavior	behavior	NN
randomwalker-info-585	370	19	?	?	.
randomwalker-info-585	371	1	Recall	recall	VB
randomwalker-info-585	371	2	that	that	IN
randomwalker-info-585	371	3	a	a	DT
randomwalker-info-585	371	4	strategy	strategy	NN
randomwalker-info-585	371	5	proposes	propose	NNS
randomwalker-info-585	371	6	which	which	WDT
randomwalker-info-585	371	7	block	block	VBP
randomwalker-info-585	371	8	to	to	TO
randomwalker-info-585	371	9	extend	extend	VB
randomwalker-info-585	371	10	,	,	,
randomwalker-info-585	371	11	how	how	WRB
randomwalker-info-585	371	12	many	many	JJ
randomwalker-info-585	371	13	transaction	transaction	NN
randomwalker-info-585	371	14	fees	fee	NNS
randomwalker-info-585	371	15	to	to	TO
randomwalker-info-585	371	16	claim	claim	VB
randomwalker-info-585	371	17	,	,	,
randomwalker-info-585	371	18	and	and	CC
randomwalker-info-585	371	19	which	which	WDT
randomwalker-info-585	371	20	blocks	block	VBZ
randomwalker-info-585	371	21	to	to	TO
randomwalker-info-585	371	22	publish	publish	VB
randomwalker-info-585	371	23	as	as	IN
randomwalker-info-585	371	24	a	a	DT
randomwalker-info-585	371	25	function	function	NN
randomwalker-info-585	371	26	of	of	IN
randomwalker-info-585	371	27	the	the	DT
randomwalker-info-585	371	28	currently	currently	RB
randomwalker-info-585	371	29	held	hold	VBN
randomwalker-info-585	371	30	information	information	NN
randomwalker-info-585	371	31	.	.	.
randomwalker-info-585	372	1	A	a	DT
randomwalker-info-585	372	2	strategy	strategy	NN
randomwalker-info-585	372	3	is	be	VBZ
randomwalker-info-585	372	4	a	a	DT
randomwalker-info-585	372	5	best	good	JJS
randomwalker-info-585	372	6	response	response	NN
randomwalker-info-585	372	7	if	if	IN
randomwalker-info-585	372	8	it	-PRON-	PRP
randomwalker-info-585	372	9	maxi-	maxi-	XX
randomwalker-info-585	372	10	mizes	mize	VBZ
randomwalker-info-585	372	11	the	the	DT
randomwalker-info-585	372	12	miner	miner	NN
randomwalker-info-585	372	13	’s	’s	POS
randomwalker-info-585	372	14	expected	expect	VBN
randomwalker-info-585	372	15	reward	reward	NN
randomwalker-info-585	372	16	(	(	-LRB-
randomwalker-info-585	372	17	taking	take	VBG
randomwalker-info-585	372	18	into	into	IN
randomwalker-info-585	372	19	account	account	NN
randomwalker-info-585	372	20	fu-	fu-	CD
randomwalker-info-585	372	21	ture	ture	NN
randomwalker-info-585	372	22	events	event	NNS
randomwalker-info-585	372	23	,	,	,
randomwalker-info-585	372	24	and	and	CC
randomwalker-info-585	372	25	in	in	IN
randomwalker-info-585	372	26	particular	particular	JJ
randomwalker-info-585	372	27	the	the	DT
randomwalker-info-585	372	28	probability	probability	NN
randomwalker-info-585	372	29	that	that	WDT
randomwalker-info-585	372	30	the	the	DT
randomwalker-info-585	372	31	cur-	cur-	NN
randomwalker-info-585	372	32	rent	rent	NN
randomwalker-info-585	372	33	block	block	NN
randomwalker-info-585	372	34	is	be	VBZ
randomwalker-info-585	372	35	in	in	IN
randomwalker-info-585	372	36	the	the	DT
randomwalker-info-585	372	37	eventual	eventual	JJ
randomwalker-info-585	372	38	longest	long	JJS
randomwalker-info-585	372	39	chain	chain	NN
randomwalker-info-585	372	40	)	)	-RRB-
randomwalker-info-585	372	41	over	over	IN
randomwalker-info-585	372	42	all	all	DT
randomwalker-info-585	372	43	potential	potential	JJ
randomwalker-info-585	372	44	strategies	strategy	NNS
randomwalker-info-585	372	45	that	that	WDT
randomwalker-info-585	372	46	miner	miner	NN
randomwalker-info-585	372	47	could	could	MD
randomwalker-info-585	372	48	have	have	VB
randomwalker-info-585	372	49	used	use	VBN
randomwalker-info-585	372	50	instead	instead	RB
randomwalker-info-585	372	51	.	.	.
randomwalker-info-585	373	1	In	in	IN
randomwalker-info-585	373	2	particular	particular	JJ
randomwalker-info-585	373	3	,	,	,
randomwalker-info-585	373	4	a	a	DT
randomwalker-info-585	373	5	best	good	JJS
randomwalker-info-585	373	6	-	-	HYPH
randomwalker-info-585	373	7	response	response	NN
randomwalker-info-585	373	8	must	must	MD
randomwalker-info-585	373	9	be	be	VB
randomwalker-info-585	373	10	at	at	IN
randomwalker-info-585	373	11	least	least	JJS
randomwalker-info-585	373	12	as	as	RB
randomwalker-info-585	373	13	good	good	JJ
randomwalker-info-585	373	14	as	as	IN
randomwalker-info-585	373	15	all	all	DT
randomwalker-info-585	373	16	other	other	JJ
randomwalker-info-585	373	17	strate-	strate-	JJ
randomwalker-info-585	373	18	gies	gy	NNS
randomwalker-info-585	373	19	that	that	WDT
randomwalker-info-585	373	20	mine	-PRON-	PRP
randomwalker-info-585	373	21	at	at	IN
randomwalker-info-585	373	22	the	the	DT
randomwalker-info-585	373	23	same	same	JJ
randomwalker-info-585	373	24	location	location	NN
randomwalker-info-585	373	25	and	and	CC
randomwalker-info-585	373	26	publish	publish	VB
randomwalker-info-585	373	27	the	the	DT
randomwalker-info-585	373	28	same	same	JJ
randomwalker-info-585	373	29	blocks	block	NNS
randomwalker-info-585	373	30	(	(	-LRB-
randomwalker-info-585	373	31	but	but	CC
randomwalker-info-585	373	32	differ	differ	VBP
randomwalker-info-585	373	33	in	in	IN
randomwalker-info-585	373	34	which	which	WDT
randomwalker-info-585	373	35	transactions	transaction	NNS
randomwalker-info-585	373	36	to	to	TO
randomwalker-info-585	373	37	include	include	VB
randomwalker-info-585	373	38	)	)	-RRB-
randomwalker-info-585	373	39	.	.	.
randomwalker-info-585	374	1	To	to	TO
randomwalker-info-585	374	2	get	get	VB
randomwalker-info-585	374	3	some	some	DT
randomwalker-info-585	374	4	intuition	intuition	NN
randomwalker-info-585	374	5	for	for	IN
randomwalker-info-585	374	6	what	what	WP
randomwalker-info-585	374	7	conditions	condition	NNS
randomwalker-info-585	374	8	a	a	DT
randomwalker-info-585	374	9	potential	potential	JJ
randomwalker-info-585	374	10	equi-	equi-	JJ
randomwalker-info-585	374	11	librium	librium	NN
randomwalker-info-585	374	12	must	must	MD
randomwalker-info-585	374	13	satisfy	satisfy	VB
randomwalker-info-585	374	14	,	,	,
randomwalker-info-585	374	15	let	let	VB
randomwalker-info-585	374	16	’s	-PRON-	PRP
randomwalker-info-585	374	17	first	first	RB
randomwalker-info-585	374	18	consider	consider	VB
randomwalker-info-585	374	19	the	the	DT
randomwalker-info-585	374	20	decision	decision	NN
randomwalker-info-585	374	21	facing	face	VBG
randomwalker-info-585	374	22	a	a	DT
randomwalker-info-585	374	23	miner	miner	NN
randomwalker-info-585	374	24	who	who	WP
randomwalker-info-585	374	25	has	have	VBZ
randomwalker-info-585	374	26	already	already	RB
randomwalker-info-585	374	27	decided	decide	VBN
randomwalker-info-585	374	28	to	to	TO
randomwalker-info-585	374	29	continue	continue	VB
randomwalker-info-585	374	30	on	on	IN
randomwalker-info-585	374	31	top	top	NN
randomwalker-info-585	374	32	of	of	IN
randomwalker-info-585	374	33	the	the	DT
randomwalker-info-585	374	34	longest	long	JJS
randomwalker-info-585	374	35	chain	chain	NN
randomwalker-info-585	374	36	and	and	CC
randomwalker-info-585	374	37	is	be	VBZ
randomwalker-info-585	374	38	just	just	RB
randomwalker-info-585	374	39	deciding	decide	VBG
randomwalker-info-585	374	40	how	how	WRB
randomwalker-info-585	374	41	many	many	JJ
randomwalker-info-585	374	42	transaction	transaction	NN
randomwalker-info-585	374	43	fees	fee	NNS
randomwalker-info-585	374	44	to	to	TO
randomwalker-info-585	374	45	include	include	VB
randomwalker-info-585	374	46	.	.	.
randomwalker-info-585	375	1	If	if	IN
randomwalker-info-585	375	2	F	F	NNP
randomwalker-info-585	375	3	denotes	denote	VBZ
randomwalker-info-585	375	4	the	the	DT
randomwalker-info-585	375	5	number	number	NN
randomwalker-info-585	375	6	of	of	IN
randomwalker-info-585	375	7	transaction	transaction	NN
randomwalker-info-585	375	8	fees	fee	NNS
randomwalker-info-585	375	9	in-	in-	RB
randomwalker-info-585	375	10	cluded	clude	VBD
randomwalker-info-585	375	11	,	,	,
randomwalker-info-585	375	12	define	define	VB
randomwalker-info-585	375	13	π(F	π(F	NNP
randomwalker-info-585	375	14	,	,	,
randomwalker-info-585	375	15	f	f	NNP
randomwalker-info-585	375	16	,	,	,
randomwalker-info-585	375	17	x	x	LS
randomwalker-info-585	375	18	)	)	-RRB-
randomwalker-info-585	375	19	to	to	TO
randomwalker-info-585	375	20	be	be	VB
randomwalker-info-585	375	21	the	the	DT
randomwalker-info-585	375	22	probability	probability	NN
randomwalker-info-585	375	23	that	that	IN
randomwalker-info-585	375	24	this	this	DT
randomwalker-info-585	375	25	block	block	NN
randomwalker-info-585	375	26	is	be	VBZ
randomwalker-info-585	375	27	included	include	VBN
randomwalker-info-585	375	28	in	in	IN
randomwalker-info-585	375	29	the	the	DT
randomwalker-info-585	375	30	eventual	eventual	JJ
randomwalker-info-585	375	31	longest	long	JJS
randomwalker-info-585	375	32	chain	chain	NN
randomwalker-info-585	375	33	,	,	,
randomwalker-info-585	375	34	conditioned	condition	VBN
randomwalker-info-585	375	35	on	on	IN
randomwalker-info-585	375	36	including	include	VBG
randomwalker-info-585	375	37	F	F	NNP
randomwalker-info-585	375	38	BTC	BTC	NNP
randomwalker-info-585	375	39	worth	worth	NN
randomwalker-info-585	375	40	of	of	IN
randomwalker-info-585	375	41	transaction	transaction	NN
randomwalker-info-585	375	42	fees	fee	NNS
randomwalker-info-585	375	43	in	in	IN
randomwalker-info-585	375	44	the	the	DT
randomwalker-info-585	375	45	block	block	NN
randomwalker-info-585	375	46	,	,	,
randomwalker-info-585	375	47	all	all	DT
randomwalker-info-585	375	48	other	other	JJ
randomwalker-info-585	375	49	miners	miner	NNS
randomwalker-info-585	375	50	using	use	VBG
randomwalker-info-585	375	51	strategy	strategy	NN
randomwalker-info-585	375	52	Function	Function	NNP
randomwalker-info-585	375	53	-	-	HYPH
randomwalker-info-585	375	54	Fork(f	Fork(f	NNP
randomwalker-info-585	375	55	)	)	-RRB-
randomwalker-info-585	375	56	,	,	,
randomwalker-info-585	375	57	and	and	CC
randomwalker-info-585	375	58	x	x	SYM
randomwalker-info-585	375	59	=	=	SYM
randomwalker-info-585	375	60	Rem(MostmH	Rem(MostmH	NNP
randomwalker-info-585	375	61	)	)	-RRB-
randomwalker-info-585	375	62	(	(	-LRB-
randomwalker-info-585	375	63	note	note	VB
randomwalker-info-585	375	64	that	that	IN
randomwalker-info-585	375	65	π	π	NN
randomwalker-info-585	375	66	is	be	VBZ
randomwalker-info-585	375	67	well	well	RB
randomwalker-info-585	375	68	-	-	HYPH
randomwalker-info-585	375	69	defined	define	VBN
randomwalker-info-585	375	70	)	)	-RRB-
randomwalker-info-585	375	71	.	.	.
randomwalker-info-585	376	1	Then	then	RB
randomwalker-info-585	376	2	the	the	DT
randomwalker-info-585	376	3	miner	miner	NN
randomwalker-info-585	376	4	’s	’s	POS
randomwalker-info-585	376	5	expected	expect	VBN
randomwalker-info-585	376	6	reward	reward	NN
randomwalker-info-585	376	7	,	,	,
randomwalker-info-585	376	8	should	should	MD
randomwalker-info-585	376	9	they	-PRON-	PRP
randomwalker-info-585	376	10	be	be	VB
randomwalker-info-585	376	11	fortunate	fortunate	JJ
randomwalker-info-585	376	12	enough	enough	RB
randomwalker-info-585	376	13	to	to	TO
randomwalker-info-585	376	14	find	find	VB
randomwalker-info-585	376	15	a	a	DT
randomwalker-info-585	376	16	block	block	NN
randomwalker-info-585	376	17	right	right	RB
randomwalker-info-585	376	18	now	now	RB
randomwalker-info-585	376	19	would	would	MD
randomwalker-info-585	376	20	be	be	VB
randomwalker-info-585	376	21	F	F	NNP
randomwalker-info-585	376	22	·	·	NFP
randomwalker-info-585	376	23	π(F	π(F	NNP
randomwalker-info-585	376	24	,	,	,
randomwalker-info-585	376	25	f	f	NNP
randomwalker-info-585	376	26	,	,	,
randomwalker-info-585	376	27	x	x	NNP
randomwalker-info-585	376	28	)	)	-RRB-
randomwalker-info-585	376	29	.	.	.
randomwalker-info-585	377	1	A	a	DT
randomwalker-info-585	377	2	best	good	JJS
randomwalker-info-585	377	3	-	-	HYPH
randomwalker-info-585	377	4	response	response	NN
randomwalker-info-585	377	5	would	would	MD
randomwalker-info-585	377	6	then	then	RB
randomwalker-info-585	377	7	be	be	VB
randomwalker-info-585	377	8	to	to	TO
randomwalker-info-585	377	9	include	include	VB
randomwalker-info-585	377	10	argmaxF≤x{F	argmaxf≤x{f	UH
randomwalker-info-585	377	11	·	·	NFP
randomwalker-info-585	377	12	π(F	π(F	NNP
randomwalker-info-585	377	13	,	,	,
randomwalker-info-585	377	14	f	f	NNP
randomwalker-info-585	377	15	,	,	,
randomwalker-info-585	377	16	x	x	NNP
randomwalker-info-585	377	17	)	)	-RRB-
randomwalker-info-585	377	18	}	}	-RRB-
randomwalker-info-585	377	19	transaction	transaction	NN
randomwalker-info-585	377	20	fees	fee	NNS
randomwalker-info-585	377	21	.	.	.
randomwalker-info-585	378	1	The	the	DT
randomwalker-info-585	378	2	strategy	strategy	NN
randomwalker-info-585	378	3	Function	function	NN
randomwalker-info-585	378	4	-	-	HYPH
randomwalker-info-585	378	5	Fork(f	Fork(f	NNP
randomwalker-info-585	378	6	)	)	-RRB-
randomwalker-info-585	378	7	would	would	MD
randomwalker-info-585	378	8	recommend	recommend	VB
randomwalker-info-585	378	9	including	include	VBG
randomwalker-info-585	378	10	f(x	f(x	NNP
randomwalker-info-585	378	11	)	)	-RRB-
randomwalker-info-585	378	12	transaction	transaction	NN
randomwalker-info-585	378	13	fees	fee	NNS
randomwalker-info-585	378	14	.	.	.
randomwalker-info-585	379	1	So	so	RB
randomwalker-info-585	379	2	for	for	IN
randomwalker-info-585	379	3	Function	function	NN
randomwalker-info-585	379	4	-	-	HYPH
randomwalker-info-585	379	5	Fork(f	Fork(f	NNP
randomwalker-info-585	379	6	)	)	-RRB-
randomwalker-info-585	379	7	to	to	TO
randomwalker-info-585	379	8	be	be	VB
randomwalker-info-585	379	9	a	a	DT
randomwalker-info-585	379	10	best	good	JJS
randomwalker-info-585	379	11	-	-	HYPH
randomwalker-info-585	379	12	response	response	NN
randomwalker-info-585	379	13	to	to	IN
randomwalker-info-585	379	14	other	other	JJ
randomwalker-info-585	379	15	min-	min-	JJ
randomwalker-info-585	379	16	ers	er	NNS
randomwalker-info-585	379	17	using	use	VBG
randomwalker-info-585	379	18	Function	Function	NNP
randomwalker-info-585	379	19	-	-	HYPH
randomwalker-info-585	379	20	fork(f	fork(f	NNP
randomwalker-info-585	379	21	)	)	-RRB-
randomwalker-info-585	379	22	,	,	,
randomwalker-info-585	379	23	it	-PRON-	PRP
randomwalker-info-585	379	24	better	better	RB
randomwalker-info-585	379	25	be	be	VB
randomwalker-info-585	379	26	the	the	DT
randomwalker-info-585	379	27	case	case	NN
randomwalker-info-585	379	28	that	that	IN
randomwalker-info-585	379	29	f(x	f(x	NNP
randomwalker-info-585	379	30	)	)	-RRB-
randomwalker-info-585	379	31	∈	∈	NNP
randomwalker-info-585	379	32	argmaxF≤x{F	argmaxF≤x{F	NFP
randomwalker-info-585	379	33	·	·	NFP
randomwalker-info-585	379	34	π(F	π(F	NNP
randomwalker-info-585	379	35	,	,	,
randomwalker-info-585	379	36	f	f	NNP
randomwalker-info-585	379	37	,	,	,
randomwalker-info-585	379	38	x	x	LS
randomwalker-info-585	379	39	)	)	-RRB-
randomwalker-info-585	379	40	}	}	-RRB-
randomwalker-info-585	379	41	for	for	IN
randomwalker-info-585	379	42	all	all	DT
randomwalker-info-585	379	43	x.	x.	NN
randomwalker-info-585	380	1	Note	note	VB
randomwalker-info-585	380	2	that	that	IN
randomwalker-info-585	380	3	this	this	DT
randomwalker-info-585	380	4	is	be	VBZ
randomwalker-info-585	380	5	a	a	DT
randomwalker-info-585	380	6	somewhat	somewhat	RB
randomwalker-info-585	380	7	strong	strong	JJ
randomwalker-info-585	380	8	condition	condition	NN
randomwalker-info-585	380	9	on	on	IN
randomwalker-info-585	380	10	f	f	NNP
randomwalker-info-585	380	11	,	,	,
randomwalker-info-585	380	12	as	as	IN
randomwalker-info-585	380	13	the	the	DT
randomwalker-info-585	380	14	fact	fact	NN
randomwalker-info-585	380	15	that	that	IN
randomwalker-info-585	380	16	the	the	DT
randomwalker-info-585	380	17	other	other	JJ
randomwalker-info-585	380	18	miners	miner	NNS
randomwalker-info-585	380	19	are	be	VBP
randomwalker-info-585	380	20	using	use	VBG
randomwalker-info-585	380	21	Function	Function	NNP
randomwalker-info-585	380	22	-	-	HYPH
randomwalker-info-585	380	23	fork(f	fork(f	NNP
randomwalker-info-585	380	24	)	)	-RRB-
randomwalker-info-585	380	25	affects	affect	VBZ
randomwalker-info-585	380	26	π(F	π(F	NNP
randomwalker-info-585	380	27	,	,	,
randomwalker-info-585	380	28	f	f	NNP
randomwalker-info-585	380	29	,	,	,
randomwalker-info-585	380	30	x	x	NNP
randomwalker-info-585	380	31	)	)	-RRB-
randomwalker-info-585	380	32	,	,	,
randomwalker-info-585	380	33	whereas	whereas	IN
randomwalker-info-585	380	34	we	-PRON-	PRP
randomwalker-info-585	380	35	also	also	RB
randomwalker-info-585	380	36	want	want	VBP
randomwalker-info-585	380	37	this	this	DT
randomwalker-info-585	380	38	miner	miner	NN
randomwalker-info-585	380	39	’s	’s	POS
randomwalker-info-585	380	40	best	good	JJS
randomwalker-info-585	380	41	response	response	NN
randomwalker-info-585	380	42	to	to	TO
randomwalker-info-585	380	43	have	have	VB
randomwalker-info-585	380	44	f(x	f(x	NNS
randomwalker-info-585	380	45	)	)	-RRB-
randomwalker-info-585	380	46	∈	∈	NNP
randomwalker-info-585	380	47	argmaxF≤x{F	argmaxF≤x{F	NFP
randomwalker-info-585	380	48	·	·	NFP
randomwalker-info-585	380	49	π(F	π(F	NNP
randomwalker-info-585	380	50	,	,	,
randomwalker-info-585	380	51	f	f	NNP
randomwalker-info-585	380	52	,	,	,
randomwalker-info-585	380	53	x	x	NNP
randomwalker-info-585	380	54	)	)	-RRB-
randomwalker-info-585	380	55	}	}	-RRB-
randomwalker-info-585	380	56	.	.	.
randomwalker-info-585	381	1	At	at	IN
randomwalker-info-585	381	2	this	this	DT
randomwalker-info-585	381	3	point	point	NN
randomwalker-info-585	381	4	,	,	,
randomwalker-info-585	381	5	we	-PRON-	PRP
randomwalker-info-585	381	6	show	show	VBP
randomwalker-info-585	381	7	that	that	IN
randomwalker-info-585	381	8	there	there	EX
randomwalker-info-585	381	9	is	be	VBZ
randomwalker-info-585	381	10	a	a	DT
randomwalker-info-585	381	11	continuous	continuous	JJ
randomwalker-info-585	381	12	and	and	CC
randomwalker-info-585	381	13	piece	piece	NN
randomwalker-info-585	381	14	-	-	JJ
randomwalker-info-585	381	15	wise	wise	JJ
randomwalker-info-585	381	16	differentiable	differentiable	JJ
randomwalker-info-585	381	17	function	function	NN
randomwalker-info-585	381	18	f	f	NNP
randomwalker-info-585	381	19	(	(	-LRB-
randomwalker-info-585	381	20	·	·	NFP
randomwalker-info-585	381	21	)	)	-RRB-
randomwalker-info-585	381	22	that	that	IN
randomwalker-info-585	381	23	satisfies	satisfy	VBZ
randomwalker-info-585	381	24	this	this	DT
randomwalker-info-585	381	25	con-	con-	NN
randomwalker-info-585	381	26	dition	dition	NN
randomwalker-info-585	381	27	.	.	.
randomwalker-info-585	382	1	We	-PRON-	PRP
randomwalker-info-585	382	2	also	also	RB
randomwalker-info-585	382	3	show	show	VBP
randomwalker-info-585	382	4	that	that	IN
randomwalker-info-585	382	5	combined	combine	VBN
randomwalker-info-585	382	6	with	with	IN
randomwalker-info-585	382	7	the	the	DT
randomwalker-info-585	382	8	fact	fact	NN
randomwalker-info-585	382	9	that	that	IN
randomwalker-info-585	382	10	f	f	NNP
randomwalker-info-585	382	11	(	(	-LRB-
randomwalker-info-585	382	12	·	·	NFP
randomwalker-info-585	382	13	)	)	-RRB-
randomwalker-info-585	382	14	is	be	VBZ
randomwalker-info-585	382	15	monotonically	monotonically	RB
randomwalker-info-585	382	16	non	non	JJ
randomwalker-info-585	382	17	-	-	JJ
randomwalker-info-585	382	18	decreasing	decreasing	JJ
randomwalker-info-585	382	19	,	,	,
randomwalker-info-585	382	20	this	this	DT
randomwalker-info-585	382	21	is	be	VBZ
randomwalker-info-585	382	22	sufficient	sufficient	JJ
randomwalker-info-585	382	23	for	for	IN
randomwalker-info-585	382	24	Function	Function	NNP
randomwalker-info-585	382	25	-	-	HYPH
randomwalker-info-585	382	26	fork(f	fork(f	NNP
randomwalker-info-585	382	27	)	)	-RRB-
randomwalker-info-585	382	28	to	to	TO
randomwalker-info-585	382	29	be	be	VB
randomwalker-info-585	382	30	an	an	DT
randomwalker-info-585	382	31	equilibrium	equilibrium	NN
randomwalker-info-585	382	32	under	under	IN
randomwalker-info-585	382	33	some	some	DT
randomwalker-info-585	382	34	as-	as-	JJ
randomwalker-info-585	382	35	sumptions	sumption	NNS
randomwalker-info-585	382	36	(	(	-LRB-
randomwalker-info-585	382	37	which	which	WDT
randomwalker-info-585	382	38	we	-PRON-	PRP
randomwalker-info-585	382	39	will	will	MD
randomwalker-info-585	382	40	discuss	discuss	VB
randomwalker-info-585	382	41	post	post	JJ
randomwalker-info-585	382	42	-	-	JJ
randomwalker-info-585	382	43	theorem	theorem	JJ
randomwalker-info-585	382	44	)	)	-RRB-
randomwalker-info-585	382	45	.	.	.
randomwalker-info-585	383	1	In	in	IN
randomwalker-info-585	383	2	the	the	DT
randomwalker-info-585	383	3	theorem	theorem	JJ
randomwalker-info-585	383	4	statement	statement	NN
randomwalker-info-585	383	5	below	below	RB
randomwalker-info-585	383	6	,	,	,
randomwalker-info-585	383	7	W0	w0	NN
randomwalker-info-585	383	8	is	be	VBZ
randomwalker-info-585	383	9	the	the	DT
randomwalker-info-585	383	10	upper	upper	JJ
randomwalker-info-585	383	11	branch	branch	NN
randomwalker-info-585	383	12	of	of	IN
randomwalker-info-585	383	13	the	the	DT
randomwalker-info-585	383	14	Lambert	Lambert	NNP
randomwalker-info-585	383	15	W	W	NNP
randomwalker-info-585	383	16	function	function	NN
randomwalker-info-585	383	17	which	which	WDT
randomwalker-info-585	383	18	satisfies	satisfy	VBZ
randomwalker-info-585	383	19	W0(xe	W0(xe	NNS
randomwalker-info-585	383	20	x	x	NNPS
randomwalker-info-585	383	21	)	)	-RRB-
randomwalker-info-585	383	22	=	=	NFP
randomwalker-info-585	383	23	x	x	NN
randomwalker-info-585	383	24	for	for	IN
randomwalker-info-585	383	25	all	all	DT
randomwalker-info-585	383	26	x	x	NN
randomwalker-info-585	383	27	∈	∈	IN
randomwalker-info-585	383	28	[	[	-LRB-
randomwalker-info-585	383	29	−1	−1	NNP
randomwalker-info-585	383	30	/	/	SYM
randomwalker-info-585	383	31	e,∞	e,∞	NNP
randomwalker-info-585	383	32	)	)	-RRB-
randomwalker-info-585	383	33	,	,	,
randomwalker-info-585	383	34	and	and	CC
randomwalker-info-585	383	35	W0(x	w0(x	NN
randomwalker-info-585	383	36	)	)	-RRB-
randomwalker-info-585	383	37	∈	∈	VBD
randomwalker-info-585	383	38	[	[	-LRB-
randomwalker-info-585	383	39	−1,∞	−1,∞	UH
randomwalker-info-585	383	40	)	)	-RRB-
randomwalker-info-585	383	41	.	.	.
randomwalker-info-585	384	1	The	the	DT
randomwalker-info-585	384	2	“	"	``
randomwalker-info-585	384	3	Furthermore	furthermore	RB
randomwalker-info-585	384	4	...	...	:
randomwalker-info-585	384	5	”	"	''
randomwalker-info-585	384	6	portion	portion	NN
randomwalker-info-585	384	7	of	of	IN
randomwalker-info-585	384	8	the	the	DT
randomwalker-info-585	384	9	theorem	theorem	NN
randomwalker-info-585	384	10	is	be	VBZ
randomwalker-info-585	384	11	proved	prove	VBN
randomwalker-info-585	384	12	by	by	IN
randomwalker-info-585	384	13	showing	show	VBG
randomwalker-info-585	384	14	a	a	DT
randomwalker-info-585	384	15	connection	connection	NN
randomwalker-info-585	384	16	between	between	IN
randomwalker-info-585	384	17	the	the	DT
randomwalker-info-585	384	18	number	number	NN
randomwalker-info-585	384	19	of	of	IN
randomwalker-info-585	384	20	backlogged	backlogged	JJ
randomwalker-info-585	384	21	transactions	transaction	NNS
randomwalker-info-585	384	22	and	and	CC
randomwalker-info-585	384	23	an	an	DT
randomwalker-info-585	384	24	un-	un-	JJ
randomwalker-info-585	384	25	biased	biased	JJ
randomwalker-info-585	384	26	single	single	JJ
randomwalker-info-585	384	27	-	-	HYPH
randomwalker-info-585	384	28	dimensional	dimensional	JJ
randomwalker-info-585	384	29	random	random	JJ
randomwalker-info-585	384	30	walk	walk	NN
randomwalker-info-585	384	31	.	.	.
randomwalker-info-585	385	1	Theorem	theorem	NN
randomwalker-info-585	385	2	5.1	5.1	CD
randomwalker-info-585	385	3	.	.	.
randomwalker-info-585	386	1	For	for	IN
randomwalker-info-585	386	2	any	any	DT
randomwalker-info-585	386	3	constant	constant	JJ
randomwalker-info-585	386	4	y	y	NN
randomwalker-info-585	386	5	≤	≤	NN
randomwalker-info-585	386	6	1/2	1/2	CD
randomwalker-info-585	386	7	such	such	JJ
randomwalker-info-585	386	8	that	that	IN
randomwalker-info-585	386	9	2y	2y	CD
randomwalker-info-585	386	10	−	−	NNP
randomwalker-info-585	386	11	ln(y	ln(y	NNP
randomwalker-info-585	386	12	)	)	-RRB-
randomwalker-info-585	386	13	≥	≥	UH
randomwalker-info-585	386	14	2,5	2,5	CD
randomwalker-info-585	386	15	define	define	NN
randomwalker-info-585	386	16	:	:	:
randomwalker-info-585	386	17	f(x	f(x	NNP
randomwalker-info-585	386	18	)	)	-RRB-
randomwalker-info-585	386	19	=	=	NFP
randomwalker-info-585	386	20	x	x	NNPS
randomwalker-info-585	386	21	,	,	,
randomwalker-info-585	386	22	∀	∀	NNP
randomwalker-info-585	386	23	x	x	NNP
randomwalker-info-585	386	24	≤	≤	NNP
randomwalker-info-585	386	25	y	y	NNP
randomwalker-info-585	386	26	(	(	-LRB-
randomwalker-info-585	386	27	1	1	CD
randomwalker-info-585	386	28	)	)	-RRB-
randomwalker-info-585	386	29	f(x	f(x	NNP
randomwalker-info-585	386	30	)	)	-RRB-
randomwalker-info-585	386	31	=	=	NFP
randomwalker-info-585	386	32	−W0(−yex−2y	−W0(−yex−2y	NNP
randomwalker-info-585	386	33	)	)	-RRB-
randomwalker-info-585	386	34	,	,	,
randomwalker-info-585	386	35	∀	∀	NNP
randomwalker-info-585	386	36	y	y	NNP
randomwalker-info-585	386	37	<	<	XX
randomwalker-info-585	386	38	x	x	NNP
randomwalker-info-585	386	39	<	<	XX
randomwalker-info-585	386	40	2y	2y	NNP
randomwalker-info-585	386	41	−	−	NNP
randomwalker-info-585	386	42	ln(y	ln(y	NNP
randomwalker-info-585	386	43	)	)	-RRB-
randomwalker-info-585	386	44	−	−	NNP
randomwalker-info-585	386	45	1	1	CD
randomwalker-info-585	386	46	(	(	-LRB-
randomwalker-info-585	386	47	2	2	CD
randomwalker-info-585	386	48	)	)	-RRB-
randomwalker-info-585	386	49	f(x	f(x	NNP
randomwalker-info-585	386	50	)	)	-RRB-
randomwalker-info-585	386	51	=	=	SYM
randomwalker-info-585	386	52	1	1	CD
randomwalker-info-585	386	53	,	,	,
randomwalker-info-585	386	54	∀	∀	NNP
randomwalker-info-585	386	55	x	x	CC
randomwalker-info-585	386	56	≥	≥	CD
randomwalker-info-585	386	57	2y	2y	CD
randomwalker-info-585	386	58	−	−	NNP
randomwalker-info-585	386	59	ln(y	ln(y	NNP
randomwalker-info-585	386	60	)	)	-RRB-
randomwalker-info-585	386	61	−	−	NNP
randomwalker-info-585	386	62	1	1	CD
randomwalker-info-585	386	63	(	(	-LRB-
randomwalker-info-585	386	64	3	3	CD
randomwalker-info-585	386	65	)	)	-RRB-
randomwalker-info-585	386	66	Then	then	RB
randomwalker-info-585	386	67	it	-PRON-	PRP
randomwalker-info-585	386	68	is	be	VBZ
randomwalker-info-585	386	69	an	an	DT
randomwalker-info-585	386	70	equilibrium	equilibrium	NN
randomwalker-info-585	386	71	for	for	IN
randomwalker-info-585	386	72	every	every	DT
randomwalker-info-585	386	73	miner	miner	NN
randomwalker-info-585	386	74	to	to	TO
randomwalker-info-585	386	75	use	use	VB
randomwalker-info-585	386	76	the	the	DT
randomwalker-info-585	386	77	strategy	strategy	NN
randomwalker-info-585	386	78	Function	Function	NNP
randomwalker-info-585	386	79	-	-	HYPH
randomwalker-info-585	386	80	fork(f	fork(f	NNP
randomwalker-info-585	386	81	)	)	-RRB-
randomwalker-info-585	386	82	as	as	RB
randomwalker-info-585	386	83	long	long	RB
randomwalker-info-585	386	84	as	as	IN
randomwalker-info-585	386	85	:	:	:
randomwalker-info-585	386	86	•	•	VB
randomwalker-info-585	386	87	Every	every	DT
randomwalker-info-585	386	88	miner	miner	NN
randomwalker-info-585	386	89	is	be	VBZ
randomwalker-info-585	386	90	non	non	JJ
randomwalker-info-585	386	91	-	-	JJ
randomwalker-info-585	386	92	atomic	atomic	JJ
randomwalker-info-585	386	93	.	.	.
randomwalker-info-585	387	1	•	•	NNP
randomwalker-info-585	387	2	Miners	miner	NNS
randomwalker-info-585	387	3	may	may	MD
randomwalker-info-585	387	4	only	only	RB
randomwalker-info-585	387	5	mine	mine	VB
randomwalker-info-585	387	6	on	on	IN
randomwalker-info-585	387	7	top	top	NN
randomwalker-info-585	387	8	of	of	IN
randomwalker-info-585	387	9	chains	chain	NNS
randomwalker-info-585	387	10	of	of	IN
randomwalker-info-585	387	11	length	length	NN
randomwalker-info-585	387	12	H	h	NN
randomwalker-info-585	387	13	or	or	CC
randomwalker-info-585	387	14	H−	H−	NNP
randomwalker-info-585	387	15	1	1	CD
randomwalker-info-585	387	16	.	.	.
randomwalker-info-585	388	1	Furthermore	furthermore	RB
randomwalker-info-585	388	2	,	,	,
randomwalker-info-585	388	3	in	in	IN
randomwalker-info-585	388	4	any	any	DT
randomwalker-info-585	388	5	such	such	JJ
randomwalker-info-585	388	6	equilibrium	equilibrium	NN
randomwalker-info-585	388	7	,	,	,
randomwalker-info-585	388	8	the	the	DT
randomwalker-info-585	388	9	expected	expected	JJ
randomwalker-info-585	388	10	number	number	NN
randomwalker-info-585	388	11	of	of	IN
randomwalker-info-585	388	12	backlogged	backlogged	JJ
randomwalker-info-585	388	13	transactions	transaction	NNS
randomwalker-info-585	388	14	after	after	IN
randomwalker-info-585	388	15	n	n	JJ
randomwalker-info-585	388	16	time	time	NN
randomwalker-info-585	388	17	steps	step	NNS
randomwalker-info-585	388	18	is	be	VBZ
randomwalker-info-585	388	19	Θ	Θ	NNP
randomwalker-info-585	388	20	(	(	-LRB-
randomwalker-info-585	388	21	√	√	NNP
randomwalker-info-585	388	22	n	n	NNP
randomwalker-info-585	388	23	)	)	-RRB-
randomwalker-info-585	388	24	.	.	.
randomwalker-info-585	389	1	5Such	5Such	NNP
randomwalker-info-585	389	2	y	y	NNP
randomwalker-info-585	389	3	exist	exist	VBP
randomwalker-info-585	389	4	.	.	.
randomwalker-info-585	390	1	This	this	DT
randomwalker-info-585	390	2	range	range	NN
randomwalker-info-585	390	3	is	be	VBZ
randomwalker-info-585	390	4	(	(	-LRB-
randomwalker-info-585	390	5	0,≈	0,≈	CD
randomwalker-info-585	390	6	0.2	0.2	CD
randomwalker-info-585	390	7	]	]	-RRB-
randomwalker-info-585	390	8	.	.	.
randomwalker-info-585	391	1	Figure	figure	NN
randomwalker-info-585	391	2	5	5	CD
randomwalker-info-585	391	3	:	:	:
randomwalker-info-585	391	4	Plot	plot	NN
randomwalker-info-585	391	5	of	of	IN
randomwalker-info-585	391	6	the	the	DT
randomwalker-info-585	391	7	Lambert	Lambert	NNP
randomwalker-info-585	391	8	function	function	NN
randomwalker-info-585	391	9	fork	fork	NN
randomwalker-info-585	391	10	starting	start	VBG
randomwalker-info-585	391	11	with	with	IN
randomwalker-info-585	391	12	a	a	DT
randomwalker-info-585	391	13	weight	weight	NN
randomwalker-info-585	391	14	of	of	IN
randomwalker-info-585	391	15	0.0001	0.0001	CD
randomwalker-info-585	391	16	and	and	CC
randomwalker-info-585	391	17	becoming	become	VBG
randomwalker-info-585	391	18	the	the	DT
randomwalker-info-585	391	19	strongest	strong	JJS
randomwalker-info-585	391	20	strategy	strategy	NN
randomwalker-info-585	391	21	in	in	IN
randomwalker-info-585	391	22	a	a	DT
randomwalker-info-585	391	23	learning	learning	NN
randomwalker-info-585	391	24	simulation	simulation	NN
randomwalker-info-585	391	25	with	with	IN
randomwalker-info-585	391	26	�	�	NNP
randomwalker-info-585	391	27	=	=	SYM
randomwalker-info-585	391	28	.01	.01	NFP
randomwalker-info-585	391	29	.	.	.
randomwalker-info-585	392	1	This	this	DT
randomwalker-info-585	392	2	simulation	simulation	NN
randomwalker-info-585	392	3	had	have	VBD
randomwalker-info-585	392	4	100	100	CD
randomwalker-info-585	392	5	miners	miner	NNS
randomwalker-info-585	392	6	,	,	,
randomwalker-info-585	392	7	and	and	CC
randomwalker-info-585	392	8	10,000	10,000	CD
randomwalker-info-585	392	9	blocks	block	NNS
randomwalker-info-585	392	10	per	per	IN
randomwalker-info-585	392	11	game	game	NN
randomwalker-info-585	392	12	.	.	.
randomwalker-info-585	393	1	These	these	DT
randomwalker-info-585	393	2	miners	miner	NNS
randomwalker-info-585	393	3	are	be	VBP
randomwalker-info-585	393	4	non	non	JJ
randomwalker-info-585	393	5	-	-	JJ
randomwalker-info-585	393	6	atomic	atomic	JJ
randomwalker-info-585	393	7	.	.	.
randomwalker-info-585	394	1	A	a	DT
randomwalker-info-585	394	2	proof	proof	NN
randomwalker-info-585	394	3	of	of	IN
randomwalker-info-585	394	4	Theorem	theorem	NN
randomwalker-info-585	394	5	5.1	5.1	CD
randomwalker-info-585	394	6	appears	appear	NNS
randomwalker-info-585	394	7	in	in	IN
randomwalker-info-585	394	8	Appendix	Appendix	NNP
randomwalker-info-585	394	9	C.	C.	NNP
randomwalker-info-585	394	10	To	to	IN
randomwalker-info-585	394	11	un-	un-	VB
randomwalker-info-585	394	12	derstand	derstand	NN
randomwalker-info-585	394	13	the	the	DT
randomwalker-info-585	394	14	impact	impact	NN
randomwalker-info-585	394	15	of	of	IN
randomwalker-info-585	394	16	Theorem	Theorem	NNP
randomwalker-info-585	394	17	5.1	5.1	CD
randomwalker-info-585	394	18	,	,	,
randomwalker-info-585	394	19	first	first	RB
randomwalker-info-585	394	20	consider	consider	VB
randomwalker-info-585	394	21	the	the	DT
randomwalker-info-585	394	22	block	block	NN
randomwalker-info-585	394	23	reward	reward	NN
randomwalker-info-585	394	24	model	model	NN
randomwalker-info-585	394	25	.	.	.
randomwalker-info-585	395	1	With	with	IN
randomwalker-info-585	395	2	non	non	JJ
randomwalker-info-585	395	3	-	-	JJ
randomwalker-info-585	395	4	atomic	atomic	JJ
randomwalker-info-585	395	5	miners	miner	NNS
randomwalker-info-585	395	6	,	,	,
randomwalker-info-585	395	7	DefaultCompli-	defaultcompli-	NN
randomwalker-info-585	395	8	ant	ant	NN
randomwalker-info-585	395	9	is	be	VBZ
randomwalker-info-585	395	10	trivially	trivially	RB
randomwalker-info-585	395	11	an	an	DT
randomwalker-info-585	395	12	equilibrium	equilibrium	NN
randomwalker-info-585	395	13	,	,	,
randomwalker-info-585	395	14	and	and	CC
randomwalker-info-585	395	15	this	this	DT
randomwalker-info-585	395	16	result	result	NN
randomwalker-info-585	395	17	is	be	VBZ
randomwalker-info-585	395	18	robust	robust	JJ
randomwalker-info-585	395	19	to	to	IN
randomwalker-info-585	395	20	general	general	JJ
randomwalker-info-585	395	21	models	model	NNS
randomwalker-info-585	395	22	of	of	IN
randomwalker-info-585	395	23	latency	latency	NN
randomwalker-info-585	395	24	(	(	-LRB-
randomwalker-info-585	395	25	proof	proof	NN
randomwalker-info-585	395	26	in	in	IN
randomwalker-info-585	395	27	Appendix	Appendix	NNP
randomwalker-info-585	395	28	D	D	NNP
randomwalker-info-585	395	29	)	)	-RRB-
randomwalker-info-585	395	30	.	.	.
randomwalker-info-585	396	1	But	but	CC
randomwalker-info-585	396	2	as	as	IN
randomwalker-info-585	396	3	we	-PRON-	PRP
randomwalker-info-585	396	4	move	move	VBP
randomwalker-info-585	396	5	to	to	IN
randomwalker-info-585	396	6	atomic	atomic	JJ
randomwalker-info-585	396	7	miners	miner	NNS
randomwalker-info-585	396	8	,	,	,
randomwalker-info-585	396	9	strategies	strategy	NNS
randomwalker-info-585	396	10	like	like	IN
randomwalker-info-585	396	11	selfish	selfish	JJ
randomwalker-info-585	396	12	mining	mining	NN
randomwalker-info-585	396	13	arise	arise	NN
randomwalker-info-585	396	14	and	and	CC
randomwalker-info-585	396	15	equilibria	equilibria	NN
randomwalker-info-585	396	16	get	get	VB
randomwalker-info-585	396	17	messy	messy	JJ
randomwalker-info-585	396	18	(	(	-LRB-
randomwalker-info-585	396	19	if	if	IN
randomwalker-info-585	396	20	they	-PRON-	PRP
randomwalker-info-585	396	21	exist	exist	VBP
randomwalker-info-585	396	22	at	at	RB
randomwalker-info-585	396	23	all	all	RB
randomwalker-info-585	396	24	)	)	-RRB-
randomwalker-info-585	396	25	.	.	.
randomwalker-info-585	397	1	Now	now	RB
randomwalker-info-585	397	2	,	,	,
randomwalker-info-585	397	3	in	in	IN
randomwalker-info-585	397	4	the	the	DT
randomwalker-info-585	397	5	transaction	transaction	NN
randomwalker-info-585	397	6	-	-	HYPH
randomwalker-info-585	397	7	fee	fee	NN
randomwalker-info-585	397	8	model	model	NN
randomwalker-info-585	397	9	,	,	,
randomwalker-info-585	397	10	even	even	RB
randomwalker-info-585	397	11	when	when	WRB
randomwalker-info-585	397	12	miners	miner	NNS
randomwalker-info-585	397	13	are	be	VBP
randomwalker-info-585	397	14	non	non	JJ
randomwalker-info-585	397	15	-	-	JJ
randomwalker-info-585	397	16	atomic	atomic	JJ
randomwalker-info-585	397	17	,	,	,
randomwalker-info-585	397	18	equilibrium	equilibrium	NN
randomwalker-info-585	397	19	behavior	behavior	NN
randomwalker-info-585	397	20	is	be	VBZ
randomwalker-info-585	397	21	complex	complex	JJ
randomwalker-info-585	397	22	and	and	CC
randomwalker-info-585	397	23	undesirable	undesirable	JJ
randomwalker-info-585	397	24	,	,	,
randomwalker-info-585	397	25	as	as	IN
randomwalker-info-585	397	26	we	-PRON-	PRP
randomwalker-info-585	397	27	have	have	VBP
randomwalker-info-585	397	28	just	just	RB
randomwalker-info-585	397	29	shown	show	VBN
randomwalker-info-585	397	30	.	.	.
randomwalker-info-585	398	1	Therefore	therefore	RB
randomwalker-info-585	398	2	,	,	,
randomwalker-info-585	398	3	we	-PRON-	PRP
randomwalker-info-585	398	4	should	should	MD
randomwalker-info-585	398	5	expect	expect	VB
randomwalker-info-585	398	6	that	that	DT
randomwalker-info-585	398	7	analysis	analysis	NN
randomwalker-info-585	398	8	with	with	IN
randomwalker-info-585	398	9	atomic	atomic	JJ
randomwalker-info-585	398	10	miners	miner	NNS
randomwalker-info-585	398	11	should	should	MD
randomwalker-info-585	398	12	conclude	conclude	VB
randomwalker-info-585	398	13	with	with	IN
randomwalker-info-585	398	14	even	even	RB
randomwalker-info-585	398	15	more	more	JJR
randomwalker-info-585	398	16	chaos	chaos	NN
randomwalker-info-585	398	17	.	.	.
randomwalker-info-585	399	1	Figure	figure	NN
randomwalker-info-585	399	2	5	5	CD
randomwalker-info-585	399	3	shows	show	VBZ
randomwalker-info-585	399	4	miners	miner	NNS
randomwalker-info-585	399	5	learning	learn	VBG
randomwalker-info-585	399	6	to	to	TO
randomwalker-info-585	399	7	play	play	VB
randomwalker-info-585	399	8	this	this	DT
randomwalker-info-585	399	9	equilibrium	equilibrium	NN
randomwalker-info-585	399	10	,	,	,
randomwalker-info-585	399	11	even	even	RB
randomwalker-info-585	399	12	with	with	IN
randomwalker-info-585	399	13	various	various	JJ
randomwalker-info-585	399	14	other	other	JJ
randomwalker-info-585	399	15	strategies	strategy	NNS
randomwalker-info-585	399	16	available	available	JJ
randomwalker-info-585	399	17	.	.	.
randomwalker-info-585	400	1	Observe	observe	VB
randomwalker-info-585	400	2	the	the	DT
randomwalker-info-585	400	3	in-	in-	JJ
randomwalker-info-585	400	4	terplay	terplay	NN
randomwalker-info-585	400	5	between	between	IN
randomwalker-info-585	400	6	theory	theory	NN
randomwalker-info-585	400	7	and	and	CC
randomwalker-info-585	400	8	simulation	simulation	NN
randomwalker-info-585	400	9	:	:	:
randomwalker-info-585	400	10	Theorem	theorem	NN
randomwalker-info-585	400	11	5.1	5.1	CD
randomwalker-info-585	400	12	guides	guide	VBZ
randomwalker-info-585	400	13	us	-PRON-	PRP
randomwalker-info-585	400	14	towards	towards	IN
randomwalker-info-585	400	15	a	a	DT
randomwalker-info-585	400	16	potentially	potentially	RB
randomwalker-info-585	400	17	strong	strong	JJ
randomwalker-info-585	400	18	strategy	strategy	NN
randomwalker-info-585	400	19	,	,	,
randomwalker-info-585	400	20	but	but	CC
randomwalker-info-585	400	21	it	-PRON-	PRP
randomwalker-info-585	400	22	is	be	VBZ
randomwalker-info-585	400	23	intractable	intractable	JJ
randomwalker-info-585	400	24	to	to	TO
randomwalker-info-585	400	25	prove	prove	VB
randomwalker-info-585	400	26	that	that	IN
randomwalker-info-585	400	27	the	the	DT
randomwalker-info-585	400	28	equilibrium	equilibrium	NN
randomwalker-info-585	400	29	will	will	MD
randomwalker-info-585	400	30	actually	actually	RB
randomwalker-info-585	400	31	arise	arise	VB
randomwalker-info-585	400	32	via	via	IN
randomwalker-info-585	400	33	learning	learn	VBG
randomwalker-info-585	400	34	even	even	RB
randomwalker-info-585	400	35	when	when	WRB
randomwalker-info-585	400	36	(	(	-LRB-
randomwalker-info-585	400	37	say	say	VB
randomwalker-info-585	400	38	)	)	-RRB-
randomwalker-info-585	400	39	99	99	CD
randomwalker-info-585	400	40	%	%	NN
randomwalker-info-585	400	41	of	of	IN
randomwalker-info-585	400	42	miners	miner	NNS
randomwalker-info-585	400	43	are	be	VBP
randomwalker-info-585	400	44	already	already	RB
randomwalker-info-585	400	45	there	there	RB
randomwalker-info-585	400	46	.	.	.
randomwalker-info-585	401	1	Simula-	Simula-	NNP
randomwalker-info-585	401	2	tion	tion	NN
randomwalker-info-585	401	3	fills	fill	VBZ
randomwalker-info-585	401	4	the	the	DT
randomwalker-info-585	401	5	gap	gap	NN
randomwalker-info-585	401	6	and	and	CC
randomwalker-info-585	401	7	shows	show	VBZ
randomwalker-info-585	401	8	an	an	DT
randomwalker-info-585	401	9	equilibrium	equilibrium	NN
randomwalker-info-585	401	10	will	will	MD
randomwalker-info-585	401	11	indeed	indeed	RB
randomwalker-info-585	401	12	even	even	RB
randomwalker-info-585	401	13	when	when	WRB
randomwalker-info-585	401	14	only	only	RB
randomwalker-info-585	401	15	.01	.01	.
randomwalker-info-585	401	16	%	%	NN
randomwalker-info-585	401	17	of	of	IN
randomwalker-info-585	401	18	the	the	DT
randomwalker-info-585	401	19	miners	miner	NNS
randomwalker-info-585	401	20	initially	initially	RB
randomwalker-info-585	401	21	use	use	VBP
randomwalker-info-585	401	22	the	the	DT
randomwalker-info-585	401	23	equilibrium	equilibrium	NN
randomwalker-info-585	401	24	strategy.6	strategy.6	NNP
randomwalker-info-585	401	25	Simulation	Simulation	NNP
randomwalker-info-585	401	26	alone	alone	RB
randomwalker-info-585	401	27	could	could	MD
randomwalker-info-585	401	28	not	not	RB
randomwalker-info-585	401	29	search	search	VB
randomwalker-info-585	401	30	through	through	IN
randomwalker-info-585	401	31	the	the	DT
randomwalker-info-585	401	32	infinitely	infinitely	RB
randomwalker-info-585	401	33	many	many	JJ
randomwalker-info-585	401	34	possible	possible	JJ
randomwalker-info-585	401	35	strategies	strategy	NNS
randomwalker-info-585	401	36	,	,	,
randomwalker-info-585	401	37	and	and	CC
randomwalker-info-585	401	38	theory	theory	NN
randomwalker-info-585	401	39	alone	alone	RB
randomwalker-info-585	401	40	can	can	MD
randomwalker-info-585	401	41	not	not	RB
randomwalker-info-585	401	42	prove	prove	VB
randomwalker-info-585	401	43	that	that	IN
randomwalker-info-585	401	44	learning	learn	VBG
randomwalker-info-585	401	45	converges	converge	NNS
randomwalker-info-585	401	46	to	to	IN
randomwalker-info-585	401	47	the	the	DT
randomwalker-info-585	401	48	desired	desire	VBN
randomwalker-info-585	401	49	equilibrium	equilibrium	NN
randomwalker-info-585	401	50	.	.	.
randomwalker-info-585	402	1	5.5	5.5	CD
randomwalker-info-585	402	2	Undercutting	undercut	VBG
randomwalker-info-585	402	3	Non	non	JJ
randomwalker-info-585	402	4	-	-	JJ
randomwalker-info-585	402	5	strategic	strategic	JJ
randomwalker-info-585	402	6	Miners	Miners	NNPS
randomwalker-info-585	402	7	Analytical	Analytical	NNP
randomwalker-info-585	402	8	and	and	CC
randomwalker-info-585	402	9	simulation	simulation	NN
randomwalker-info-585	402	10	result	result	NN
randomwalker-info-585	402	11	:	:	:
randomwalker-info-585	402	12	even	even	RB
randomwalker-info-585	402	13	if	if	IN
randomwalker-info-585	402	14	66	66	CD
randomwalker-info-585	402	15	%	%	NN
randomwalker-info-585	402	16	of	of	IN
randomwalker-info-585	402	17	miners	miner	NNS
randomwalker-info-585	402	18	remain	remain	VBP
randomwalker-info-585	402	19	default	default	NN
randomwalker-info-585	402	20	compliant	compliant	NN
randomwalker-info-585	402	21	,	,	,
randomwalker-info-585	402	22	undercutting	undercutting	NN
randomwalker-info-585	402	23	is	be	VBZ
randomwalker-info-585	402	24	profitable	profitable	JJ
randomwalker-info-585	402	25	.	.	.
randomwalker-info-585	403	1	Our	-PRON-	PRP$
randomwalker-info-585	403	2	analysis	analysis	NN
randomwalker-info-585	403	3	and	and	CC
randomwalker-info-585	403	4	simulations	simulation	NNS
randomwalker-info-585	403	5	in	in	IN
randomwalker-info-585	403	6	the	the	DT
randomwalker-info-585	403	7	previous	previous	JJ
randomwalker-info-585	403	8	sections	section	NNS
randomwalker-info-585	403	9	as-	as-	CD
randomwalker-info-585	403	10	sumed	sum	VBD
randomwalker-info-585	403	11	that	that	IN
randomwalker-info-585	403	12	all	all	DT
randomwalker-info-585	403	13	miners	miner	NNS
randomwalker-info-585	403	14	were	be	VBD
randomwalker-info-585	403	15	strategic	strategic	JJ
randomwalker-info-585	403	16	learners	learner	NNS
randomwalker-info-585	403	17	.	.	.
randomwalker-info-585	404	1	While	while	IN
randomwalker-info-585	404	2	we	-PRON-	PRP
randomwalker-info-585	404	3	clearly	clearly	RB
randomwalker-info-585	404	4	learn	learn	VBP
randomwalker-info-585	404	5	a	a	DT
randomwalker-info-585	404	6	lot	lot	NN
randomwalker-info-585	404	7	from	from	IN
randomwalker-info-585	404	8	this	this	DT
randomwalker-info-585	404	9	analysis	analysis	NN
randomwalker-info-585	404	10	,	,	,
randomwalker-info-585	404	11	it	-PRON-	PRP
randomwalker-info-585	404	12	is	be	VBZ
randomwalker-info-585	404	13	perhaps	perhaps	RB
randomwalker-info-585	404	14	more	more	RBR
randomwalker-info-585	404	15	realistic	realistic	JJ
randomwalker-info-585	404	16	to	to	TO
randomwalker-info-585	404	17	also	also	RB
randomwalker-info-585	404	18	consider	consider	VB
randomwalker-info-585	404	19	a	a	DT
randomwalker-info-585	404	20	setting	setting	NN
randomwalker-info-585	404	21	where	where	WRB
randomwalker-info-585	404	22	some	some	DT
randomwalker-info-585	404	23	miners	miner	NNS
randomwalker-info-585	404	24	will	will	MD
randomwalker-info-585	404	25	stubbornly	stubbornly	RB
randomwalker-info-585	404	26	(	(	-LRB-
randomwalker-info-585	404	27	or	or	CC
randomwalker-info-585	404	28	honestly	honestly	RB
randomwalker-info-585	404	29	,	,	,
randomwalker-info-585	404	30	depending	depend	VBG
randomwalker-info-585	404	31	on	on	IN
randomwalker-info-585	404	32	your	-PRON-	PRP$
randomwalker-info-585	404	33	perspective	perspective	NN
randomwalker-info-585	404	34	)	)	-RRB-
randomwalker-info-585	404	35	,	,	,
randomwalker-info-585	404	36	continue	continue	VB
randomwalker-info-585	404	37	running	run	VBG
randomwalker-info-585	404	38	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	404	39	even	even	RB
randomwalker-info-585	404	40	if	if	IN
randomwalker-info-585	404	41	it	-PRON-	PRP
randomwalker-info-585	404	42	is	be	VBZ
randomwalker-info-585	404	43	subop-	subop-	JJ
randomwalker-info-585	404	44	timal	timal	JJ
randomwalker-info-585	404	45	.	.	.
randomwalker-info-585	405	1	If	if	IN
randomwalker-info-585	405	2	a	a	DT
randomwalker-info-585	405	3	large	large	JJ
randomwalker-info-585	405	4	fraction	fraction	NN
randomwalker-info-585	405	5	of	of	IN
randomwalker-info-585	405	6	the	the	DT
randomwalker-info-585	405	7	miners	miner	NNS
randomwalker-info-585	405	8	are	be	VBP
randomwalker-info-585	405	9	non	non	JJ
randomwalker-info-585	405	10	-	-	JJ
randomwalker-info-585	405	11	strategic	strategic	JJ
randomwalker-info-585	405	12	,	,	,
randomwalker-info-585	405	13	6It	6it	CD
randomwalker-info-585	405	14	is	be	VBZ
randomwalker-info-585	405	15	hard	hard	JJ
randomwalker-info-585	405	16	to	to	TO
randomwalker-info-585	405	17	see	see	VB
randomwalker-info-585	405	18	in	in	IN
randomwalker-info-585	405	19	Figure	Figure	NNP
randomwalker-info-585	405	20	5	5	CD
randomwalker-info-585	405	21	,	,	,
randomwalker-info-585	405	22	but	but	CC
randomwalker-info-585	405	23	the	the	DT
randomwalker-info-585	405	24	weight	weight	NN
randomwalker-info-585	405	25	assigned	assign	VBN
randomwalker-info-585	405	26	to	to	IN
randomwalker-info-585	405	27	“	"	``
randomwalker-info-585	405	28	Lambert	Lambert	NNP
randomwalker-info-585	405	29	”	"	''
randomwalker-info-585	405	30	is	be	VBZ
randomwalker-info-585	405	31	initially	initially	RB
randomwalker-info-585	405	32	.0001	.0001	.
randomwalker-info-585	405	33	.	.	.
randomwalker-info-585	405	34	then	then	RB
randomwalker-info-585	405	35	function	function	NN
randomwalker-info-585	405	36	-	-	HYPH
randomwalker-info-585	405	37	forking	forking	NN
randomwalker-info-585	405	38	becomes	become	VBZ
randomwalker-info-585	405	39	immediately	immediately	RB
randomwalker-info-585	405	40	less	less	RBR
randomwalker-info-585	405	41	profitable	profitable	JJ
randomwalker-info-585	405	42	,	,	,
randomwalker-info-585	405	43	because	because	IN
randomwalker-info-585	405	44	only	only	RB
randomwalker-info-585	405	45	a	a	DT
randomwalker-info-585	405	46	small	small	JJ
randomwalker-info-585	405	47	fraction	fraction	NN
randomwalker-info-585	405	48	of	of	IN
randomwalker-info-585	405	49	the	the	DT
randomwalker-info-585	405	50	network	network	NN
randomwalker-info-585	405	51	will	will	MD
randomwalker-info-585	405	52	actually	actually	RB
randomwalker-info-585	405	53	mine	mine	VB
randomwalker-info-585	405	54	on	on	IN
randomwalker-info-585	405	55	top	top	NN
randomwalker-info-585	405	56	of	of	IN
randomwalker-info-585	405	57	your	-PRON-	PRP$
randomwalker-info-585	405	58	block	block	NN
randomwalker-info-585	405	59	when	when	WRB
randomwalker-info-585	405	60	you	-PRON-	PRP
randomwalker-info-585	405	61	undercut	undercut	VBD
randomwalker-info-585	405	62	.	.	.
randomwalker-info-585	406	1	In	in	IN
randomwalker-info-585	406	2	particu-	particu-	NN
randomwalker-info-585	406	3	lar	lar	NN
randomwalker-info-585	406	4	,	,	,
randomwalker-info-585	406	5	if	if	IN
randomwalker-info-585	406	6	100	100	CD
randomwalker-info-585	406	7	%	%	NN
randomwalker-info-585	406	8	of	of	IN
randomwalker-info-585	406	9	other	other	JJ
randomwalker-info-585	406	10	miners	miner	NNS
randomwalker-info-585	406	11	are	be	VBP
randomwalker-info-585	406	12	non	non	JJ
randomwalker-info-585	406	13	-	-	JJ
randomwalker-info-585	406	14	strategic	strategic	JJ
randomwalker-info-585	406	15	,	,	,
randomwalker-info-585	406	16	undercutting	undercutting	NN
randomwalker-info-585	406	17	serves	serve	VBZ
randomwalker-info-585	406	18	no	no	DT
randomwalker-info-585	406	19	purpose	purpose	NN
randomwalker-info-585	406	20	.	.	.
randomwalker-info-585	407	1	In	in	IN
randomwalker-info-585	407	2	this	this	DT
randomwalker-info-585	407	3	section	section	NN
randomwalker-info-585	407	4	,	,	,
randomwalker-info-585	407	5	we	-PRON-	PRP
randomwalker-info-585	407	6	detail	detail	VBP
randomwalker-info-585	407	7	results	result	NNS
randomwalker-info-585	407	8	from	from	IN
randomwalker-info-585	407	9	our	-PRON-	PRP$
randomwalker-info-585	407	10	simulation	simulation	NN
randomwalker-info-585	407	11	when	when	WRB
randomwalker-info-585	407	12	varying	vary	VBG
randomwalker-info-585	407	13	fractions	fraction	NNS
randomwalker-info-585	407	14	of	of	IN
randomwalker-info-585	407	15	miners	miner	NNS
randomwalker-info-585	407	16	are	be	VBP
randomwalker-info-585	407	17	non	non	JJ
randomwalker-info-585	407	18	-	-	JJ
randomwalker-info-585	407	19	strategic	strategic	JJ
randomwalker-info-585	407	20	.	.	.
randomwalker-info-585	408	1	In	in	IN
randomwalker-info-585	408	2	these	these	DT
randomwalker-info-585	408	3	sim-	sim-	JJ
randomwalker-info-585	408	4	ulations	ulation	NNS
randomwalker-info-585	408	5	,	,	,
randomwalker-info-585	408	6	we	-PRON-	PRP
randomwalker-info-585	408	7	fix	fix	VBP
randomwalker-info-585	408	8	a	a	DT
randomwalker-info-585	408	9	fraction	fraction	NN
randomwalker-info-585	408	10	of	of	IN
randomwalker-info-585	408	11	the	the	DT
randomwalker-info-585	408	12	network	network	NN
randomwalker-info-585	408	13	to	to	TO
randomwalker-info-585	408	14	always	always	RB
randomwalker-info-585	408	15	mine	mine	VB
randomwalker-info-585	408	16	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	408	17	,	,	,
randomwalker-info-585	408	18	and	and	CC
randomwalker-info-585	408	19	play	play	VB
randomwalker-info-585	408	20	enough	enough	JJ
randomwalker-info-585	408	21	games	game	NNS
randomwalker-info-585	408	22	until	until	IN
randomwalker-info-585	408	23	the	the	DT
randomwalker-info-585	408	24	dis-	dis-	NN
randomwalker-info-585	408	25	tribution	tribution	NN
randomwalker-info-585	408	26	of	of	IN
randomwalker-info-585	408	27	learned	learned	JJ
randomwalker-info-585	408	28	strategies	strategy	NNS
randomwalker-info-585	408	29	stabilize.7Figure	stabilize.7Figure	NNP
randomwalker-info-585	408	30	6	6	CD
randomwalker-info-585	408	31	shows	show	VBZ
randomwalker-info-585	408	32	a	a	DT
randomwalker-info-585	408	33	stacked	stack	VBN
randomwalker-info-585	408	34	area	area	NN
randomwalker-info-585	408	35	plot	plot	NN
randomwalker-info-585	408	36	of	of	IN
randomwalker-info-585	408	37	our	-PRON-	PRP$
randomwalker-info-585	408	38	simulation	simulation	NN
randomwalker-info-585	408	39	results	result	NNS
randomwalker-info-585	408	40	for	for	IN
randomwalker-info-585	408	41	equilibria	equilibria	NN
randomwalker-info-585	408	42	at	at	IN
randomwalker-info-585	408	43	different	different	JJ
randomwalker-info-585	408	44	fractions	fraction	NNS
randomwalker-info-585	408	45	of	of	IN
randomwalker-info-585	408	46	miners	miner	NNS
randomwalker-info-585	408	47	refusing	refuse	VBG
randomwalker-info-585	408	48	to	to	TO
randomwalker-info-585	408	49	abandon	abandon	VB
randomwalker-info-585	408	50	Default-	Default-	NNP
randomwalker-info-585	408	51	Compliant	Compliant	NNP
randomwalker-info-585	408	52	.	.	.
randomwalker-info-585	409	1	There	there	EX
randomwalker-info-585	409	2	are	be	VBP
randomwalker-info-585	409	3	many	many	JJ
randomwalker-info-585	409	4	interesting	interesting	JJ
randomwalker-info-585	409	5	features	feature	NNS
randomwalker-info-585	409	6	of	of	IN
randomwalker-info-585	409	7	the	the	DT
randomwalker-info-585	409	8	plot	plot	NN
randomwalker-info-585	409	9	,	,	,
randomwalker-info-585	409	10	but	but	CC
randomwalker-info-585	409	11	we	-PRON-	PRP
randomwalker-info-585	409	12	focus	focus	VBP
randomwalker-info-585	409	13	on	on	IN
randomwalker-info-585	409	14	one	one	CD
randomwalker-info-585	409	15	:	:	:
randomwalker-info-585	409	16	even	even	RB
randomwalker-info-585	409	17	if	if	IN
randomwalker-info-585	409	18	the	the	DT
randomwalker-info-585	409	19	majority	majority	NN
randomwalker-info-585	409	20	of	of	IN
randomwalker-info-585	409	21	miners	miner	NNS
randomwalker-info-585	409	22	choose	choose	VBP
randomwalker-info-585	409	23	to	to	TO
randomwalker-info-585	409	24	stay	stay	VB
randomwalker-info-585	409	25	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	409	26	(	(	-LRB-
randomwalker-info-585	409	27	and	and	CC
randomwalker-info-585	409	28	the	the	DT
randomwalker-info-585	409	29	rest	rest	NN
randomwalker-info-585	409	30	strategize	strategize	NN
randomwalker-info-585	409	31	)	)	-RRB-
randomwalker-info-585	409	32	,	,	,
randomwalker-info-585	409	33	then	then	RB
randomwalker-info-585	409	34	forking	fork	VBG
randomwalker-info-585	409	35	strategies	strategy	NNS
randomwalker-info-585	409	36	start	start	VBP
randomwalker-info-585	409	37	to	to	TO
randomwalker-info-585	409	38	become	become	VB
randomwalker-info-585	409	39	viable	viable	JJ
randomwalker-info-585	409	40	.	.	.
randomwalker-info-585	410	1	A	a	DT
randomwalker-info-585	410	2	theoretical	theoretical	JJ
randomwalker-info-585	410	3	analysis	analysis	NN
randomwalker-info-585	410	4	indeed	indeed	RB
randomwalker-info-585	410	5	predicts	predict	VBZ
randomwalker-info-585	410	6	the	the	DT
randomwalker-info-585	410	7	continuing	continue	VBG
randomwalker-info-585	410	8	pres-	pres-	NN
randomwalker-info-585	410	9	ence	ence	NN
randomwalker-info-585	410	10	of	of	IN
randomwalker-info-585	410	11	FunctionFork(x	FunctionFork(x	NNP
randomwalker-info-585	410	12	)	)	-RRB-
randomwalker-info-585	410	13	until	until	IN
randomwalker-info-585	410	14	2/3	2/3	CD
randomwalker-info-585	410	15	of	of	IN
randomwalker-info-585	410	16	the	the	DT
randomwalker-info-585	410	17	miners	miner	NNS
randomwalker-info-585	410	18	remain	remain	VBP
randomwalker-info-585	410	19	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	410	20	.	.	.
randomwalker-info-585	411	1	To	to	TO
randomwalker-info-585	411	2	see	see	VB
randomwalker-info-585	411	3	this	this	DT
randomwalker-info-585	411	4	,	,	,
randomwalker-info-585	411	5	imagine	imagine	VB
randomwalker-info-585	411	6	that	that	IN
randomwalker-info-585	411	7	every	every	DT
randomwalker-info-585	411	8	miner	miner	NN
randomwalker-info-585	411	9	is	be	VBZ
randomwalker-info-585	411	10	the	the	DT
randomwalker-info-585	411	11	system	system	NN
randomwalker-info-585	411	12	is	be	VBZ
randomwalker-info-585	411	13	currently	currently	RB
randomwalker-info-585	411	14	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	411	15	or	or	CC
randomwalker-info-585	411	16	Petty-	Petty-	NNP
randomwalker-info-585	411	17	Compliant	Compliant	NNP
randomwalker-info-585	411	18	,	,	,
randomwalker-info-585	411	19	and	and	CC
randomwalker-info-585	411	20	we	-PRON-	PRP
randomwalker-info-585	411	21	want	want	VBP
randomwalker-info-585	411	22	to	to	TO
randomwalker-info-585	411	23	see	see	VB
randomwalker-info-585	411	24	if	if	IN
randomwalker-info-585	411	25	it	-PRON-	PRP
randomwalker-info-585	411	26	is	be	VBZ
randomwalker-info-585	411	27	profitable	profitable	JJ
randomwalker-info-585	411	28	for	for	IN
randomwalker-info-585	411	29	a	a	DT
randomwalker-info-585	411	30	Pet-	Pet-	NNP
randomwalker-info-585	411	31	tyCompliant	tyCompliant	NNP
randomwalker-info-585	411	32	miner	miner	NN
randomwalker-info-585	411	33	to	to	TO
randomwalker-info-585	411	34	switch	switch	VB
randomwalker-info-585	411	35	to	to	IN
randomwalker-info-585	411	36	FunctionFork(x	FunctionFork(x	NNP
randomwalker-info-585	411	37	)	)	-RRB-
randomwalker-info-585	411	38	.	.	.
randomwalker-info-585	412	1	At	at	IN
randomwalker-info-585	412	2	any	any	DT
randomwalker-info-585	412	3	point	point	NN
randomwalker-info-585	412	4	in	in	IN
randomwalker-info-585	412	5	time	time	NN
randomwalker-info-585	412	6	,	,	,
randomwalker-info-585	412	7	consider	consider	VB
randomwalker-info-585	412	8	the	the	DT
randomwalker-info-585	412	9	current	current	JJ
randomwalker-info-585	412	10	MostH.	MostH.	NNS
randomwalker-info-585	413	1	Then	then	RB
randomwalker-info-585	413	2	if	if	IN
randomwalker-info-585	413	3	the	the	DT
randomwalker-info-585	413	4	miner	miner	NN
randomwalker-info-585	413	5	runs	run	VBZ
randomwalker-info-585	413	6	PettyCompliant	PettyCompliant	NNP
randomwalker-info-585	413	7	,	,	,
randomwalker-info-585	413	8	they	-PRON-	PRP
randomwalker-info-585	413	9	will	will	MD
randomwalker-info-585	413	10	always	always	RB
randomwalker-info-585	413	11	try	try	VB
randomwalker-info-585	413	12	to	to	TO
randomwalker-info-585	413	13	con-	con-	NNP
randomwalker-info-585	413	14	tinue	tinue	VB
randomwalker-info-585	413	15	,	,	,
randomwalker-info-585	413	16	and	and	CC
randomwalker-info-585	413	17	will	will	MD
randomwalker-info-585	413	18	get	get	VB
randomwalker-info-585	413	19	Rem(MostH	rem(mosth	ADD
randomwalker-info-585	413	20	)	)	-RRB-
randomwalker-info-585	413	21	should	should	MD
randomwalker-info-585	413	22	they	-PRON-	PRP
randomwalker-info-585	413	23	find	find	VB
randomwalker-info-585	413	24	a	a	DT
randomwalker-info-585	413	25	block	block	NN
randomwalker-info-585	413	26	(	(	-LRB-
randomwalker-info-585	413	27	because	because	IN
randomwalker-info-585	413	28	no	no	DT
randomwalker-info-585	413	29	one	one	NN
randomwalker-info-585	413	30	else	else	RB
randomwalker-info-585	413	31	in	in	IN
randomwalker-info-585	413	32	the	the	DT
randomwalker-info-585	413	33	network	network	NN
randomwalker-info-585	413	34	is	be	VBZ
randomwalker-info-585	413	35	undercutting	undercut	VBG
randomwalker-info-585	413	36	)	)	-RRB-
randomwalker-info-585	413	37	.	.	.
randomwalker-info-585	414	1	If	if	IN
randomwalker-info-585	414	2	in-	in-	DT
randomwalker-info-585	414	3	stead	stead	VBP
randomwalker-info-585	414	4	they	-PRON-	PRP
randomwalker-info-585	414	5	run	run	VBP
randomwalker-info-585	414	6	FunctionFork(x	FunctionFork(x	NNP
randomwalker-info-585	414	7	)	)	-RRB-
randomwalker-info-585	414	8	,	,	,
randomwalker-info-585	414	9	they	-PRON-	PRP
randomwalker-info-585	414	10	will	will	MD
randomwalker-info-585	414	11	continue	continue	VB
randomwalker-info-585	414	12	when-	when-	NN
randomwalker-info-585	414	13	ever	ever	RB
randomwalker-info-585	414	14	Rem(MostH	rem(mosth	ADD
randomwalker-info-585	414	15	)	)	-RRB-
randomwalker-info-585	414	16	>	>	XX
randomwalker-info-585	414	17	GapH	GapH	NNP
randomwalker-info-585	414	18	and	and	CC
randomwalker-info-585	414	19	undercut	undercut	VBD
randomwalker-info-585	414	20	otherwise	otherwise	RB
randomwalker-info-585	414	21	.	.	.
randomwalker-info-585	415	1	When	when	WRB
randomwalker-info-585	415	2	they	-PRON-	PRP
randomwalker-info-585	415	3	continue	continue	VBP
randomwalker-info-585	415	4	,	,	,
randomwalker-info-585	415	5	they	-PRON-	PRP
randomwalker-info-585	415	6	will	will	MD
randomwalker-info-585	415	7	always	always	RB
randomwalker-info-585	415	8	get	get	VB
randomwalker-info-585	415	9	Rem(MostH	rem(mosth	ADD
randomwalker-info-585	415	10	)	)	-RRB-
randomwalker-info-585	415	11	.	.	.
randomwalker-info-585	416	1	When	when	WRB
randomwalker-info-585	416	2	they	-PRON-	PRP
randomwalker-info-585	416	3	undercut	undercut	VBD
randomwalker-info-585	416	4	,	,	,
randomwalker-info-585	416	5	they	-PRON-	PRP
randomwalker-info-585	416	6	would	would	MD
randomwalker-info-585	416	7	include	include	VB
randomwalker-info-585	416	8	GapH	GapH	NNP
randomwalker-info-585	416	9	transaction	transaction	NN
randomwalker-info-585	416	10	fees	fee	NNS
randomwalker-info-585	416	11	.	.	.
randomwalker-info-585	417	1	If	if	IN
randomwalker-info-585	417	2	the	the	DT
randomwalker-info-585	417	3	next	next	JJ
randomwalker-info-585	417	4	miner	miner	NN
randomwalker-info-585	417	5	to	to	TO
randomwalker-info-585	417	6	find	find	VB
randomwalker-info-585	417	7	a	a	DT
randomwalker-info-585	417	8	block	block	NN
randomwalker-info-585	417	9	is	be	VBZ
randomwalker-info-585	417	10	PettyCompliant	PettyCompliant	NNP
randomwalker-info-585	417	11	(	(	-LRB-
randomwalker-info-585	417	12	or	or	CC
randomwalker-info-585	417	13	this	this	DT
randomwalker-info-585	417	14	miner	miner	NN
randomwalker-info-585	417	15	)	)	-RRB-
randomwalker-info-585	417	16	,	,	,
randomwalker-info-585	417	17	then	then	RB
randomwalker-info-585	417	18	the	the	DT
randomwalker-info-585	417	19	undercut	undercut	NN
randomwalker-info-585	417	20	will	will	MD
randomwalker-info-585	417	21	be	be	VB
randomwalker-info-585	417	22	successful	successful	JJ
randomwalker-info-585	417	23	and	and	CC
randomwalker-info-585	417	24	the	the	DT
randomwalker-info-585	417	25	miner	miner	NN
randomwalker-info-585	417	26	will	will	MD
randomwalker-info-585	417	27	receive	receive	VB
randomwalker-info-585	417	28	GapH	GapH	NNP
randomwalker-info-585	417	29	in	in	IN
randomwalker-info-585	417	30	rewards	reward	NNS
randomwalker-info-585	417	31	.	.	.
randomwalker-info-585	418	1	But	but	CC
randomwalker-info-585	418	2	if	if	IN
randomwalker-info-585	418	3	the	the	DT
randomwalker-info-585	418	4	next	next	JJ
randomwalker-info-585	418	5	block	block	NN
randomwalker-info-585	418	6	is	be	VBZ
randomwalker-info-585	418	7	found	find	VBN
randomwalker-info-585	418	8	by	by	IN
randomwalker-info-585	418	9	a	a	DT
randomwalker-info-585	418	10	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	418	11	miner	miner	NN
randomwalker-info-585	418	12	,	,	,
randomwalker-info-585	418	13	the	the	DT
randomwalker-info-585	418	14	undercut	undercut	NN
randomwalker-info-585	418	15	fails	fail	VBZ
randomwalker-info-585	418	16	and	and	CC
randomwalker-info-585	418	17	they	-PRON-	PRP
randomwalker-info-585	418	18	get	get	VBP
randomwalker-info-585	418	19	nothing	nothing	NN
randomwalker-info-585	418	20	.	.	.
randomwalker-info-585	419	1	So	so	CC
randomwalker-info-585	419	2	if	if	IN
randomwalker-info-585	419	3	y	y	NNP
randomwalker-info-585	419	4	is	be	VBZ
randomwalker-info-585	419	5	the	the	DT
randomwalker-info-585	419	6	fraction	fraction	NN
randomwalker-info-585	419	7	of	of	IN
randomwalker-info-585	419	8	the	the	DT
randomwalker-info-585	419	9	network	network	NN
randomwalker-info-585	419	10	that	that	WDT
randomwalker-info-585	419	11	remains	remain	VBZ
randomwalker-info-585	419	12	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	419	13	,	,	,
randomwalker-info-585	419	14	we	-PRON-	PRP
randomwalker-info-585	419	15	see	see	VBP
randomwalker-info-585	419	16	that	that	IN
randomwalker-info-585	419	17	the	the	DT
randomwalker-info-585	419	18	expected	expect	VBN
randomwalker-info-585	419	19	reward	reward	NN
randomwalker-info-585	419	20	obtained	obtain	VBN
randomwalker-info-585	419	21	by	by	IN
randomwalker-info-585	419	22	FunctionFork(x	FunctionFork(x	NNP
randomwalker-info-585	419	23	)	)	-RRB-
randomwalker-info-585	419	24	is	be	VBZ
randomwalker-info-585	419	25	proportional	proportional	JJ
randomwalker-info-585	419	26	to:8	to:8	.
randomwalker-info-585	419	27	We	-PRON-	PRP
randomwalker-info-585	419	28	emphasize	emphasize	VBP
randomwalker-info-585	419	29	that	that	IN
randomwalker-info-585	419	30	while	while	IN
randomwalker-info-585	419	31	the	the	DT
randomwalker-info-585	419	32	theory	theory	NN
randomwalker-info-585	419	33	gives	give	VBZ
randomwalker-info-585	419	34	us	-PRON-	PRP
randomwalker-info-585	419	35	a	a	DT
randomwalker-info-585	419	36	crisp	crisp	JJ
randomwalker-info-585	419	37	un-	un-	JJ
randomwalker-info-585	419	38	derstanding	derstanding	NN
randomwalker-info-585	419	39	of	of	IN
randomwalker-info-585	419	40	what	what	WP
randomwalker-info-585	419	41	should	should	MD
randomwalker-info-585	419	42	happen	happen	VB
randomwalker-info-585	419	43	when	when	WRB
randomwalker-info-585	419	44	exactly	exactly	RB
randomwalker-info-585	419	45	2/3	2/3	CD
randomwalker-info-585	419	46	of	of	IN
randomwalker-info-585	419	47	the	the	DT
randomwalker-info-585	419	48	miners	miner	NNS
randomwalker-info-585	419	49	are	be	VBP
randomwalker-info-585	419	50	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	419	51	,	,	,
randomwalker-info-585	419	52	it	-PRON-	PRP
randomwalker-info-585	419	53	is	be	VBZ
randomwalker-info-585	419	54	intractable	intractable	JJ
randomwalker-info-585	419	55	to	to	TO
randomwalker-info-585	419	56	rigor-	rigor-	VB
randomwalker-info-585	419	57	ously	ously	RB
randomwalker-info-585	419	58	analyze	analyze	VB
randomwalker-info-585	419	59	the	the	DT
randomwalker-info-585	419	60	equilibria	equilibria	NN
randomwalker-info-585	419	61	at	at	IN
randomwalker-info-585	419	62	various	various	JJ
randomwalker-info-585	419	63	other	other	JJ
randomwalker-info-585	419	64	fractions	fraction	NNS
randomwalker-info-585	419	65	of	of	IN
randomwalker-info-585	419	66	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	419	67	miners	miner	NNS
randomwalker-info-585	419	68	.	.	.
randomwalker-info-585	420	1	Thus	thus	RB
randomwalker-info-585	420	2	our	-PRON-	PRP$
randomwalker-info-585	420	3	simulation	simulation	NN
randomwalker-info-585	420	4	both	both	CC
randomwalker-info-585	420	5	con-	con-	NN
randomwalker-info-585	420	6	firms	firm	NNS
randomwalker-info-585	420	7	and	and	CC
randomwalker-info-585	420	8	extends	extend	VBZ
randomwalker-info-585	420	9	our	-PRON-	PRP$
randomwalker-info-585	420	10	theoretical	theoretical	JJ
randomwalker-info-585	420	11	understanding	understanding	NN
randomwalker-info-585	420	12	(	(	-LRB-
randomwalker-info-585	420	13	Figure	Figure	NNP
randomwalker-info-585	420	14	6	6	CD
randomwalker-info-585	420	15	)	)	-RRB-
randomwalker-info-585	420	16	.	.	.
randomwalker-info-585	421	1	E[Rem(MostH	e[rem(mosth	LS
randomwalker-info-585	421	2	)	)	-RRB-
randomwalker-info-585	421	3	·	·	NFP
randomwalker-info-585	421	4	I(Rem(MostH	i(rem(mosth	NN
randomwalker-info-585	421	5	)	)	-RRB-
randomwalker-info-585	421	6	>	>	XX
randomwalker-info-585	421	7	GapH	GapH	NNP
randomwalker-info-585	421	8	)	)	-RRB-
randomwalker-info-585	421	9	]	]	-RRB-
randomwalker-info-585	421	10	+	+	CC
randomwalker-info-585	421	11	(	(	-LRB-
randomwalker-info-585	421	12	1	1	CD
randomwalker-info-585	421	13	−y	−y	CD
randomwalker-info-585	421	14	)	)	-RRB-
randomwalker-info-585	421	15	·	·	NFP
randomwalker-info-585	421	16	E[GapH	e[gaph	NN
randomwalker-info-585	421	17	·	·	NFP
randomwalker-info-585	421	18	I(GapH	I(GapH	-LRB-
randomwalker-info-585	421	19	>	>	XX
randomwalker-info-585	421	20	GapH	GapH	NNP
randomwalker-info-585	421	21	)	)	-RRB-
randomwalker-info-585	421	22	]	]	-RRB-
randomwalker-info-585	421	23	Finally	finally	RB
randomwalker-info-585	421	24	,	,	,
randomwalker-info-585	421	25	because	because	IN
randomwalker-info-585	421	26	Rem(MostH	Rem(MostH	NNP
randomwalker-info-585	421	27	)	)	-RRB-
randomwalker-info-585	421	28	and	and	CC
randomwalker-info-585	421	29	GapH	GapH	NNP
randomwalker-info-585	421	30	are	be	VBP
randomwalker-info-585	421	31	i.i.d	i.i.d	JJ
randomwalker-info-585	421	32	.	.	.
randomwalker-info-585	422	1	exponen-	exponen-	NNP
randomwalker-info-585	422	2	tial	tial	JJ
randomwalker-info-585	422	3	random	random	JJ
randomwalker-info-585	422	4	variables	variable	NNS
randomwalker-info-585	422	5	with	with	IN
randomwalker-info-585	422	6	mean	mean	NNP
randomwalker-info-585	422	7	1	1	CD
randomwalker-info-585	422	8	,	,	,
randomwalker-info-585	422	9	we	-PRON-	PRP
randomwalker-info-585	422	10	have	have	VBP
randomwalker-info-585	422	11	that	that	DT
randomwalker-info-585	422	12	E[GapH	E[GapH	NNP
randomwalker-info-585	422	13	·	·	NFP
randomwalker-info-585	422	14	I(GapH	I(GapH	-LRB-
randomwalker-info-585	422	15	>	>	XX
randomwalker-info-585	422	16	Rem(MostH	Rem(MostH	NNP
randomwalker-info-585	422	17	)	)	-RRB-
randomwalker-info-585	422	18	)	)	-RRB-
randomwalker-info-585	422	19	]	]	-RRB-
randomwalker-info-585	422	20	=	=	NFP
randomwalker-info-585	422	21	E[Rem(MostH)·I(Rem(MostH	e[rem(mosth)·i(rem(mosth	UH
randomwalker-info-585	422	22	)	)	-RRB-
randomwalker-info-585	422	23	>	>	XX
randomwalker-info-585	422	24	GapH	GapH	NNP
randomwalker-info-585	422	25	)	)	-RRB-
randomwalker-info-585	422	26	]	]	-RRB-
randomwalker-info-585	422	27	=	=	SYM
randomwalker-info-585	422	28	3/4	3/4	CD
randomwalker-info-585	422	29	.	.	.
randomwalker-info-585	423	1	Therefore	therefore	RB
randomwalker-info-585	423	2	,	,	,
randomwalker-info-585	423	3	whenever	whenever	WRB
randomwalker-info-585	423	4	y	y	NNP
randomwalker-info-585	423	5	≤	≤	NNP
randomwalker-info-585	423	6	2/3	2/3	CD
randomwalker-info-585	423	7	,	,	,
randomwalker-info-585	423	8	the	the	DT
randomwalker-info-585	423	9	reward	reward	NN
randomwalker-info-585	423	10	from	from	IN
randomwalker-info-585	423	11	FunctionFork(x	FunctionFork(x	NNP
randomwalker-info-585	423	12	)	)	-RRB-
randomwalker-info-585	423	13	is	be	VBZ
randomwalker-info-585	423	14	at	at	RB
randomwalker-info-585	423	15	least	least	RBS
randomwalker-info-585	423	16	one	one	CD
randomwalker-info-585	423	17	,	,	,
randomwalker-info-585	423	18	and	and	CC
randomwalker-info-585	423	19	therefore	therefore	RB
randomwalker-info-585	423	20	it	-PRON-	PRP
randomwalker-info-585	423	21	is	be	VBZ
randomwalker-info-585	423	22	a	a	DT
randomwalker-info-585	423	23	better	well	JJR
randomwalker-info-585	423	24	choice	choice	NN
randomwalker-info-585	423	25	than	than	IN
randomwalker-info-585	423	26	PettyCompliant	PettyCompliant	NNP
randomwalker-info-585	423	27	(	(	-LRB-
randomwalker-info-585	423	28	which	which	WDT
randomwalker-info-585	423	29	gets	get	VBZ
randomwalker-info-585	423	30	expected	expect	VBN
randomwalker-info-585	423	31	reward	reward	NN
randomwalker-info-585	423	32	exactly	exactly	RB
randomwalker-info-585	423	33	one	one	CD
randomwalker-info-585	423	34	)	)	-RRB-
randomwalker-info-585	423	35	.	.	.
randomwalker-info-585	424	1	7Note	7note	VB
randomwalker-info-585	424	2	that	that	IN
randomwalker-info-585	424	3	learning	learning	NN
randomwalker-info-585	424	4	is	be	VBZ
randomwalker-info-585	424	5	by	by	IN
randomwalker-info-585	424	6	no	no	DT
randomwalker-info-585	424	7	means	means	NN
randomwalker-info-585	424	8	guaranteed	guarantee	VBN
randomwalker-info-585	424	9	to	to	TO
randomwalker-info-585	424	10	result	result	VB
randomwalker-info-585	424	11	in	in	IN
randomwalker-info-585	424	12	a	a	DT
randomwalker-info-585	424	13	static	static	JJ
randomwalker-info-585	424	14	equilibrium	equilibrium	NN
randomwalker-info-585	424	15	at	at	RB
randomwalker-info-585	424	16	all	all	RB
randomwalker-info-585	424	17	,	,	,
randomwalker-info-585	424	18	although	although	IN
randomwalker-info-585	424	19	in	in	IN
randomwalker-info-585	424	20	these	these	DT
randomwalker-info-585	424	21	simulations	simulation	NNS
randomwalker-info-585	424	22	that	that	WDT
randomwalker-info-585	424	23	happens	happen	VBZ
randomwalker-info-585	424	24	to	to	TO
randomwalker-info-585	424	25	be	be	VB
randomwalker-info-585	424	26	the	the	DT
randomwalker-info-585	424	27	result	result	NN
randomwalker-info-585	424	28	.	.	.
randomwalker-info-585	425	1	8E[X	8E[X	NFP
randomwalker-info-585	425	2	]	]	-RRB-
randomwalker-info-585	425	3	denotes	denote	VBZ
randomwalker-info-585	425	4	the	the	DT
randomwalker-info-585	425	5	expectation	expectation	NN
randomwalker-info-585	425	6	of	of	IN
randomwalker-info-585	425	7	the	the	DT
randomwalker-info-585	425	8	random	random	JJ
randomwalker-info-585	425	9	variable	variable	JJ
randomwalker-info-585	425	10	X	x	NN
randomwalker-info-585	425	11	,	,	,
randomwalker-info-585	425	12	and	and	CC
randomwalker-info-585	425	13	I(E	I(E	NNP
randomwalker-info-585	425	14	)	)	-RRB-
randomwalker-info-585	425	15	denotes	denote	VBZ
randomwalker-info-585	425	16	the	the	DT
randomwalker-info-585	425	17	indicator	indicator	NN
randomwalker-info-585	425	18	random	random	JJ
randomwalker-info-585	425	19	variable	variable	JJ
randomwalker-info-585	425	20	for	for	IN
randomwalker-info-585	425	21	event	event	NN
randomwalker-info-585	425	22	E	e	NN
randomwalker-info-585	425	23	(	(	-LRB-
randomwalker-info-585	425	24	that	that	RB
randomwalker-info-585	425	25	is	is	RB
randomwalker-info-585	425	26	1	1	CD
randomwalker-info-585	425	27	when	when	WRB
randomwalker-info-585	425	28	E	e	NN
randomwalker-info-585	425	29	occurs	occur	VBZ
randomwalker-info-585	425	30	and	and	CC
randomwalker-info-585	425	31	0	0	CD
randomwalker-info-585	425	32	otherwise	otherwise	RB
randomwalker-info-585	425	33	)	)	-RRB-
randomwalker-info-585	425	34	.	.	.
randomwalker-info-585	426	1	Figure	figure	NN
randomwalker-info-585	426	2	6	6	CD
randomwalker-info-585	426	3	:	:	:
randomwalker-info-585	426	4	Stacked	stack	VBN
randomwalker-info-585	426	5	area	area	NN
randomwalker-info-585	426	6	chart	chart	NN
randomwalker-info-585	426	7	showing	show	VBG
randomwalker-info-585	426	8	the	the	DT
randomwalker-info-585	426	9	equilib-	equilib-	NNP
randomwalker-info-585	426	10	rium	rium	NN
randomwalker-info-585	426	11	distributions	distribution	NNS
randomwalker-info-585	426	12	of	of	IN
randomwalker-info-585	426	13	strategies	strategy	NNS
randomwalker-info-585	426	14	covered	cover	VBN
randomwalker-info-585	426	15	thus	thus	RB
randomwalker-info-585	426	16	far	far	RB
randomwalker-info-585	426	17	,	,	,
randomwalker-info-585	426	18	given	give	VBN
randomwalker-info-585	426	19	that	that	IN
randomwalker-info-585	426	20	a	a	DT
randomwalker-info-585	426	21	fraction	fraction	NN
randomwalker-info-585	426	22	of	of	IN
randomwalker-info-585	426	23	miners	miner	NNS
randomwalker-info-585	426	24	will	will	MD
randomwalker-info-585	426	25	always	always	RB
randomwalker-info-585	426	26	use	use	VB
randomwalker-info-585	426	27	the	the	DT
randomwalker-info-585	426	28	de-	de-	NN
randomwalker-info-585	426	29	fault	fault	NN
randomwalker-info-585	426	30	strategy	strategy	NN
randomwalker-info-585	426	31	.	.	.
randomwalker-info-585	427	1	These	these	DT
randomwalker-info-585	427	2	simulations	simulation	NNS
randomwalker-info-585	427	3	involved	involve	VBD
randomwalker-info-585	427	4	100	100	CD
randomwalker-info-585	427	5	min-	min-	JJ
randomwalker-info-585	427	6	ers	er	NNS
randomwalker-info-585	427	7	,	,	,
randomwalker-info-585	427	8	with	with	IN
randomwalker-info-585	427	9	10,000	10,000	CD
randomwalker-info-585	427	10	blocks	block	NNS
randomwalker-info-585	427	11	per	per	IN
randomwalker-info-585	427	12	game	game	NN
randomwalker-info-585	427	13	.	.	.
randomwalker-info-585	428	1	We	-PRON-	PRP
randomwalker-info-585	428	2	found	find	VBD
randomwalker-info-585	428	3	that	that	IN
randomwalker-info-585	428	4	the	the	DT
randomwalker-info-585	428	5	strategies	strategy	NNS
randomwalker-info-585	428	6	would	would	MD
randomwalker-info-585	428	7	reach	reach	VB
randomwalker-info-585	428	8	an	an	DT
randomwalker-info-585	428	9	equilibrium	equilibrium	NN
randomwalker-info-585	428	10	around	around	IN
randomwalker-info-585	428	11	300000	300000	CD
randomwalker-info-585	428	12	games	game	NNS
randomwalker-info-585	428	13	with	with	IN
randomwalker-info-585	428	14	�	�	NNP
randomwalker-info-585	428	15	=	=	SYM
randomwalker-info-585	428	16	0.01	0.01	CD
randomwalker-info-585	428	17	.	.	.
randomwalker-info-585	429	1	6	6	CD
randomwalker-info-585	429	2	.	.	.
randomwalker-info-585	430	1	SELFISH	SELFISH	NNP
randomwalker-info-585	430	2	MINING	mining	NN
randomwalker-info-585	430	3	WITH	with	IN
randomwalker-info-585	430	4	TRANSACTION	transaction	NN
randomwalker-info-585	430	5	FEES	fees	RB
randomwalker-info-585	430	6	Selfish	selfish	JJ
randomwalker-info-585	430	7	mining	mining	NN
randomwalker-info-585	430	8	is	be	VBZ
randomwalker-info-585	430	9	a	a	DT
randomwalker-info-585	430	10	deviant	deviant	NN
randomwalker-info-585	430	11	strategy	strategy	NN
randomwalker-info-585	430	12	first	first	RB
randomwalker-info-585	430	13	identified	identify	VBN
randomwalker-info-585	430	14	by	by	IN
randomwalker-info-585	430	15	Eyal	Eyal	NNP
randomwalker-info-585	430	16	and	and	CC
randomwalker-info-585	430	17	Sirer	Sirer	NNP
randomwalker-info-585	430	18	[	[	-LRB-
randomwalker-info-585	430	19	9	9	CD
randomwalker-info-585	430	20	]	]	-RRB-
randomwalker-info-585	430	21	.	.	.
randomwalker-info-585	431	1	Essentially	essentially	RB
randomwalker-info-585	431	2	,	,	,
randomwalker-info-585	431	3	a	a	DT
randomwalker-info-585	431	4	selfish	selfish	JJ
randomwalker-info-585	431	5	miner	miner	NN
randomwalker-info-585	431	6	chooses	choose	VBZ
randomwalker-info-585	431	7	not	not	RB
randomwalker-info-585	431	8	to	to	TO
randomwalker-info-585	431	9	release	release	VB
randomwalker-info-585	431	10	blocks	block	NNS
randomwalker-info-585	431	11	immediately	immediately	RB
randomwalker-info-585	431	12	upon	upon	IN
randomwalker-info-585	431	13	being	be	VBG
randomwalker-info-585	431	14	found	find	VBN
randomwalker-info-585	431	15	,	,	,
randomwalker-info-585	431	16	instead	instead	RB
randomwalker-info-585	431	17	with-	with-	VBP
randomwalker-info-585	431	18	holding	hold	VBG
randomwalker-info-585	431	19	them	-PRON-	PRP
randomwalker-info-585	431	20	in	in	IN
randomwalker-info-585	431	21	hopes	hope	NNS
randomwalker-info-585	431	22	of	of	IN
randomwalker-info-585	431	23	tricking	trick	VBG
randomwalker-info-585	431	24	the	the	DT
randomwalker-info-585	431	25	rest	rest	NN
randomwalker-info-585	431	26	of	of	IN
randomwalker-info-585	431	27	the	the	DT
randomwalker-info-585	431	28	network	network	NN
randomwalker-info-585	431	29	into	into	IN
randomwalker-info-585	431	30	wasting	waste	VBG
randomwalker-info-585	431	31	their	-PRON-	PRP$
randomwalker-info-585	431	32	mining	mining	NN
randomwalker-info-585	431	33	power	power	NN
randomwalker-info-585	431	34	mining	mining	NN
randomwalker-info-585	431	35	blocks	block	NNS
randomwalker-info-585	431	36	that	that	WDT
randomwalker-info-585	431	37	will	will	MD
randomwalker-info-585	431	38	be	be	VB
randomwalker-info-585	431	39	orphaned	orphan	VBN
randomwalker-info-585	431	40	.	.	.
randomwalker-info-585	432	1	We	-PRON-	PRP
randomwalker-info-585	432	2	find	find	VBP
randomwalker-info-585	432	3	that	that	IN
randomwalker-info-585	432	4	the	the	DT
randomwalker-info-585	432	5	selfish	selfish	JJ
randomwalker-info-585	432	6	mining	mining	NN
randomwalker-info-585	432	7	strategy	strategy	NN
randomwalker-info-585	432	8	performs	perform	VBZ
randomwalker-info-585	432	9	even	even	RB
randomwalker-info-585	432	10	better	well	RBR
randomwalker-info-585	432	11	in	in	IN
randomwalker-info-585	432	12	the	the	DT
randomwalker-info-585	432	13	transaction	transaction	NN
randomwalker-info-585	432	14	fees	fee	NNS
randomwalker-info-585	432	15	model	model	NN
randomwalker-info-585	432	16	than	than	IN
randomwalker-info-585	432	17	the	the	DT
randomwalker-info-585	432	18	block	block	NN
randomwalker-info-585	432	19	-	-	HYPH
randomwalker-info-585	432	20	reward	reward	NN
randomwalker-info-585	432	21	model	model	NN
randomwalker-info-585	432	22	.	.	.
randomwalker-info-585	433	1	A	a	DT
randomwalker-info-585	433	2	priori	priori	JJ
randomwalker-info-585	433	3	,	,	,
randomwalker-info-585	433	4	there	there	EX
randomwalker-info-585	433	5	’s	’	VBZ
randomwalker-info-585	433	6	no	no	DT
randomwalker-info-585	433	7	reason	reason	NN
randomwalker-info-585	433	8	to	to	TO
randomwalker-info-585	433	9	expect	expect	VB
randomwalker-info-585	433	10	this	this	DT
randomwalker-info-585	433	11	.	.	.
randomwalker-info-585	434	1	In	in	IN
randomwalker-info-585	434	2	this	this	DT
randomwalker-info-585	434	3	sec-	sec-	JJ
randomwalker-info-585	434	4	tion	tion	NN
randomwalker-info-585	434	5	we	-PRON-	PRP
randomwalker-info-585	434	6	provide	provide	VBP
randomwalker-info-585	434	7	simulation	simulation	NN
randomwalker-info-585	434	8	results	result	NNS
randomwalker-info-585	434	9	,	,	,
randomwalker-info-585	434	10	along	along	IN
randomwalker-info-585	434	11	with	with	IN
randomwalker-info-585	434	12	some	some	DT
randomwalker-info-585	434	13	intuition	intuition	NN
randomwalker-info-585	434	14	and	and	CC
randomwalker-info-585	434	15	a	a	DT
randomwalker-info-585	434	16	theoretical	theoretical	JJ
randomwalker-info-585	434	17	analysis	analysis	NN
randomwalker-info-585	434	18	proving	prove	VBG
randomwalker-info-585	434	19	this	this	DT
randomwalker-info-585	434	20	.	.	.
randomwalker-info-585	435	1	Essentially	essentially	RB
randomwalker-info-585	435	2	what	what	WP
randomwalker-info-585	435	3	winds	wind	VBZ
randomwalker-info-585	435	4	up	up	RP
randomwalker-info-585	435	5	happening	happen	VBG
randomwalker-info-585	435	6	is	be	VBZ
randomwalker-info-585	435	7	that	that	IN
randomwalker-info-585	435	8	while	while	IN
randomwalker-info-585	435	9	the	the	DT
randomwalker-info-585	435	10	selfish	selfish	JJ
randomwalker-info-585	435	11	miner	miner	NN
randomwalker-info-585	435	12	mines	mine	NNS
randomwalker-info-585	435	13	the	the	DT
randomwalker-info-585	435	14	same	same	JJ
randomwalker-info-585	435	15	fraction	fraction	NN
randomwalker-info-585	435	16	of	of	IN
randomwalker-info-585	435	17	blocks	block	NNS
randomwalker-info-585	435	18	in	in	IN
randomwalker-info-585	435	19	either	either	DT
randomwalker-info-585	435	20	reward	reward	NN
randomwalker-info-585	435	21	model	model	NN
randomwalker-info-585	435	22	,	,	,
randomwalker-info-585	435	23	the	the	DT
randomwalker-info-585	435	24	self-	self-	NNP
randomwalker-info-585	435	25	ish	ish	NNP
randomwalker-info-585	435	26	miner	miner	NNP
randomwalker-info-585	435	27	’s	’s	POS
randomwalker-info-585	435	28	blocks	block	NNS
randomwalker-info-585	435	29	will	will	MD
randomwalker-info-585	435	30	tend	tend	VB
randomwalker-info-585	435	31	to	to	TO
randomwalker-info-585	435	32	be	be	VB
randomwalker-info-585	435	33	larger	large	JJR
randomwalker-info-585	435	34	.	.	.
randomwalker-info-585	436	1	In	in	IN
randomwalker-info-585	436	2	the	the	DT
randomwalker-info-585	436	3	block	block	NN
randomwalker-info-585	436	4	-	-	HYPH
randomwalker-info-585	436	5	reward	reward	NN
randomwalker-info-585	436	6	model	model	NN
randomwalker-info-585	436	7	,	,	,
randomwalker-info-585	436	8	this	this	DT
randomwalker-info-585	436	9	does	do	VBZ
randomwalker-info-585	436	10	n’t	not	RB
randomwalker-info-585	436	11	matter	matter	VB
randomwalker-info-585	436	12	because	because	IN
randomwalker-info-585	436	13	all	all	DT
randomwalker-info-585	436	14	blocks	block	NNS
randomwalker-info-585	436	15	are	be	VBP
randomwalker-info-585	436	16	worth	worth	JJ
randomwalker-info-585	436	17	the	the	DT
randomwalker-info-585	436	18	same	same	JJ
randomwalker-info-585	436	19	,	,	,
randomwalker-info-585	436	20	but	but	CC
randomwalker-info-585	436	21	in	in	IN
randomwalker-info-585	436	22	the	the	DT
randomwalker-info-585	436	23	transaction	transaction	NN
randomwalker-info-585	436	24	fees	fee	NNS
randomwalker-info-585	436	25	model	model	NN
randomwalker-info-585	436	26	this	this	DT
randomwalker-info-585	436	27	means	mean	VBZ
randomwalker-info-585	436	28	the	the	DT
randomwalker-info-585	436	29	self-	self-	NNP
randomwalker-info-585	436	30	ish	ish	NNP
randomwalker-info-585	436	31	miner	miner	NNP
randomwalker-info-585	436	32	gets	get	VBZ
randomwalker-info-585	436	33	greater	great	JJR
randomwalker-info-585	436	34	reward	reward	NN
randomwalker-info-585	436	35	.	.	.
randomwalker-info-585	437	1	6.1	6.1	CD
randomwalker-info-585	437	2	The	the	DT
randomwalker-info-585	437	3	Selfish	Selfish	NNP
randomwalker-info-585	437	4	Mining	Mining	NNP
randomwalker-info-585	437	5	Strategy	Strategy	NNP
randomwalker-info-585	437	6	Analytical	Analytical	NNP
randomwalker-info-585	437	7	and	and	CC
randomwalker-info-585	437	8	simulation	simulation	NN
randomwalker-info-585	437	9	result	result	NN
randomwalker-info-585	437	10	:	:	:
randomwalker-info-585	437	11	selfish	selfish	JJ
randomwalker-info-585	437	12	mining	mining	NN
randomwalker-info-585	437	13	performs	perform	VBZ
randomwalker-info-585	437	14	slightly	slightly	RB
randomwalker-info-585	437	15	better	well	JJR
randomwalker-info-585	437	16	in	in	IN
randomwalker-info-585	437	17	the	the	DT
randomwalker-info-585	437	18	transaction	transaction	NN
randomwalker-info-585	437	19	fee	fee	NN
randomwalker-info-585	437	20	model	model	NN
randomwalker-info-585	437	21	.	.	.
randomwalker-info-585	438	1	The	the	DT
randomwalker-info-585	438	2	goal	goal	NN
randomwalker-info-585	438	3	of	of	IN
randomwalker-info-585	438	4	a	a	DT
randomwalker-info-585	438	5	miner	miner	NN
randomwalker-info-585	438	6	employing	employ	VBG
randomwalker-info-585	438	7	the	the	DT
randomwalker-info-585	438	8	selfish	selfish	JJ
randomwalker-info-585	438	9	mining	mining	NN
randomwalker-info-585	438	10	strategy	strategy	NN
randomwalker-info-585	438	11	is	be	VBZ
randomwalker-info-585	438	12	to	to	TO
randomwalker-info-585	438	13	essentially	essentially	RB
randomwalker-info-585	438	14	trick	trick	VB
randomwalker-info-585	438	15	the	the	DT
randomwalker-info-585	438	16	other	other	JJ
randomwalker-info-585	438	17	miners	miner	NNS
randomwalker-info-585	438	18	in	in	IN
randomwalker-info-585	438	19	the	the	DT
randomwalker-info-585	438	20	Bitcoin	Bitcoin	NNP
randomwalker-info-585	438	21	network	network	NN
randomwalker-info-585	438	22	to	to	TO
randomwalker-info-585	438	23	mine	-PRON-	PRP
randomwalker-info-585	438	24	on	on	IN
randomwalker-info-585	438	25	top	top	NN
randomwalker-info-585	438	26	of	of	IN
randomwalker-info-585	438	27	a	a	DT
randomwalker-info-585	438	28	block	block	NN
randomwalker-info-585	438	29	that	that	WDT
randomwalker-info-585	438	30	will	will	MD
randomwalker-info-585	438	31	be	be	VB
randomwalker-info-585	438	32	orphaned	orphan	VBN
randomwalker-info-585	438	33	.	.	.
randomwalker-info-585	439	1	By	by	IN
randomwalker-info-585	439	2	having	have	VBG
randomwalker-info-585	439	3	other	other	JJ
randomwalker-info-585	439	4	miners	miner	NNS
randomwalker-info-585	439	5	waste	waste	VB
randomwalker-info-585	439	6	their	-PRON-	PRP$
randomwalker-info-585	439	7	power	power	NN
randomwalker-info-585	439	8	,	,	,
randomwalker-info-585	439	9	the	the	DT
randomwalker-info-585	439	10	selfish	selfish	JJ
randomwalker-info-585	439	11	miner	miner	NN
randomwalker-info-585	439	12	is	be	VBZ
randomwalker-info-585	439	13	capa-	capa-	NNP
randomwalker-info-585	439	14	ble	ble	NNP
randomwalker-info-585	439	15	of	of	IN
randomwalker-info-585	439	16	exaggerating	exaggerate	VBG
randomwalker-info-585	439	17	their	-PRON-	PRP$
randomwalker-info-585	439	18	own	own	JJ
randomwalker-info-585	439	19	portion	portion	NN
randomwalker-info-585	439	20	of	of	IN
randomwalker-info-585	439	21	the	the	DT
randomwalker-info-585	439	22	overall	overall	JJ
randomwalker-info-585	439	23	network	network	NN
randomwalker-info-585	439	24	hash	hash	NN
randomwalker-info-585	439	25	-	-	HYPH
randomwalker-info-585	439	26	rate	rate	NN
randomwalker-info-585	439	27	.	.	.
randomwalker-info-585	440	1	Selfish	selfish	JJ
randomwalker-info-585	440	2	miners	miner	NNS
randomwalker-info-585	440	3	do	do	VBP
randomwalker-info-585	440	4	this	this	DT
randomwalker-info-585	440	5	by	by	IN
randomwalker-info-585	440	6	maintaining	maintain	VBG
randomwalker-info-585	440	7	a	a	DT
randomwalker-info-585	440	8	chain	chain	NN
randomwalker-info-585	440	9	in	in	IN
randomwalker-info-585	440	10	private	private	JJ
randomwalker-info-585	440	11	that	that	IN
randomwalker-info-585	440	12	only	only	RB
randomwalker-info-585	440	13	they	-PRON-	PRP
randomwalker-info-585	440	14	know	know	VBP
randomwalker-info-585	440	15	about	about	IN
randomwalker-info-585	440	16	.	.	.
randomwalker-info-585	441	1	When	when	WRB
randomwalker-info-585	441	2	the	the	DT
randomwalker-info-585	441	3	selfish	selfish	JJ
randomwalker-info-585	441	4	miner	miner	NN
randomwalker-info-585	441	5	initially	initially	RB
randomwalker-info-585	441	6	finds	find	VBZ
randomwalker-info-585	441	7	a	a	DT
randomwalker-info-585	441	8	block	block	NN
randomwalker-info-585	441	9	,	,	,
randomwalker-info-585	441	10	they	-PRON-	PRP
randomwalker-info-585	441	11	will	will	MD
randomwalker-info-585	441	12	not	not	RB
randomwalker-info-585	441	13	announce	announce	VB
randomwalker-info-585	441	14	their	-PRON-	PRP$
randomwalker-info-585	441	15	block	block	NN
randomwalker-info-585	441	16	to	to	IN
randomwalker-info-585	441	17	the	the	DT
randomwalker-info-585	441	18	rest	rest	NN
randomwalker-info-585	441	19	of	of	IN
randomwalker-info-585	441	20	the	the	DT
randomwalker-info-585	441	21	network	network	NN
randomwalker-info-585	441	22	.	.	.
randomwalker-info-585	442	1	They	-PRON-	PRP
randomwalker-info-585	442	2	will	will	MD
randomwalker-info-585	442	3	continue	continue	VB
randomwalker-info-585	442	4	to	to	TO
randomwalker-info-585	442	5	mine	mine	VB
randomwalker-info-585	442	6	on	on	IN
randomwalker-info-585	442	7	their	-PRON-	PRP$
randomwalker-info-585	442	8	private	private	JJ
randomwalker-info-585	442	9	block	block	NN
randomwalker-info-585	442	10	,	,	,
randomwalker-info-585	442	11	hoping	hope	VBG
randomwalker-info-585	442	12	to	to	TO
randomwalker-info-585	442	13	find	find	VB
randomwalker-info-585	442	14	a	a	DT
randomwalker-info-585	442	15	second	second	JJ
randomwalker-info-585	442	16	block	block	NN
randomwalker-info-585	442	17	before	before	IN
randomwalker-info-585	442	18	the	the	DT
randomwalker-info-585	442	19	rest	rest	NN
randomwalker-info-585	442	20	of	of	IN
randomwalker-info-585	442	21	the	the	DT
randomwalker-info-585	442	22	network	network	NN
randomwalker-info-585	442	23	finds	find	VBZ
randomwalker-info-585	442	24	a	a	DT
randomwalker-info-585	442	25	block	block	NN
randomwalker-info-585	442	26	.	.	.
randomwalker-info-585	443	1	If	if	IN
randomwalker-info-585	443	2	the	the	DT
randomwalker-info-585	443	3	miner	miner	NN
randomwalker-info-585	443	4	succeeds	succeed	VBZ
randomwalker-info-585	443	5	,	,	,
randomwalker-info-585	443	6	now	now	RB
randomwalker-info-585	443	7	they	-PRON-	PRP
randomwalker-info-585	443	8	’re	be	VBZ
randomwalker-info-585	443	9	in	in	IN
randomwalker-info-585	443	10	a	a	DT
randomwalker-info-585	443	11	very	very	RB
randomwalker-info-585	443	12	strong	strong	JJ
randomwalker-info-585	443	13	posi-	posi-	NN
randomwalker-info-585	443	14	tion	tion	NN
randomwalker-info-585	443	15	:	:	:
randomwalker-info-585	443	16	they	-PRON-	PRP
randomwalker-info-585	443	17	know	know	VBP
randomwalker-info-585	443	18	of	of	IN
randomwalker-info-585	443	19	a	a	DT
randomwalker-info-585	443	20	block	block	NN
randomwalker-info-585	443	21	with	with	IN
randomwalker-info-585	443	22	height	height	NN
randomwalker-info-585	443	23	H	h	NN
randomwalker-info-585	443	24	+	+	SYM
randomwalker-info-585	443	25	2	2	CD
randomwalker-info-585	443	26	,	,	,
randomwalker-info-585	443	27	whereas	whereas	IN
randomwalker-info-585	443	28	the	the	DT
randomwalker-info-585	443	29	rest	rest	NN
randomwalker-info-585	443	30	of	of	IN
randomwalker-info-585	443	31	the	the	DT
randomwalker-info-585	443	32	network	network	NN
randomwalker-info-585	443	33	only	only	RB
randomwalker-info-585	443	34	knows	know	VBZ
randomwalker-info-585	443	35	a	a	DT
randomwalker-info-585	443	36	block	block	NN
randomwalker-info-585	443	37	of	of	IN
randomwalker-info-585	443	38	height	height	NN
randomwalker-info-585	443	39	H.	H.	NNP
randomwalker-info-585	443	40	If	if	IN
randomwalker-info-585	443	41	the	the	DT
randomwalker-info-585	443	42	rest	rest	NN
randomwalker-info-585	443	43	of	of	IN
randomwalker-info-585	443	44	the	the	DT
randomwalker-info-585	443	45	network	network	NN
randomwalker-info-585	443	46	finds	find	VBZ
randomwalker-info-585	443	47	the	the	DT
randomwalker-info-585	443	48	next	next	JJ
randomwalker-info-585	443	49	block	block	NN
randomwalker-info-585	443	50	at	at	IN
randomwalker-info-585	443	51	height	height	NN
randomwalker-info-585	443	52	H	h	NN
randomwalker-info-585	443	53	+	+	CC
randomwalker-info-585	443	54	1	1	CD
randomwalker-info-585	443	55	,	,	,
randomwalker-info-585	443	56	the	the	DT
randomwalker-info-585	443	57	selfish	selfish	JJ
randomwalker-info-585	443	58	miner	miner	NN
randomwalker-info-585	443	59	can	can	MD
randomwalker-info-585	443	60	reveal	reveal	VB
randomwalker-info-585	443	61	their	-PRON-	PRP$
randomwalker-info-585	443	62	private	private	JJ
randomwalker-info-585	443	63	chain	chain	NN
randomwalker-info-585	443	64	and	and	CC
randomwalker-info-585	443	65	the	the	DT
randomwalker-info-585	443	66	public	public	JJ
randomwalker-info-585	443	67	block	block	NN
randomwalker-info-585	443	68	will	will	MD
randomwalker-info-585	443	69	be	be	VB
randomwalker-info-585	443	70	immediately	immediately	RB
randomwalker-info-585	443	71	orphaned	orphan	VBN
randomwalker-info-585	443	72	.	.	.
randomwalker-info-585	444	1	Of	of	RB
randomwalker-info-585	444	2	course	course	RB
randomwalker-info-585	444	3	,	,	,
randomwalker-info-585	444	4	maybe	maybe	RB
randomwalker-info-585	444	5	the	the	DT
randomwalker-info-585	444	6	selfish	selfish	JJ
randomwalker-info-585	444	7	miner	miner	NN
randomwalker-info-585	444	8	will	will	MD
randomwalker-info-585	444	9	find	find	VB
randomwalker-info-585	444	10	the	the	DT
randomwalker-info-585	444	11	third	third	JJ
randomwalker-info-585	444	12	block	block	NN
randomwalker-info-585	444	13	as	as	RB
randomwalker-info-585	444	14	well	well	RB
randomwalker-info-585	444	15	.	.	.
randomwalker-info-585	445	1	In	in	IN
randomwalker-info-585	445	2	this	this	DT
randomwalker-info-585	445	3	case	case	NN
randomwalker-info-585	445	4	,	,	,
randomwalker-info-585	445	5	they	-PRON-	PRP
randomwalker-info-585	445	6	’re	be	VBZ
randomwalker-info-585	445	7	in	in	IN
randomwalker-info-585	445	8	an	an	DT
randomwalker-info-585	445	9	even	even	RB
randomwalker-info-585	445	10	better	well	JJR
randomwalker-info-585	445	11	position	position	NN
randomwalker-info-585	445	12	and	and	CC
randomwalker-info-585	445	13	can	can	MD
randomwalker-info-585	445	14	waste	waste	VB
randomwalker-info-585	445	15	even	even	RB
randomwalker-info-585	445	16	more	more	JJR
randomwalker-info-585	445	17	of	of	IN
randomwalker-info-585	445	18	the	the	DT
randomwalker-info-585	445	19	network	network	NN
randomwalker-info-585	445	20	’s	’s	POS
randomwalker-info-585	445	21	power	power	NN
randomwalker-info-585	445	22	.	.	.
randomwalker-info-585	446	1	But	but	CC
randomwalker-info-585	446	2	the	the	DT
randomwalker-info-585	446	3	point	point	NN
randomwalker-info-585	446	4	is	be	VBZ
randomwalker-info-585	446	5	that	that	IN
randomwalker-info-585	446	6	with	with	IN
randomwalker-info-585	446	7	a	a	DT
randomwalker-info-585	446	8	lead	lead	NN
randomwalker-info-585	446	9	of	of	IN
randomwalker-info-585	446	10	two	two	CD
randomwalker-info-585	446	11	or	or	CC
randomwalker-info-585	446	12	more	more	JJR
randomwalker-info-585	446	13	,	,	,
randomwalker-info-585	446	14	the	the	DT
randomwalker-info-585	446	15	selfish	selfish	JJ
randomwalker-info-585	446	16	miner	miner	NN
randomwalker-info-585	446	17	can	can	MD
randomwalker-info-585	446	18	guarantee	guarantee	VB
randomwalker-info-585	446	19	that	that	IN
randomwalker-info-585	446	20	the	the	DT
randomwalker-info-585	446	21	rest	rest	NN
randomwalker-info-585	446	22	of	of	IN
randomwalker-info-585	446	23	the	the	DT
randomwalker-info-585	446	24	network	network	NN
randomwalker-info-585	446	25	is	be	VBZ
randomwalker-info-585	446	26	wasting	waste	VBG
randomwalker-info-585	446	27	power	power	NN
randomwalker-info-585	446	28	.	.	.
randomwalker-info-585	447	1	Of	of	RB
randomwalker-info-585	447	2	course	course	RB
randomwalker-info-585	447	3	,	,	,
randomwalker-info-585	447	4	the	the	DT
randomwalker-info-585	447	5	selfish	selfish	JJ
randomwalker-info-585	447	6	miner	miner	NN
randomwalker-info-585	447	7	might	may	MD
randomwalker-info-585	447	8	also	also	RB
randomwalker-info-585	447	9	fail	fail	VB
randomwalker-info-585	447	10	to	to	TO
randomwalker-info-585	447	11	find	find	VB
randomwalker-info-585	447	12	a	a	DT
randomwalker-info-585	447	13	sec-	sec-	JJ
randomwalker-info-585	447	14	ond	ond	NN
randomwalker-info-585	447	15	block	block	NN
randomwalker-info-585	447	16	before	before	IN
randomwalker-info-585	447	17	the	the	DT
randomwalker-info-585	447	18	rest	rest	NN
randomwalker-info-585	447	19	of	of	IN
randomwalker-info-585	447	20	the	the	DT
randomwalker-info-585	447	21	network	network	NN
randomwalker-info-585	447	22	finds	find	VBZ
randomwalker-info-585	447	23	their	-PRON-	PRP$
randomwalker-info-585	447	24	first	first	JJ
randomwalker-info-585	447	25	.	.	.
randomwalker-info-585	448	1	In	in	IN
randomwalker-info-585	448	2	this	this	DT
randomwalker-info-585	448	3	case	case	NN
randomwalker-info-585	448	4	,	,	,
randomwalker-info-585	448	5	they	-PRON-	PRP
randomwalker-info-585	448	6	immediately	immediately	RB
randomwalker-info-585	448	7	release	release	VBP
randomwalker-info-585	448	8	their	-PRON-	PRP$
randomwalker-info-585	448	9	block	block	NN
randomwalker-info-585	448	10	and	and	CC
randomwalker-info-585	448	11	hope	hope	VB
randomwalker-info-585	448	12	that	that	IN
randomwalker-info-585	448	13	others	other	NNS
randomwalker-info-585	448	14	hear	hear	VBP
randomwalker-info-585	448	15	about	about	IN
randomwalker-info-585	448	16	theirs	-PRON-	PRP
randomwalker-info-585	448	17	first	first	RB
randomwalker-info-585	448	18	.	.	.
randomwalker-info-585	449	1	Obviously	obviously	RB
randomwalker-info-585	449	2	this	this	DT
randomwalker-info-585	449	3	is	be	VBZ
randomwalker-info-585	449	4	not	not	RB
randomwalker-info-585	449	5	ideal	ideal	JJ
randomwalker-info-585	449	6	:	:	:
randomwalker-info-585	449	7	had	have	VBD
randomwalker-info-585	449	8	they	-PRON-	PRP
randomwalker-info-585	449	9	released	release	VBN
randomwalker-info-585	449	10	their	-PRON-	PRP$
randomwalker-info-585	449	11	block	block	NN
randomwalker-info-585	449	12	immediately	immediately	RB
randomwalker-info-585	449	13	,	,	,
randomwalker-info-585	449	14	they	-PRON-	PRP
randomwalker-info-585	449	15	could	could	MD
randomwalker-info-585	449	16	have	have	VB
randomwalker-info-585	449	17	guaranteed	guarantee	VBN
randomwalker-info-585	449	18	that	that	IN
randomwalker-info-585	449	19	it	-PRON-	PRP
randomwalker-info-585	449	20	was	be	VBD
randomwalker-info-585	449	21	heard	hear	VBN
randomwalker-info-585	449	22	about	about	IN
randomwalker-info-585	449	23	first	first	RB
randomwalker-info-585	449	24	.	.	.
randomwalker-info-585	450	1	So	so	CC
randomwalker-info-585	450	2	there	there	EX
randomwalker-info-585	450	3	’s	’	VBZ
randomwalker-info-585	450	4	a	a	DT
randomwalker-info-585	450	5	tradeoff	tradeoff	NN
randomwalker-info-585	450	6	—	—	:
randomwalker-info-585	450	7	withholding	withhold	VBG
randomwalker-info-585	450	8	the	the	DT
randomwalker-info-585	450	9	block	block	NN
randomwalker-info-585	450	10	has	have	VBZ
randomwalker-info-585	450	11	a	a	DT
randomwalker-info-585	450	12	chance	chance	NN
randomwalker-info-585	450	13	to	to	TO
randomwalker-info-585	450	14	give	give	VB
randomwalker-info-585	450	15	the	the	DT
randomwalker-info-585	450	16	selfish	selfish	JJ
randomwalker-info-585	450	17	miner	miner	NN
randomwalker-info-585	450	18	a	a	DT
randomwalker-info-585	450	19	private	private	JJ
randomwalker-info-585	450	20	chain	chain	NN
randomwalker-info-585	450	21	of	of	IN
randomwalker-info-585	450	22	length	length	NN
randomwalker-info-585	450	23	two	two	CD
randomwalker-info-585	450	24	or	or	CC
randomwalker-info-585	450	25	more	more	JJR
randomwalker-info-585	450	26	,	,	,
randomwalker-info-585	450	27	in	in	IN
randomwalker-info-585	450	28	which	which	WDT
randomwalker-info-585	450	29	case	case	NN
randomwalker-info-585	450	30	the	the	DT
randomwalker-info-585	450	31	selfish	selfish	JJ
randomwalker-info-585	450	32	miner	miner	NN
randomwalker-info-585	450	33	benefits	benefit	NNS
randomwalker-info-585	450	34	,	,	,
randomwalker-info-585	450	35	but	but	CC
randomwalker-info-585	450	36	it	-PRON-	PRP
randomwalker-info-585	450	37	could	could	MD
randomwalker-info-585	450	38	also	also	RB
randomwalker-info-585	450	39	cause	cause	VB
randomwalker-info-585	450	40	their	-PRON-	PRP$
randomwalker-info-585	450	41	block	block	NN
randomwalker-info-585	450	42	to	to	TO
randomwalker-info-585	450	43	be	be	VB
randomwalker-info-585	450	44	orphaned	orphan	VBN
randomwalker-info-585	450	45	,	,	,
randomwalker-info-585	450	46	resulting	result	VBG
randomwalker-info-585	450	47	in	in	IN
randomwalker-info-585	450	48	less	less	JJR
randomwalker-info-585	450	49	profits	profit	NNS
randomwalker-info-585	450	50	.	.	.
randomwalker-info-585	451	1	Selfish	selfish	JJ
randomwalker-info-585	451	2	-	-	HYPH
randomwalker-info-585	451	3	Mine	mine	JJ
randomwalker-info-585	451	4	:	:	:
randomwalker-info-585	451	5	Selfish	selfish	JJ
randomwalker-info-585	451	6	mining	mining	NN
randomwalker-info-585	451	7	strategy	strategy	NN
randomwalker-info-585	451	8	from	from	IN
randomwalker-info-585	451	9	[	[	-LRB-
randomwalker-info-585	451	10	9	9	CD
randomwalker-info-585	451	11	]	]	-RRB-
randomwalker-info-585	451	12	.	.	.
randomwalker-info-585	452	1	This	this	DT
randomwalker-info-585	452	2	miner	miner	NN
randomwalker-info-585	452	3	hides	hide	VBZ
randomwalker-info-585	452	4	their	-PRON-	PRP$
randomwalker-info-585	452	5	blocks	block	NNS
randomwalker-info-585	452	6	,	,	,
randomwalker-info-585	452	7	which	which	WDT
randomwalker-info-585	452	8	risks	risk	VBZ
randomwalker-info-585	452	9	losing	lose	VBG
randomwalker-info-585	452	10	their	-PRON-	PRP$
randomwalker-info-585	452	11	first	first	JJ
randomwalker-info-585	452	12	block	block	NN
randomwalker-info-585	452	13	,	,	,
randomwalker-info-585	452	14	in	in	IN
randomwalker-info-585	452	15	order	order	NN
randomwalker-info-585	452	16	to	to	TO
randomwalker-info-585	452	17	try	try	VB
randomwalker-info-585	452	18	to	to	TO
randomwalker-info-585	452	19	get	get	VB
randomwalker-info-585	452	20	the	the	DT
randomwalker-info-585	452	21	rest	rest	NN
randomwalker-info-585	452	22	of	of	IN
randomwalker-info-585	452	23	the	the	DT
randomwalker-info-585	452	24	network	network	NN
randomwalker-info-585	452	25	mining	mining	NN
randomwalker-info-585	452	26	in	in	IN
randomwalker-info-585	452	27	a	a	DT
randomwalker-info-585	452	28	useless	useless	JJ
randomwalker-info-585	452	29	location	location	NN
randomwalker-info-585	452	30	,	,	,
randomwalker-info-585	452	31	amplifying	amplify	VBG
randomwalker-info-585	452	32	their	-PRON-	PRP$
randomwalker-info-585	452	33	own	own	JJ
randomwalker-info-585	452	34	apparent	apparent	JJ
randomwalker-info-585	452	35	hash	hash	NN
randomwalker-info-585	452	36	power	power	NN
randomwalker-info-585	452	37	.	.	.
randomwalker-info-585	453	1	Which	which	WDT
randomwalker-info-585	453	2	Block	Block	NNP
randomwalker-info-585	453	3	:	:	:
randomwalker-info-585	453	4	OldestmPrivatem	OldestmPrivatem	NNP
randomwalker-info-585	453	5	.	.	.
randomwalker-info-585	454	1	How	how	WRB
randomwalker-info-585	454	2	much	much	JJ
randomwalker-info-585	454	3	:	:	:
randomwalker-info-585	454	4	include	include	VBP
randomwalker-info-585	454	5	Rem(Mining(m	Rem(Mining(m	NNP
randomwalker-info-585	454	6	)	)	-RRB-
randomwalker-info-585	454	7	)	)	-RRB-
randomwalker-info-585	454	8	.	.	.
randomwalker-info-585	455	1	Publish(B	Publish(B	VBN
randomwalker-info-585	455	2	)	)	-RRB-
randomwalker-info-585	455	3	?	?	.
randomwalker-info-585	456	1	:	:	:
randomwalker-info-585	456	2	if	if	IN
randomwalker-info-585	456	3	Height(B	height(b	NN
randomwalker-info-585	456	4	)	)	-RRB-
randomwalker-info-585	456	5	=	=	NFP
randomwalker-info-585	456	6	H	h	NN
randomwalker-info-585	456	7	yes	yes	UH
randomwalker-info-585	456	8	.	.	.
randomwalker-info-585	457	1	elseif	elseif	NNP
randomwalker-info-585	457	2	RacingmH	RacingmH	NNP
randomwalker-info-585	457	3	,	,	,
randomwalker-info-585	457	4	and	and	CC
randomwalker-info-585	457	5	Private	private	JJ
randomwalker-info-585	457	6	m	m	NN
randomwalker-info-585	457	7	=	=	SYM
randomwalker-info-585	457	8	H	h	NN
randomwalker-info-585	457	9	+	+	CC
randomwalker-info-585	457	10	1	1	CD
randomwalker-info-585	457	11	yes	yes	UH
randomwalker-info-585	457	12	.	.	.
randomwalker-info-585	458	1	else	else	RB
randomwalker-info-585	458	2	no	no	UH
randomwalker-info-585	458	3	.	.	.
randomwalker-info-585	459	1	Assuming	assume	VBG
randomwalker-info-585	459	2	the	the	DT
randomwalker-info-585	459	3	selfish	selfish	JJ
randomwalker-info-585	459	4	miner	miner	NN
randomwalker-info-585	459	5	has	have	VBZ
randomwalker-info-585	459	6	less	less	JJR
randomwalker-info-585	459	7	than	than	IN
randomwalker-info-585	459	8	half	half	NN
randomwalker-info-585	459	9	of	of	IN
randomwalker-info-585	459	10	the	the	DT
randomwalker-info-585	459	11	overall	overall	JJ
randomwalker-info-585	459	12	hash	hash	NN
randomwalker-info-585	459	13	power	power	NN
randomwalker-info-585	459	14	of	of	IN
randomwalker-info-585	459	15	the	the	DT
randomwalker-info-585	459	16	network	network	NN
randomwalker-info-585	459	17	,	,	,
randomwalker-info-585	459	18	they	-PRON-	PRP
randomwalker-info-585	459	19	will	will	MD
randomwalker-info-585	459	20	eventually	eventually	RB
randomwalker-info-585	459	21	need	need	VB
randomwalker-info-585	459	22	to	to	TO
randomwalker-info-585	459	23	pub-	pub-	VB
randomwalker-info-585	459	24	lish	lish	VB
randomwalker-info-585	459	25	their	-PRON-	PRP$
randomwalker-info-585	459	26	private	private	JJ
randomwalker-info-585	459	27	chain	chain	NN
randomwalker-info-585	459	28	.	.	.
randomwalker-info-585	460	1	In	in	IN
randomwalker-info-585	460	2	order	order	NN
randomwalker-info-585	460	3	to	to	TO
randomwalker-info-585	460	4	maintain	maintain	VB
randomwalker-info-585	460	5	our	-PRON-	PRP$
randomwalker-info-585	460	6	focus	focus	NN
randomwalker-info-585	460	7	on	on	IN
randomwalker-info-585	460	8	the	the	DT
randomwalker-info-585	460	9	difference	difference	NN
randomwalker-info-585	460	10	between	between	IN
randomwalker-info-585	460	11	transaction	transaction	NN
randomwalker-info-585	460	12	fees	fee	NNS
randomwalker-info-585	460	13	and	and	CC
randomwalker-info-585	460	14	fixed	fix	VBN
randomwalker-info-585	460	15	block	block	NN
randomwalker-info-585	460	16	-	-	HYPH
randomwalker-info-585	460	17	rewards	reward	NNS
randomwalker-info-585	460	18	,	,	,
randomwalker-info-585	460	19	we	-PRON-	PRP
randomwalker-info-585	460	20	consider	consider	VBP
randomwalker-info-585	460	21	just	just	RB
randomwalker-info-585	460	22	“	"	``
randomwalker-info-585	460	23	vanilla	vanilla	NN
randomwalker-info-585	460	24	”	"	''
randomwalker-info-585	460	25	selfish	selfish	JJ
randomwalker-info-585	460	26	mining	mining	NN
randomwalker-info-585	460	27	,	,	,
randomwalker-info-585	460	28	although	although	IN
randomwalker-info-585	460	29	it	-PRON-	PRP
randomwalker-info-585	460	30	is	be	VBZ
randomwalker-info-585	460	31	an	an	DT
randomwalker-info-585	460	32	interesting	interesting	JJ
randomwalker-info-585	460	33	consideration	consideration	NN
randomwalker-info-585	460	34	for	for	IN
randomwalker-info-585	460	35	future	future	JJ
randomwalker-info-585	460	36	work	work	NN
randomwalker-info-585	460	37	to	to	TO
randomwalker-info-585	460	38	consider	consider	VB
randomwalker-info-585	460	39	selfish	selfish	JJ
randomwalker-info-585	460	40	miners	miner	NNS
randomwalker-info-585	460	41	who	who	WP
randomwalker-info-585	460	42	also	also	RB
randomwalker-info-585	460	43	undercut	undercut	VBD
randomwalker-info-585	460	44	,	,	,
randomwalker-info-585	460	45	or	or	CC
randomwalker-info-585	460	46	various	various	JJ
randomwalker-info-585	460	47	other	other	JJ
randomwalker-info-585	460	48	generalizations	generalization	NNS
randomwalker-info-585	460	49	(	(	-LRB-
randomwalker-info-585	460	50	e.g.	e.g.	RB
randomwalker-info-585	461	1	[	[	-LRB-
randomwalker-info-585	461	2	7	7	CD
randomwalker-info-585	461	3	,	,	,
randomwalker-info-585	461	4	20	20	CD
randomwalker-info-585	461	5	,	,	,
randomwalker-info-585	461	6	23	23	CD
randomwalker-info-585	461	7	]	]	-RRB-
randomwalker-info-585	461	8	)	)	-RRB-
randomwalker-info-585	461	9	.	.	.
randomwalker-info-585	462	1	Similarly	similarly	RB
randomwalker-info-585	462	2	to	to	IN
randomwalker-info-585	462	3	[	[	-LRB-
randomwalker-info-585	462	4	9	9	CD
randomwalker-info-585	462	5	]	]	-RRB-
randomwalker-info-585	462	6	,	,	,
randomwalker-info-585	462	7	we	-PRON-	PRP
randomwalker-info-585	462	8	examine	examine	VBP
randomwalker-info-585	462	9	the	the	DT
randomwalker-info-585	462	10	potential	potential	JJ
randomwalker-info-585	462	11	rewards	reward	VBZ
randomwalker-info-585	462	12	a	a	DT
randomwalker-info-585	462	13	selfish	selfish	JJ
randomwalker-info-585	462	14	miner	miner	NN
randomwalker-info-585	462	15	would	would	MD
randomwalker-info-585	462	16	receive	receive	VB
randomwalker-info-585	462	17	assuming	assume	VBG
randomwalker-info-585	462	18	that	that	IN
randomwalker-info-585	462	19	the	the	DT
randomwalker-info-585	462	20	rest	rest	NN
randomwalker-info-585	462	21	of	of	IN
randomwalker-info-585	462	22	the	the	DT
randomwalker-info-585	462	23	network	network	NN
randomwalker-info-585	462	24	is	be	VBZ
randomwalker-info-585	462	25	default	default	NN
randomwalker-info-585	462	26	mining	mining	NN
randomwalker-info-585	462	27	.	.	.
randomwalker-info-585	463	1	In	in	IN
randomwalker-info-585	463	2	our	-PRON-	PRP$
randomwalker-info-585	463	3	analysis	analysis	NN
randomwalker-info-585	463	4	,	,	,
randomwalker-info-585	463	5	we	-PRON-	PRP
randomwalker-info-585	463	6	also	also	RB
randomwalker-info-585	463	7	use	use	VBP
randomwalker-info-585	463	8	α	α	PRP
randomwalker-info-585	463	9	to	to	TO
randomwalker-info-585	463	10	denote	denote	VB
randomwalker-info-585	463	11	the	the	DT
randomwalker-info-585	463	12	fraction	fraction	NN
randomwalker-info-585	463	13	of	of	IN
randomwalker-info-585	463	14	the	the	DT
randomwalker-info-585	463	15	total	total	JJ
randomwalker-info-585	463	16	mining	mining	NN
randomwalker-info-585	463	17	power	power	NN
randomwalker-info-585	463	18	pos-	pos-	VBN
randomwalker-info-585	463	19	sessed	sesse	VBN
randomwalker-info-585	463	20	by	by	IN
randomwalker-info-585	463	21	the	the	DT
randomwalker-info-585	463	22	selfish	selfish	JJ
randomwalker-info-585	463	23	miner	miner	NN
randomwalker-info-585	463	24	,	,	,
randomwalker-info-585	463	25	and	and	CC
randomwalker-info-585	463	26	γ	γ	LS
randomwalker-info-585	463	27	to	to	TO
randomwalker-info-585	463	28	be	be	VB
randomwalker-info-585	463	29	the	the	DT
randomwalker-info-585	463	30	probability	probability	NN
randomwalker-info-585	463	31	that	that	IN
randomwalker-info-585	463	32	in	in	IN
randomwalker-info-585	463	33	the	the	DT
randomwalker-info-585	463	34	event	event	NN
randomwalker-info-585	463	35	of	of	IN
randomwalker-info-585	463	36	a	a	DT
randomwalker-info-585	463	37	race	race	NN
randomwalker-info-585	463	38	(	(	-LRB-
randomwalker-info-585	463	39	selfish	selfish	JJ
randomwalker-info-585	463	40	miner	miner	NN
randomwalker-info-585	463	41	is	be	VBZ
randomwalker-info-585	463	42	triggered	trigger	VBN
randomwalker-info-585	463	43	to	to	TO
randomwalker-info-585	463	44	release	release	VB
randomwalker-info-585	463	45	a	a	DT
randomwalker-info-585	463	46	private	private	JJ
randomwalker-info-585	463	47	block	block	NN
randomwalker-info-585	463	48	of	of	IN
randomwalker-info-585	463	49	length	length	NN
randomwalker-info-585	463	50	one	one	CD
randomwalker-info-585	463	51	)	)	-RRB-
randomwalker-info-585	463	52	that	that	WDT
randomwalker-info-585	463	53	ends	end	VBZ
randomwalker-info-585	463	54	with	with	IN
randomwalker-info-585	463	55	the	the	DT
randomwalker-info-585	463	56	honest	honest	JJ
randomwalker-info-585	463	57	portion	portion	NN
randomwalker-info-585	463	58	of	of	IN
randomwalker-info-585	463	59	the	the	DT
randomwalker-info-585	463	60	network	network	NN
randomwalker-info-585	463	61	finding	find	VBG
randomwalker-info-585	463	62	the	the	DT
randomwalker-info-585	463	63	next	next	JJ
randomwalker-info-585	463	64	block	block	NN
randomwalker-info-585	463	65	,	,	,
randomwalker-info-585	463	66	that	that	IN
randomwalker-info-585	463	67	the	the	DT
randomwalker-info-585	463	68	self-	self-	NNP
randomwalker-info-585	463	69	ish	ish	NNP
randomwalker-info-585	463	70	miner	miner	NNP
randomwalker-info-585	463	71	’s	’s	POS
randomwalker-info-585	463	72	block	block	NN
randomwalker-info-585	463	73	is	be	VBZ
randomwalker-info-585	463	74	not	not	RB
randomwalker-info-585	463	75	orphaned	orphan	VBN
randomwalker-info-585	463	76	.	.	.
randomwalker-info-585	464	1	We	-PRON-	PRP
randomwalker-info-585	464	2	introduce	introduce	VBP
randomwalker-info-585	464	3	notation	notation	NN
randomwalker-info-585	464	4	Privatem	Privatem	NNP
randomwalker-info-585	464	5	to	to	TO
randomwalker-info-585	464	6	denote	denote	VB
randomwalker-info-585	464	7	the	the	DT
randomwalker-info-585	464	8	height	height	NN
randomwalker-info-585	464	9	of	of	IN
randomwalker-info-585	464	10	the	the	DT
randomwalker-info-585	464	11	longest	long	JJS
randomwalker-info-585	464	12	chain	chain	NN
randomwalker-info-585	464	13	that	that	IN
randomwalker-info-585	464	14	m	m	NNP
randomwalker-info-585	464	15	is	be	VBZ
randomwalker-info-585	464	16	aware	aware	JJ
randomwalker-info-585	464	17	of	of	IN
randomwalker-info-585	464	18	(	(	-LRB-
randomwalker-info-585	464	19	at	at	IN
randomwalker-info-585	464	20	least	least	JJS
randomwalker-info-585	464	21	as	as	RB
randomwalker-info-585	464	22	long	long	RB
randomwalker-info-585	464	23	as	as	IN
randomwalker-info-585	464	24	H	h	NN
randomwalker-info-585	464	25	,	,	,
randomwalker-info-585	464	26	and	and	CC
randomwalker-info-585	464	27	possibly	possibly	RB
randomwalker-info-585	464	28	longer	long	RBR
randomwalker-info-585	464	29	if	if	IN
randomwalker-info-585	464	30	m	m	NNP
randomwalker-info-585	464	31	is	be	VBZ
randomwalker-info-585	464	32	keeping	keep	VBG
randomwalker-info-585	464	33	any	any	DT
randomwalker-info-585	464	34	blocks	block	NNS
randomwalker-info-585	464	35	private	private	JJ
randomwalker-info-585	464	36	)	)	-RRB-
randomwalker-info-585	464	37	.	.	.
randomwalker-info-585	465	1	We	-PRON-	PRP
randomwalker-info-585	465	2	also	also	RB
randomwalker-info-585	465	3	introduce	introduce	VBP
randomwalker-info-585	465	4	notation	notation	NN
randomwalker-info-585	465	5	Racingmi	Racingmi	NNP
randomwalker-info-585	465	6	to	to	TO
randomwalker-info-585	465	7	be	be	VB
randomwalker-info-585	465	8	a	a	DT
randomwalker-info-585	465	9	boolean	boolean	NN
randomwalker-info-585	465	10	variable	variable	NN
randomwalker-info-585	465	11	that	that	WDT
randomwalker-info-585	465	12	is	be	VBZ
randomwalker-info-585	465	13	true	true	JJ
randomwalker-info-585	465	14	iff	iff	NN
randomwalker-info-585	465	15	there	there	EX
randomwalker-info-585	465	16	exist	exist	VBP
randomwalker-info-585	465	17	two	two	CD
randomwalker-info-585	465	18	blocks	block	NNS
randomwalker-info-585	465	19	B1,B2	B1,B2	NNP
randomwalker-info-585	465	20	with	with	IN
randomwalker-info-585	465	21	Height(B1	Height(B1	NNP
randomwalker-info-585	465	22	)	)	-RRB-
randomwalker-info-585	465	23	=	=	NFP
randomwalker-info-585	465	24	Height(B2	Height(B2	NNP
randomwalker-info-585	465	25	)	)	-RRB-
randomwalker-info-585	465	26	=	=	NFP
randomwalker-info-585	465	27	i	i	PRP
randomwalker-info-585	465	28	,	,	,
randomwalker-info-585	465	29	and	and	CC
randomwalker-info-585	465	30	Owner(B1	Owner(B1	NNP
randomwalker-info-585	465	31	)	)	-RRB-
randomwalker-info-585	465	32	=	=	NFP
randomwalker-info-585	465	33	m	m	NNP
randomwalker-info-585	465	34	6=	6=	NNP
randomwalker-info-585	465	35	Owner(B2	Owner(B2	NNP
randomwalker-info-585	465	36	)	)	-RRB-
randomwalker-info-585	465	37	.	.	.
randomwalker-info-585	466	1	In	in	IN
randomwalker-info-585	466	2	other	other	JJ
randomwalker-info-585	466	3	words	word	NNS
randomwalker-info-585	466	4	,	,	,
randomwalker-info-585	466	5	Racingmi	Racingmi	NNP
randomwalker-info-585	466	6	denotes	denote	VBZ
randomwalker-info-585	466	7	whether	whether	IN
randomwalker-info-585	466	8	or	or	CC
randomwalker-info-585	466	9	not	not	RB
randomwalker-info-585	466	10	there	there	EX
randomwalker-info-585	466	11	are	be	VBP
randomwalker-info-585	466	12	two	two	CD
randomwalker-info-585	466	13	competing	compete	VBG
randomwalker-info-585	466	14	blocks	block	NNS
randomwalker-info-585	466	15	of	of	IN
randomwalker-info-585	466	16	height	height	NN
randomwalker-info-585	466	17	i	i	PRP
randomwalker-info-585	466	18	,	,	,
randomwalker-info-585	466	19	one	one	CD
randomwalker-info-585	466	20	of	of	IN
randomwalker-info-585	466	21	which	which	WDT
randomwalker-info-585	466	22	was	be	VBD
randomwalker-info-585	466	23	produced	produce	VBN
randomwalker-info-585	466	24	by	by	IN
randomwalker-info-585	466	25	m.	m.	NN
randomwalker-info-585	466	26	Analysis	Analysis	NNP
randomwalker-info-585	466	27	.	.	.
randomwalker-info-585	467	1	We	-PRON-	PRP
randomwalker-info-585	467	2	proceed	proceed	VBP
randomwalker-info-585	467	3	now	now	RB
randomwalker-info-585	467	4	with	with	IN
randomwalker-info-585	467	5	an	an	DT
randomwalker-info-585	467	6	analysis	analysis	NN
randomwalker-info-585	467	7	of	of	IN
randomwalker-info-585	467	8	the	the	DT
randomwalker-info-585	467	9	rewards	reward	NNS
randomwalker-info-585	467	10	obtained	obtain	VBN
randomwalker-info-585	467	11	in	in	IN
randomwalker-info-585	467	12	the	the	DT
randomwalker-info-585	467	13	transaction	transaction	NN
randomwalker-info-585	467	14	fee	fee	NN
randomwalker-info-585	467	15	model	model	NN
randomwalker-info-585	467	16	by	by	IN
randomwalker-info-585	467	17	a	a	DT
randomwalker-info-585	467	18	selfish	selfish	JJ
randomwalker-info-585	467	19	miner	miner	NN
randomwalker-info-585	467	20	.	.	.
randomwalker-info-585	468	1	Parts	part	NNS
randomwalker-info-585	468	2	will	will	MD
randomwalker-info-585	468	3	look	look	VB
randomwalker-info-585	468	4	similar	similar	JJ
randomwalker-info-585	468	5	to	to	IN
randomwalker-info-585	468	6	the	the	DT
randomwalker-info-585	468	7	analysis	analysis	NN
randomwalker-info-585	468	8	done	do	VBN
randomwalker-info-585	468	9	in	in	IN
randomwalker-info-585	468	10	[	[	-LRB-
randomwalker-info-585	468	11	9	9	CD
randomwalker-info-585	468	12	]	]	-RRB-
randomwalker-info-585	468	13	.	.	.
randomwalker-info-585	469	1	For	for	IN
randomwalker-info-585	469	2	every	every	DT
randomwalker-info-585	469	3	infinitesi-	infinitesi-	JJ
randomwalker-info-585	469	4	mally	mally	RB
randomwalker-info-585	469	5	small	small	JJ
randomwalker-info-585	469	6	transaction	transaction	NN
randomwalker-info-585	469	7	fee	fee	NN
randomwalker-info-585	469	8	that	that	WDT
randomwalker-info-585	469	9	arrives	arrive	VBZ
randomwalker-info-585	469	10	,	,	,
randomwalker-info-585	469	11	we	-PRON-	PRP
randomwalker-info-585	469	12	wish	wish	VBP
randomwalker-info-585	469	13	to	to	TO
randomwalker-info-585	469	14	compute	compute	VB
randomwalker-info-585	469	15	the	the	DT
randomwalker-info-585	469	16	probability	probability	NN
randomwalker-info-585	469	17	that	that	WDT
randomwalker-info-585	469	18	it	-PRON-	PRP
randomwalker-info-585	469	19	winds	wind	VBZ
randomwalker-info-585	469	20	up	up	RP
randomwalker-info-585	469	21	in	in	IN
randomwalker-info-585	469	22	a	a	DT
randomwalker-info-585	469	23	block	block	NN
randomwalker-info-585	469	24	mined	mine	VBN
randomwalker-info-585	469	25	by	by	IN
randomwalker-info-585	469	26	the	the	DT
randomwalker-info-585	469	27	self-	self-	NNP
randomwalker-info-585	469	28	ish	ish	NNP
randomwalker-info-585	469	29	miner	miner	NN
randomwalker-info-585	469	30	.	.	.
randomwalker-info-585	470	1	Note	note	VB
randomwalker-info-585	470	2	that	that	IN
randomwalker-info-585	470	3	if	if	IN
randomwalker-info-585	470	4	the	the	DT
randomwalker-info-585	470	5	selfish	selfish	JJ
randomwalker-info-585	470	6	miner	miner	NN
randomwalker-info-585	470	7	just	just	RB
randomwalker-info-585	470	8	used	use	VBD
randomwalker-info-585	470	9	default	default	NN
randomwalker-info-585	470	10	mining	mining	NN
randomwalker-info-585	470	11	instead	instead	RB
randomwalker-info-585	470	12	,	,	,
randomwalker-info-585	470	13	this	this	DT
randomwalker-info-585	470	14	probability	probability	NN
randomwalker-info-585	470	15	would	would	MD
randomwalker-info-585	470	16	be	be	VB
randomwalker-info-585	470	17	exactly	exactly	RB
randomwalker-info-585	470	18	α	α	XX
randomwalker-info-585	470	19	.	.	.
randomwalker-info-585	471	1	The	the	DT
randomwalker-info-585	471	2	determining	determine	VBG
randomwalker-info-585	471	3	factor	factor	NN
randomwalker-info-585	471	4	in	in	IN
randomwalker-info-585	471	5	this	this	DT
randomwalker-info-585	471	6	probability	probability	NN
randomwalker-info-585	471	7	will	will	MD
randomwalker-info-585	471	8	be	be	VB
randomwalker-info-585	471	9	the	the	DT
randomwalker-info-585	471	10	size	size	NN
randomwalker-info-585	471	11	of	of	IN
randomwalker-info-585	471	12	the	the	DT
randomwalker-info-585	471	13	selfish	selfish	JJ
randomwalker-info-585	471	14	miner	miner	NN
randomwalker-info-585	471	15	’s	’s	POS
randomwalker-info-585	471	16	private	private	JJ
randomwalker-info-585	471	17	chain	chain	NN
randomwalker-info-585	471	18	.	.	.
randomwalker-info-585	472	1	To	to	IN
randomwalker-info-585	472	2	this	this	DT
randomwalker-info-585	472	3	end	end	NN
randomwalker-info-585	472	4	,	,	,
randomwalker-info-585	472	5	let	let	VB
randomwalker-info-585	472	6	’s	-PRON-	PRP
randomwalker-info-585	472	7	de-	de-	RB
randomwalker-info-585	472	8	fine	fine	RB
randomwalker-info-585	472	9	the	the	DT
randomwalker-info-585	472	10	following	follow	VBG
randomwalker-info-585	472	11	states	state	NNS
randomwalker-info-585	472	12	(	(	-LRB-
randomwalker-info-585	472	13	same	same	JJ
randomwalker-info-585	472	14	states	state	NNS
randomwalker-info-585	472	15	used	use	VBN
randomwalker-info-585	472	16	in	in	IN
randomwalker-info-585	472	17	[	[	-LRB-
randomwalker-info-585	472	18	9	9	CD
randomwalker-info-585	472	19	]	]	-RRB-
randomwalker-info-585	472	20	)	)	-RRB-
randomwalker-info-585	472	21	,	,	,
randomwalker-info-585	472	22	and	and	CC
randomwalker-info-585	472	23	we	-PRON-	PRP
randomwalker-info-585	472	24	’ll	will	MD
randomwalker-info-585	472	25	compute	compute	VB
randomwalker-info-585	472	26	this	this	DT
randomwalker-info-585	472	27	probability	probability	NN
randomwalker-info-585	472	28	separately	separately	RB
randomwalker-info-585	472	29	for	for	IN
randomwalker-info-585	472	30	each	each	DT
randomwalker-info-585	472	31	state	state	NN
randomwalker-info-585	472	32	.	.	.
randomwalker-info-585	473	1	•	•	NNP
randomwalker-info-585	473	2	State	state	NN
randomwalker-info-585	473	3	0	0	NFP
randomwalker-info-585	473	4	:	:	:
randomwalker-info-585	473	5	Everyone	everyone	NN
randomwalker-info-585	473	6	agrees	agree	VBZ
randomwalker-info-585	473	7	on	on	IN
randomwalker-info-585	473	8	the	the	DT
randomwalker-info-585	473	9	longest	long	JJS
randomwalker-info-585	473	10	chain	chain	NN
randomwalker-info-585	473	11	—	—	:
randomwalker-info-585	473	12	RacingmH	racingmh	NN
randomwalker-info-585	473	13	=	=	SYM
randomwalker-info-585	473	14	false	false	JJ
randomwalker-info-585	473	15	.	.	.
randomwalker-info-585	474	1	•	•	NNP
randomwalker-info-585	474	2	State	state	NN
randomwalker-info-585	474	3	i	i	PRP
randomwalker-info-585	474	4	>	>	VBP
randomwalker-info-585	474	5	0	0	XX
randomwalker-info-585	474	6	:	:	:
randomwalker-info-585	474	7	The	the	DT
randomwalker-info-585	474	8	selfish	selfish	JJ
randomwalker-info-585	474	9	miner	miner	NN
randomwalker-info-585	474	10	m	m	NNP
randomwalker-info-585	474	11	has	have	VBZ
randomwalker-info-585	474	12	a	a	DT
randomwalker-info-585	474	13	private	private	JJ
randomwalker-info-585	474	14	chain	chain	NN
randomwalker-info-585	474	15	of	of	IN
randomwalker-info-585	474	16	length	length	NN
randomwalker-info-585	474	17	i	i	PRP
randomwalker-info-585	474	18	—	—	:
randomwalker-info-585	474	19	Privatem	Privatem	NNP
randomwalker-info-585	474	20	=	=	SYM
randomwalker-info-585	474	21	H	h	NN
randomwalker-info-585	474	22	+	+	SYM
randomwalker-info-585	474	23	i.	i.	NN
randomwalker-info-585	475	1	•	•	NNP
randomwalker-info-585	475	2	State	state	NN
randomwalker-info-585	475	3	0′	0′	NN
randomwalker-info-585	475	4	:	:	:
randomwalker-info-585	475	5	There	there	EX
randomwalker-info-585	475	6	are	be	VBP
randomwalker-info-585	475	7	competing	compete	VBG
randomwalker-info-585	475	8	blocks	block	NNS
randomwalker-info-585	475	9	of	of	IN
randomwalker-info-585	475	10	height	height	NN
randomwalker-info-585	475	11	H	h	NN
randomwalker-info-585	475	12	,	,	,
randomwalker-info-585	475	13	one	one	CD
randomwalker-info-585	475	14	of	of	IN
randomwalker-info-585	475	15	which	which	WDT
randomwalker-info-585	475	16	was	be	VBD
randomwalker-info-585	475	17	produced	produce	VBN
randomwalker-info-585	475	18	by	by	IN
randomwalker-info-585	475	19	the	the	DT
randomwalker-info-585	475	20	selfish	selfish	JJ
randomwalker-info-585	475	21	miner	miner	NN
randomwalker-info-585	475	22	,	,	,
randomwalker-info-585	475	23	and	and	CC
randomwalker-info-585	475	24	the	the	DT
randomwalker-info-585	475	25	selfish	selfish	JJ
randomwalker-info-585	475	26	miner	miner	NN
randomwalker-info-585	475	27	has	have	VBZ
randomwalker-info-585	475	28	no	no	DT
randomwalker-info-585	475	29	private	private	JJ
randomwalker-info-585	475	30	blocks	block	NNS
randomwalker-info-585	475	31	—	—	:
randomwalker-info-585	475	32	RacingmH	racingmh	NN
randomwalker-info-585	475	33	=	=	SYM
randomwalker-info-585	475	34	true	true	JJ
randomwalker-info-585	475	35	and	and	CC
randomwalker-info-585	475	36	Privatem	Privatem	NNP
randomwalker-info-585	475	37	=	=	SYM
randomwalker-info-585	475	38	H.	H.	NNP
randomwalker-info-585	475	39	Let	let	VB
randomwalker-info-585	475	40	fs	fs	NNP
randomwalker-info-585	475	41	denote	denote	VB
randomwalker-info-585	475	42	the	the	DT
randomwalker-info-585	475	43	probability	probability	NN
randomwalker-info-585	475	44	that	that	IN
randomwalker-info-585	475	45	a	a	DT
randomwalker-info-585	475	46	transaction	transaction	NN
randomwalker-info-585	475	47	winds	wind	VBZ
randomwalker-info-585	475	48	up	up	RP
randomwalker-info-585	475	49	in	in	IN
randomwalker-info-585	475	50	a	a	DT
randomwalker-info-585	475	51	block	block	NN
randomwalker-info-585	475	52	mined	mine	VBN
randomwalker-info-585	475	53	by	by	IN
randomwalker-info-585	475	54	the	the	DT
randomwalker-info-585	475	55	selfish	selfish	JJ
randomwalker-info-585	475	56	miner	miner	NN
randomwalker-info-585	475	57	in	in	IN
randomwalker-info-585	475	58	the	the	DT
randomwalker-info-585	475	59	eventual	eventual	JJ
randomwalker-info-585	475	60	longest	long	JJS
randomwalker-info-585	475	61	chain	chain	NN
randomwalker-info-585	475	62	,	,	,
randomwalker-info-585	475	63	conditioned	condition	VBN
randomwalker-info-585	475	64	on	on	IN
randomwalker-info-585	475	65	the	the	DT
randomwalker-info-585	475	66	system	system	NN
randomwalker-info-585	475	67	being	be	VBG
randomwalker-info-585	475	68	in	in	IN
randomwalker-info-585	475	69	state	state	NN
randomwalker-info-585	475	70	s	s	NNPS
randomwalker-info-585	475	71	when	when	WRB
randomwalker-info-585	475	72	the	the	DT
randomwalker-info-585	475	73	transaction	transaction	NN
randomwalker-info-585	475	74	is	be	VBZ
randomwalker-info-585	475	75	announced	announce	VBN
randomwalker-info-585	475	76	.	.	.
randomwalker-info-585	476	1	We	-PRON-	PRP
randomwalker-info-585	476	2	compute	compute	VBP
randomwalker-info-585	476	3	there	there	EX
randomwalker-info-585	476	4	probabilities	probability	NNS
randomwalker-info-585	476	5	below	below	RB
randomwalker-info-585	476	6	.	.	.
randomwalker-info-585	477	1	If	if	IN
randomwalker-info-585	477	2	we	-PRON-	PRP
randomwalker-info-585	477	3	then	then	RB
randomwalker-info-585	477	4	define	define	VBP
randomwalker-info-585	477	5	ps	ps	NNP
randomwalker-info-585	477	6	to	to	TO
randomwalker-info-585	477	7	be	be	VB
randomwalker-info-585	477	8	the	the	DT
randomwalker-info-585	477	9	probability	probability	NN
randomwalker-info-585	477	10	that	that	IN
randomwalker-info-585	477	11	the	the	DT
randomwalker-info-585	477	12	system	system	NN
randomwalker-info-585	477	13	is	be	VBZ
randomwalker-info-585	477	14	in	in	IN
randomwalker-info-585	477	15	state	state	NN
randomwalker-info-585	477	16	s	s	NNPS
randomwalker-info-585	477	17	,	,	,
randomwalker-info-585	477	18	we	-PRON-	PRP
randomwalker-info-585	477	19	can	can	MD
randomwalker-info-585	477	20	then	then	RB
randomwalker-info-585	477	21	observe	observe	VB
randomwalker-info-585	477	22	that	that	IN
randomwalker-info-585	477	23	the	the	DT
randomwalker-info-585	477	24	expected	expect	VBN
randomwalker-info-585	477	25	fraction	fraction	NN
randomwalker-info-585	477	26	of	of	IN
randomwalker-info-585	477	27	transaction	transaction	NN
randomwalker-info-585	477	28	fees	fee	NNS
randomwalker-info-585	477	29	claimed	claim	VBN
randomwalker-info-585	477	30	by	by	IN
randomwalker-info-585	477	31	the	the	DT
randomwalker-info-585	477	32	selfish	selfish	JJ
randomwalker-info-585	477	33	miner	miner	NN
randomwalker-info-585	477	34	is	be	VBZ
randomwalker-info-585	477	35	exactly	exactly	RB
randomwalker-info-585	477	36	∑	∑	.
randomwalker-info-585	477	37	s	s	NNP
randomwalker-info-585	477	38	fs	fs	NNPS
randomwalker-info-585	477	39	·	·	NFP
randomwalker-info-585	477	40	ps	ps	XX
randomwalker-info-585	477	41	.	.	.
randomwalker-info-585	478	1	Eyal	Eyal	NNP
randomwalker-info-585	478	2	and	and	CC
randomwalker-info-585	478	3	Sirer	Sirer	NNP
randomwalker-info-585	478	4	[	[	-LRB-
randomwalker-info-585	478	5	9	9	CD
randomwalker-info-585	478	6	]	]	-RRB-
randomwalker-info-585	478	7	have	have	VBP
randomwalker-info-585	478	8	already	already	RB
randomwalker-info-585	478	9	computed	compute	VBN
randomwalker-info-585	478	10	ps	ps	NNP
randomwalker-info-585	478	11	for	for	IN
randomwalker-info-585	478	12	all	all	DT
randomwalker-info-585	478	13	s.	s.	NN
randomwalker-info-585	478	14	The	the	DT
randomwalker-info-585	478	15	values	value	NNS
randomwalker-info-585	478	16	for	for	IN
randomwalker-info-585	478	17	ps	ps	NNP
randomwalker-info-585	478	18	are	be	VBP
randomwalker-info-585	478	19	:	:	:
randomwalker-info-585	478	20	p0	p0	NN
randomwalker-info-585	478	21	=	=	SYM
randomwalker-info-585	478	22	1	1	CD
randomwalker-info-585	478	23	−	−	NNP
randomwalker-info-585	478	24	2α	2α	CD
randomwalker-info-585	478	25	2α3	2α3	CD
randomwalker-info-585	478	26	−	−	NNP
randomwalker-info-585	478	27	4α2	4α2	CD
randomwalker-info-585	478	28	+	+	SYM
randomwalker-info-585	478	29	1	1	CD
randomwalker-info-585	478	30	p0′	p0′	NN
randomwalker-info-585	478	31	=	=	NNS
randomwalker-info-585	478	32	(	(	-LRB-
randomwalker-info-585	478	33	1	1	CD
randomwalker-info-585	478	34	−α)(α−	−α)(α−	JJ
randomwalker-info-585	478	35	2α2	2α2	CD
randomwalker-info-585	478	36	)	)	-RRB-
randomwalker-info-585	478	37	2α3	2α3	CD
randomwalker-info-585	478	38	−	−	NNP
randomwalker-info-585	478	39	4α2	4α2	CD
randomwalker-info-585	478	40	+	+	SYM
randomwalker-info-585	478	41	1	1	CD
randomwalker-info-585	478	42	pi	pi	NN
randomwalker-info-585	478	43	=	=	NNS
randomwalker-info-585	478	44	(	(	-LRB-
randomwalker-info-585	478	45	α	α	DT
randomwalker-info-585	478	46	1	1	CD
randomwalker-info-585	478	47	−α	−α	CD
randomwalker-info-585	478	48	)	)	-RRB-
randomwalker-info-585	478	49	i−1	i−1	NNP
randomwalker-info-585	478	50	α−	α−	NNP
randomwalker-info-585	478	51	2α2	2α2	CD
randomwalker-info-585	478	52	2α3	2α3	CD
randomwalker-info-585	478	53	−	−	NNP
randomwalker-info-585	478	54	4α2	4α2	CD
randomwalker-info-585	478	55	+	+	SYM
randomwalker-info-585	478	56	1	1	CD
randomwalker-info-585	478	57	,	,	,
randomwalker-info-585	478	58	i	i	PRP
randomwalker-info-585	478	59	>	>	XX
randomwalker-info-585	478	60	0	0	NFP
randomwalker-info-585	478	61	To	to	TO
randomwalker-info-585	478	62	complete	complete	VB
randomwalker-info-585	478	63	the	the	DT
randomwalker-info-585	478	64	analysis	analysis	NN
randomwalker-info-585	478	65	,	,	,
randomwalker-info-585	478	66	we	-PRON-	PRP
randomwalker-info-585	478	67	just	just	RB
randomwalker-info-585	478	68	need	need	VBP
randomwalker-info-585	478	69	to	to	TO
randomwalker-info-585	478	70	compute	compute	VB
randomwalker-info-585	478	71	fs	f	NNS
randomwalker-info-585	478	72	for	for	IN
randomwalker-info-585	478	73	each	each	DT
randomwalker-info-585	478	74	s.	s.	JJ
randomwalker-info-585	478	75	Appendix	Appendix	NNP
randomwalker-info-585	478	76	E	E	NNP
randomwalker-info-585	478	77	contains	contain	VBZ
randomwalker-info-585	478	78	the	the	DT
randomwalker-info-585	478	79	derivation	derivation	NN
randomwalker-info-585	478	80	of	of	IN
randomwalker-info-585	478	81	fs	f	NNS
randomwalker-info-585	478	82	for	for	IN
randomwalker-info-585	478	83	all	all	DT
randomwalker-info-585	478	84	s	s	NNPS
randomwalker-info-585	478	85	,	,	,
randomwalker-info-585	478	86	which	which	WDT
randomwalker-info-585	478	87	are	be	VBP
randomwalker-info-585	478	88	stated	state	VBN
randomwalker-info-585	478	89	below	below	IN
randomwalker-info-585	478	90	:	:	:
randomwalker-info-585	478	91	f0	f0	NN
randomwalker-info-585	478	92	=	=	SYM
randomwalker-info-585	478	93	α	α	NNP
randomwalker-info-585	478	94	2	2	CD
randomwalker-info-585	478	95	+	+	SYM
randomwalker-info-585	478	96	α(1	α(1	NFP
randomwalker-info-585	478	97	−α	−α	CD
randomwalker-info-585	478	98	)	)	-RRB-
randomwalker-info-585	478	99	(	(	-LRB-
randomwalker-info-585	478	100	α	α	NNP
randomwalker-info-585	478	101	+	+	SYM
randomwalker-info-585	478	102	γ(1	γ(1	$
randomwalker-info-585	478	103	−α	−α	CD
randomwalker-info-585	478	104	)	)	-RRB-
randomwalker-info-585	478	105	)	)	-RRB-
randomwalker-info-585	478	106	.	.	.
randomwalker-info-585	479	1	f0′	f0′	NNP
randomwalker-info-585	479	2	=	=	SYM
randomwalker-info-585	479	3	α	α	XX
randomwalker-info-585	479	4	.	.	NNP
randomwalker-info-585	479	5	f1	f1	NNP
randomwalker-info-585	479	6	=	=	SYM
randomwalker-info-585	479	7	α	α	NNP
randomwalker-info-585	479	8	+	+	SYM
randomwalker-info-585	479	9	(	(	-LRB-
randomwalker-info-585	479	10	1	1	CD
randomwalker-info-585	479	11	−α)α	−α)α	NNS
randomwalker-info-585	479	12	=	=	SYM
randomwalker-info-585	479	13	α(2	α(2	$
randomwalker-info-585	479	14	−α	−α	CD
randomwalker-info-585	479	15	)	)	-RRB-
randomwalker-info-585	479	16	.	.	.
randomwalker-info-585	480	1	fi	fi	NN
randomwalker-info-585	480	2	=	=	SYM
randomwalker-info-585	480	3	1	1	CD
randomwalker-info-585	480	4	−	−	NNP
randomwalker-info-585	480	5	(	(	-LRB-
randomwalker-info-585	480	6	(	(	-LRB-
randomwalker-info-585	480	7	1	1	CD
randomwalker-info-585	480	8	−α)i−1(1	−α)i−1(1	NNP
randomwalker-info-585	480	9	−f0	−f0	NNP
randomwalker-info-585	480	10	)	)	-RRB-
randomwalker-info-585	480	11	)	)	-RRB-
randomwalker-info-585	480	12	.	.	.
randomwalker-info-585	481	1	Finally	finally	RB
randomwalker-info-585	481	2	,	,	,
randomwalker-info-585	481	3	when	when	WRB
randomwalker-info-585	481	4	α	α	LS
randomwalker-info-585	481	5	∈	∈	NNP
randomwalker-info-585	481	6	(	(	-LRB-
randomwalker-info-585	481	7	0	0	NFP
randomwalker-info-585	481	8	,	,	,
randomwalker-info-585	481	9	.5	.5	.
randomwalker-info-585	481	10	)	)	-RRB-
randomwalker-info-585	481	11	and	and	CC
randomwalker-info-585	481	12	γ	γ	LS
randomwalker-info-585	481	13	∈	∈	NNP
randomwalker-info-585	481	14	[	[	-LRB-
randomwalker-info-585	481	15	0	0	CD
randomwalker-info-585	481	16	,	,	,
randomwalker-info-585	481	17	1	1	CD
randomwalker-info-585	481	18	]	]	-RRB-
randomwalker-info-585	481	19	,	,	,
randomwalker-info-585	481	20	we	-PRON-	PRP
randomwalker-info-585	481	21	show	show	VBP
randomwalker-info-585	481	22	in	in	IN
randomwalker-info-585	481	23	the	the	DT
randomwalker-info-585	481	24	Appendix	Appendix	NNP
randomwalker-info-585	481	25	E	E	NNP
randomwalker-info-585	481	26	that	that	IN
randomwalker-info-585	481	27	the	the	DT
randomwalker-info-585	481	28	selfish	selfish	JJ
randomwalker-info-585	481	29	miner	miner	NN
randomwalker-info-585	481	30	’s	’s	POS
randomwalker-info-585	481	31	rewards	reward	NNS
randomwalker-info-585	481	32	are	be	VBP
randomwalker-info-585	481	33	given	give	VBN
randomwalker-info-585	481	34	by	by	IN
randomwalker-info-585	481	35	Reward(α	reward(α	NN
randomwalker-info-585	481	36	,	,	,
randomwalker-info-585	481	37	γ	γ	NNP
randomwalker-info-585	481	38	)	)	-RRB-
randomwalker-info-585	481	39	=	=	SYM
randomwalker-info-585	481	40	5α2	5α2	CD
randomwalker-info-585	481	41	−	−	NNP
randomwalker-info-585	481	42	12α3	12α3	CD
randomwalker-info-585	481	43	+	+	SYM
randomwalker-info-585	481	44	9α4	9α4	CD
randomwalker-info-585	481	45	−	−	NNP
randomwalker-info-585	481	46	2α5	2α5	CD
randomwalker-info-585	481	47	+	+	SYM
randomwalker-info-585	481	48	γ(α−	γ(α−	NNP
randomwalker-info-585	481	49	4α2	4α2	CD
randomwalker-info-585	481	50	+	+	SYM
randomwalker-info-585	481	51	6α3	6α3	CD
randomwalker-info-585	481	52	−	−	NNP
randomwalker-info-585	481	53	5α4	5α4	CD
randomwalker-info-585	481	54	+	+	SYM
randomwalker-info-585	481	55	2α5	2α5	CD
randomwalker-info-585	481	56	)	)	-RRB-
randomwalker-info-585	481	57	2α3	2α3	CD
randomwalker-info-585	481	58	−	−	NNP
randomwalker-info-585	481	59	4α2	4α2	CD
randomwalker-info-585	481	60	+	+	SYM
randomwalker-info-585	481	61	1	1	CD
randomwalker-info-585	481	62	Figure	figure	NN
randomwalker-info-585	481	63	7	7	CD
randomwalker-info-585	481	64	:	:	:
randomwalker-info-585	481	65	We	-PRON-	PRP
randomwalker-info-585	481	66	see	see	VBP
randomwalker-info-585	481	67	simulation	simulation	NN
randomwalker-info-585	481	68	matching	match	VBG
randomwalker-info-585	481	69	the	the	DT
randomwalker-info-585	481	70	theory	theory	NN
randomwalker-info-585	481	71	for	for	IN
randomwalker-info-585	481	72	selfish	selfish	JJ
randomwalker-info-585	481	73	mining	mining	NN
randomwalker-info-585	481	74	in	in	IN
randomwalker-info-585	481	75	a	a	DT
randomwalker-info-585	481	76	transaction	transaction	NN
randomwalker-info-585	481	77	based	base	VBN
randomwalker-info-585	481	78	model	model	NN
randomwalker-info-585	481	79	for	for	IN
randomwalker-info-585	481	80	γ	γ	NNP
randomwalker-info-585	481	81	=	=	SYM
randomwalker-info-585	481	82	0	0	CD
randomwalker-info-585	481	83	,	,	,
randomwalker-info-585	481	84	0.5	0.5	CD
randomwalker-info-585	481	85	,	,	,
randomwalker-info-585	481	86	and	and	CC
randomwalker-info-585	481	87	1	1	CD
randomwalker-info-585	481	88	.	.	.
randomwalker-info-585	482	1	We	-PRON-	PRP
randomwalker-info-585	482	2	make	make	VBP
randomwalker-info-585	482	3	the	the	DT
randomwalker-info-585	482	4	following	follow	VBG
randomwalker-info-585	482	5	observations	observation	NNS
randomwalker-info-585	482	6	:	:	:
randomwalker-info-585	482	7	•	•	NNP
randomwalker-info-585	482	8	Simulation	simulation	NN
randomwalker-info-585	482	9	confirms	confirm	VBZ
randomwalker-info-585	482	10	the	the	DT
randomwalker-info-585	482	11	above	above	IN
randomwalker-info-585	482	12	analytical	analytical	JJ
randomwalker-info-585	482	13	formula	formula	NN
randomwalker-info-585	482	14	for	for	IN
randomwalker-info-585	482	15	Reward(α	reward(α	NN
randomwalker-info-585	482	16	,	,	,
randomwalker-info-585	482	17	γ	γ	NNP
randomwalker-info-585	482	18	)	)	-RRB-
randomwalker-info-585	482	19	(	(	-LRB-
randomwalker-info-585	482	20	Figure	figure	NN
randomwalker-info-585	482	21	7	7	CD
randomwalker-info-585	482	22	)	)	-RRB-
randomwalker-info-585	482	23	•	•	NN
randomwalker-info-585	482	24	This	this	DT
randomwalker-info-585	482	25	function	function	NN
randomwalker-info-585	482	26	is	be	VBZ
randomwalker-info-585	482	27	extremely	extremely	RB
randomwalker-info-585	482	28	close	close	JJ
randomwalker-info-585	482	29	to	to	IN
randomwalker-info-585	482	30	the	the	DT
randomwalker-info-585	482	31	reward	reward	NN
randomwalker-info-585	482	32	function	function	NN
randomwalker-info-585	482	33	with	with	IN
randomwalker-info-585	482	34	block	block	NN
randomwalker-info-585	482	35	rewards	reward	NNS
randomwalker-info-585	482	36	(	(	-LRB-
randomwalker-info-585	482	37	α(1−α)2(4α+γ(1−2α))−α3	α(1−α)2(4α+γ(1−2α))−α3	NNP
randomwalker-info-585	482	38	1−α(1+(2−α)α	1−α(1+(2−α)α	CD
randomwalker-info-585	482	39	)	)	-RRB-
randomwalker-info-585	482	40	)	)	-RRB-
randomwalker-info-585	482	41	from	from	IN
randomwalker-info-585	482	42	[	[	-LRB-
randomwalker-info-585	482	43	9	9	CD
randomwalker-info-585	482	44	]	]	-RRB-
randomwalker-info-585	482	45	.	.	.
randomwalker-info-585	483	1	We	-PRON-	PRP
randomwalker-info-585	483	2	find	find	VBP
randomwalker-info-585	483	3	,	,	,
randomwalker-info-585	483	4	numerically	numerically	RB
randomwalker-info-585	483	5	,	,	,
randomwalker-info-585	483	6	that	that	IN
randomwalker-info-585	483	7	the	the	DT
randomwalker-info-585	483	8	absolute	absolute	JJ
randomwalker-info-585	483	9	difference	difference	NN
randomwalker-info-585	483	10	never	never	RB
randomwalker-info-585	483	11	exceeds	exceed	VBZ
randomwalker-info-585	483	12	0.026	0.026	CD
randomwalker-info-585	483	13	in	in	IN
randomwalker-info-585	483	14	the	the	DT
randomwalker-info-585	483	15	region	region	NN
randomwalker-info-585	483	16	of	of	IN
randomwalker-info-585	483	17	interest	interest	NN
randomwalker-info-585	483	18	.	.	.
randomwalker-info-585	484	1	•	•	VB
randomwalker-info-585	484	2	For	for	IN
randomwalker-info-585	484	3	0	0	CD
randomwalker-info-585	484	4	≤	≤	NN
randomwalker-info-585	484	5	γ	γ	NN
randomwalker-info-585	484	6	<	<	XX
randomwalker-info-585	484	7	0.55	0.55	CD
randomwalker-info-585	484	8	(	(	-LRB-
randomwalker-info-585	484	9	in	in	IN
randomwalker-info-585	484	10	particular	particular	JJ
randomwalker-info-585	484	11	,	,	,
randomwalker-info-585	484	12	for	for	IN
randomwalker-info-585	484	13	γ	γ	NNP
randomwalker-info-585	484	14	=	=	SYM
randomwalker-info-585	484	15	0	0	CD
randomwalker-info-585	484	16	)	)	-RRB-
randomwalker-info-585	484	17	,	,	,
randomwalker-info-585	484	18	for	for	IN
randomwalker-info-585	484	19	all	all	DT
randomwalker-info-585	484	20	α	α	XX
randomwalker-info-585	484	21	∈	∈	NNP
randomwalker-info-585	484	22	(	(	-LRB-
randomwalker-info-585	484	23	0	0	NFP
randomwalker-info-585	484	24	,	,	,
randomwalker-info-585	484	25	0.5	0.5	CD
randomwalker-info-585	484	26	)	)	-RRB-
randomwalker-info-585	484	27	,	,	,
randomwalker-info-585	484	28	the	the	DT
randomwalker-info-585	484	29	reward	reward	NN
randomwalker-info-585	484	30	is	be	VBZ
randomwalker-info-585	484	31	strictly	strictly	RB
randomwalker-info-585	484	32	greater	great	JJR
randomwalker-info-585	484	33	in	in	IN
randomwalker-info-585	484	34	the	the	DT
randomwalker-info-585	484	35	transaction	transaction	NN
randomwalker-info-585	484	36	fee	fee	NN
randomwalker-info-585	484	37	model	model	NN
randomwalker-info-585	484	38	than	than	IN
randomwalker-info-585	484	39	in	in	IN
randomwalker-info-585	484	40	the	the	DT
randomwalker-info-585	484	41	block	block	NN
randomwalker-info-585	484	42	reward	reward	NNP
randomwalker-info-585	484	43	model	model	NN
randomwalker-info-585	484	44	.	.	.
randomwalker-info-585	485	1	We	-PRON-	PRP
randomwalker-info-585	485	2	provide	provide	VBP
randomwalker-info-585	485	3	some	some	DT
randomwalker-info-585	485	4	intuition	intuition	NN
randomwalker-info-585	485	5	for	for	IN
randomwalker-info-585	485	6	this	this	DT
randomwalker-info-585	485	7	last	last	JJ
randomwalker-info-585	485	8	point	point	NN
randomwalker-info-585	485	9	.	.	.
randomwalker-info-585	486	1	First	first	RB
randomwalker-info-585	486	2	,	,	,
randomwalker-info-585	486	3	it	-PRON-	PRP
randomwalker-info-585	486	4	is	be	VBZ
randomwalker-info-585	486	5	clear	clear	JJ
randomwalker-info-585	486	6	that	that	IN
randomwalker-info-585	486	7	the	the	DT
randomwalker-info-585	486	8	fraction	fraction	NN
randomwalker-info-585	486	9	of	of	IN
randomwalker-info-585	486	10	blocks	block	NNS
randomwalker-info-585	486	11	mined	mine	VBN
randomwalker-info-585	486	12	by	by	IN
randomwalker-info-585	486	13	the	the	DT
randomwalker-info-585	486	14	selfish	selfish	NNP
randomwalker-info-585	486	15	vs.	vs.	CC
randomwalker-info-585	486	16	default	default	NN
randomwalker-info-585	486	17	miners	miner	NNS
randomwalker-info-585	486	18	is	be	VBZ
randomwalker-info-585	486	19	independent	independent	JJ
randomwalker-info-585	486	20	of	of	IN
randomwalker-info-585	486	21	the	the	DT
randomwalker-info-585	486	22	reward	reward	NN
randomwalker-info-585	486	23	model	model	NN
randomwalker-info-585	486	24	.	.	.
randomwalker-info-585	487	1	So	so	RB
randomwalker-info-585	487	2	the	the	DT
randomwalker-info-585	487	3	gap	gap	NN
randomwalker-info-585	487	4	must	must	MD
randomwalker-info-585	487	5	come	come	VB
randomwalker-info-585	487	6	from	from	IN
randomwalker-info-585	487	7	the	the	DT
randomwalker-info-585	487	8	size	size	NN
randomwalker-info-585	487	9	of	of	IN
randomwalker-info-585	487	10	blocks	block	NNS
randomwalker-info-585	487	11	found	find	VBN
randomwalker-info-585	487	12	by	by	IN
randomwalker-info-585	487	13	the	the	DT
randomwalker-info-585	487	14	respec-	respec-	NN
randomwalker-info-585	487	15	tive	tive	JJ
randomwalker-info-585	487	16	miners	miner	NNS
randomwalker-info-585	487	17	.	.	.
randomwalker-info-585	488	1	Let	let	VB
randomwalker-info-585	488	2	’s	-PRON-	PRP
randomwalker-info-585	488	3	assume	assume	VB
randomwalker-info-585	488	4	just	just	RB
randomwalker-info-585	488	5	for	for	IN
randomwalker-info-585	488	6	the	the	DT
randomwalker-info-585	488	7	sake	sake	NN
randomwalker-info-585	488	8	of	of	IN
randomwalker-info-585	488	9	example	example	NN
randomwalker-info-585	488	10	that	that	IN
randomwalker-info-585	488	11	we	-PRON-	PRP
randomwalker-info-585	488	12	are	be	VBP
randomwalker-info-585	488	13	in	in	IN
randomwalker-info-585	488	14	state	state	NN
randomwalker-info-585	488	15	100	100	CD
randomwalker-info-585	488	16	and	and	CC
randomwalker-info-585	488	17	the	the	DT
randomwalker-info-585	488	18	selfish	selfish	JJ
randomwalker-info-585	488	19	miner	miner	NN
randomwalker-info-585	488	20	has	have	VBZ
randomwalker-info-585	488	21	an	an	DT
randomwalker-info-585	488	22	α	α	NN
randomwalker-info-585	488	23	=	=	SYM
randomwalker-info-585	488	24	1/10	1/10	CD
randomwalker-info-585	488	25	fraction	fraction	NN
randomwalker-info-585	488	26	of	of	IN
randomwalker-info-585	488	27	the	the	DT
randomwalker-info-585	488	28	mining	mining	NN
randomwalker-info-585	488	29	power	power	NN
randomwalker-info-585	488	30	.	.	.
randomwalker-info-585	489	1	Almost	almost	RB
randomwalker-info-585	489	2	certainly	certainly	RB
randomwalker-info-585	489	3	,	,	,
randomwalker-info-585	489	4	the	the	DT
randomwalker-info-585	489	5	next	next	JJ
randomwalker-info-585	489	6	un	un	NNP
randomwalker-info-585	489	7	-	-	HYPH
randomwalker-info-585	489	8	orphaned	orphan	VBN
randomwalker-info-585	489	9	block	block	NN
randomwalker-info-585	489	10	will	will	MD
randomwalker-info-585	489	11	be	be	VB
randomwalker-info-585	489	12	found	find	VBN
randomwalker-info-585	489	13	by	by	IN
randomwalker-info-585	489	14	the	the	DT
randomwalker-info-585	489	15	selfish	selfish	JJ
randomwalker-info-585	489	16	miner	miner	NN
randomwalker-info-585	489	17	.	.	.
randomwalker-info-585	490	1	How	how	WRB
randomwalker-info-585	490	2	long	long	RB
randomwalker-info-585	490	3	will	will	MD
randomwalker-info-585	490	4	it	-PRON-	PRP
randomwalker-info-585	490	5	take	take	VB
randomwalker-info-585	490	6	for	for	IN
randomwalker-info-585	490	7	this	this	DT
randomwalker-info-585	490	8	block	block	NN
randomwalker-info-585	490	9	to	to	TO
randomwalker-info-585	490	10	be	be	VB
randomwalker-info-585	490	11	found	find	VBN
randomwalker-info-585	490	12	?	?	.
randomwalker-info-585	491	1	The	the	DT
randomwalker-info-585	491	2	answer	answer	NN
randomwalker-info-585	491	3	is	be	VBZ
randomwalker-info-585	491	4	approximately	approximately	RB
randomwalker-info-585	491	5	10	10	CD
randomwalker-info-585	491	6	time	time	NN
randomwalker-info-585	491	7	steps	step	NNS
randomwalker-info-585	491	8	.	.	.
randomwalker-info-585	492	1	This	this	DT
randomwalker-info-585	492	2	is	be	VBZ
randomwalker-info-585	492	3	because	because	IN
randomwalker-info-585	492	4	while	while	IN
randomwalker-info-585	492	5	the	the	DT
randomwalker-info-585	492	6	en-	en-	NNP
randomwalker-info-585	492	7	tire	tire	NN
randomwalker-info-585	492	8	network	network	NN
randomwalker-info-585	492	9	finds	find	VBZ
randomwalker-info-585	492	10	a	a	DT
randomwalker-info-585	492	11	block	block	NN
randomwalker-info-585	492	12	roughly	roughly	RB
randomwalker-info-585	492	13	every	every	DT
randomwalker-info-585	492	14	time	time	NN
randomwalker-info-585	492	15	step	step	NN
randomwalker-info-585	492	16	,	,	,
randomwalker-info-585	492	17	because	because	IN
randomwalker-info-585	492	18	the	the	DT
randomwalker-info-585	492	19	selfish	selfish	JJ
randomwalker-info-585	492	20	miner	miner	NN
randomwalker-info-585	492	21	is	be	VBZ
randomwalker-info-585	492	22	the	the	DT
randomwalker-info-585	492	23	only	only	JJ
randomwalker-info-585	492	24	miner	miner	NN
randomwalker-info-585	492	25	extending	extend	VBG
randomwalker-info-585	492	26	his	-PRON-	PRP$
randomwalker-info-585	492	27	chain	chain	NN
randomwalker-info-585	492	28	(	(	-LRB-
randomwalker-info-585	492	29	and	and	CC
randomwalker-info-585	492	30	he	-PRON-	PRP
randomwalker-info-585	492	31	mines	mine	VBZ
randomwalker-info-585	492	32	at	at	IN
randomwalker-info-585	492	33	1/10	1/10	CD
randomwalker-info-585	492	34	the	the	DT
randomwalker-info-585	492	35	speed	speed	NN
randomwalker-info-585	492	36	of	of	IN
randomwalker-info-585	492	37	the	the	DT
randomwalker-info-585	492	38	full	full	JJ
randomwalker-info-585	492	39	network	network	NN
randomwalker-info-585	492	40	)	)	-RRB-
randomwalker-info-585	492	41	it	-PRON-	PRP
randomwalker-info-585	492	42	will	will	MD
randomwalker-info-585	492	43	take	take	VB
randomwalker-info-585	492	44	ten	ten	CD
randomwalker-info-585	492	45	times	time	NNS
randomwalker-info-585	492	46	as	as	RB
randomwalker-info-585	492	47	long	long	RB
randomwalker-info-585	492	48	.	.	.
randomwalker-info-585	493	1	What	what	WP
randomwalker-info-585	493	2	this	this	DT
randomwalker-info-585	493	3	means	mean	VBZ
randomwalker-info-585	493	4	is	be	VBZ
randomwalker-info-585	493	5	that	that	IN
randomwalker-info-585	493	6	blocks	block	NNS
randomwalker-info-585	493	7	found	find	VBN
randomwalker-info-585	493	8	by	by	IN
randomwalker-info-585	493	9	the	the	DT
randomwalker-info-585	493	10	selfish	selfish	JJ
randomwalker-info-585	493	11	miner	miner	NN
randomwalker-info-585	493	12	while	while	IN
randomwalker-info-585	493	13	the	the	DT
randomwalker-info-585	493	14	selfish	selfish	JJ
randomwalker-info-585	493	15	miner	miner	NN
randomwalker-info-585	493	16	has	have	VBZ
randomwalker-info-585	493	17	a	a	DT
randomwalker-info-585	493	18	huge	huge	JJ
randomwalker-info-585	493	19	lead	lead	NN
randomwalker-info-585	493	20	are	be	VBP
randomwalker-info-585	493	21	disproportionately	disproportionately	RB
randomwalker-info-585	493	22	large	large	JJ
randomwalker-info-585	493	23	compared	compare	VBN
randomwalker-info-585	493	24	to	to	IN
randomwalker-info-585	493	25	blocks	block	NNS
randomwalker-info-585	493	26	found	find	VBN
randomwalker-info-585	493	27	when	when	WRB
randomwalker-info-585	493	28	the	the	DT
randomwalker-info-585	493	29	selfish	selfish	JJ
randomwalker-info-585	493	30	miner	miner	NN
randomwalker-info-585	493	31	has	have	VBZ
randomwalker-info-585	493	32	no	no	DT
randomwalker-info-585	493	33	lead	lead	NN
randomwalker-info-585	493	34	(	(	-LRB-
randomwalker-info-585	493	35	or	or	CC
randomwalker-info-585	493	36	a	a	DT
randomwalker-info-585	493	37	tiny	tiny	JJ
randomwalker-info-585	493	38	lead	lead	NN
randomwalker-info-585	493	39	)	)	-RRB-
randomwalker-info-585	493	40	.	.	.
randomwalker-info-585	494	1	So	so	RB
randomwalker-info-585	494	2	even	even	RB
randomwalker-info-585	494	3	though	though	IN
randomwalker-info-585	494	4	the	the	DT
randomwalker-info-585	494	5	selfish	selfish	JJ
randomwalker-info-585	494	6	miner	miner	NN
randomwalker-info-585	494	7	wins	win	VBZ
randomwalker-info-585	494	8	the	the	DT
randomwalker-info-585	494	9	same	same	JJ
randomwalker-info-585	494	10	fraction	fraction	NN
randomwalker-info-585	494	11	of	of	IN
randomwalker-info-585	494	12	blocks	block	NNS
randomwalker-info-585	494	13	,	,	,
randomwalker-info-585	494	14	some	some	DT
randomwalker-info-585	494	15	of	of	IN
randomwalker-info-585	494	16	these	these	DT
randomwalker-info-585	494	17	blocks	block	NNS
randomwalker-info-585	494	18	are	be	VBP
randomwalker-info-585	494	19	much	much	RB
randomwalker-info-585	494	20	larger	large	JJR
randomwalker-info-585	494	21	than	than	IN
randomwalker-info-585	494	22	those	those	DT
randomwalker-info-585	494	23	won	win	VBN
randomwalker-info-585	494	24	by	by	IN
randomwalker-info-585	494	25	the	the	DT
randomwalker-info-585	494	26	default	default	NN
randomwalker-info-585	494	27	miners	miner	NNS
randomwalker-info-585	494	28	.	.	.
randomwalker-info-585	495	1	A	a	DT
randomwalker-info-585	495	2	brief	brief	JJ
randomwalker-info-585	495	3	discussion	discussion	NN
randomwalker-info-585	495	4	.	.	.
randomwalker-info-585	496	1	The	the	DT
randomwalker-info-585	496	2	main	main	JJ
randomwalker-info-585	496	3	point	point	NN
randomwalker-info-585	496	4	of	of	IN
randomwalker-info-585	496	5	this	this	DT
randomwalker-info-585	496	6	section	section	NN
randomwalker-info-585	496	7	is	be	VBZ
randomwalker-info-585	496	8	to	to	TO
randomwalker-info-585	496	9	highlight	highlight	VB
randomwalker-info-585	496	10	one	one	CD
randomwalker-info-585	496	11	example	example	NN
randomwalker-info-585	496	12	of	of	IN
randomwalker-info-585	496	13	surprising	surprising	JJ
randomwalker-info-585	496	14	incentive	incentive	NN
randomwalker-info-585	496	15	issues	issue	NNS
randomwalker-info-585	496	16	that	that	WDT
randomwalker-info-585	496	17	dif-	dif-	VBP
randomwalker-info-585	496	18	fer	fer	VBP
randomwalker-info-585	496	19	between	between	IN
randomwalker-info-585	496	20	the	the	DT
randomwalker-info-585	496	21	transaction	transaction	NN
randomwalker-info-585	496	22	fees	fee	NNS
randomwalker-info-585	496	23	model	model	NN
randomwalker-info-585	496	24	and	and	CC
randomwalker-info-585	496	25	the	the	DT
randomwalker-info-585	496	26	block	block	NN
randomwalker-info-585	496	27	-	-	HYPH
randomwalker-info-585	496	28	reward	reward	NN
randomwalker-info-585	496	29	model	model	NN
randomwalker-info-585	496	30	,	,	,
randomwalker-info-585	496	31	not	not	RB
randomwalker-info-585	496	32	to	to	TO
randomwalker-info-585	496	33	argue	argue	VB
randomwalker-info-585	496	34	that	that	IN
randomwalker-info-585	496	35	selfish	selfish	JJ
randomwalker-info-585	496	36	mining	mining	NN
randomwalker-info-585	496	37	becomes	become	VBZ
randomwalker-info-585	496	38	significantly	significantly	RB
randomwalker-info-585	496	39	better	well	JJR
randomwalker-info-585	496	40	(	(	-LRB-
randomwalker-info-585	496	41	the	the	DT
randomwalker-info-585	496	42	improvement	improvement	NN
randomwalker-info-585	496	43	is	be	VBZ
randomwalker-info-585	496	44	minor	minor	JJ
randomwalker-info-585	496	45	)	)	-RRB-
randomwalker-info-585	496	46	.	.	.
randomwalker-info-585	497	1	Still	still	RB
randomwalker-info-585	497	2	,	,	,
randomwalker-info-585	497	3	we	-PRON-	PRP
randomwalker-info-585	497	4	wish	wish	VBP
randomwalker-info-585	497	5	to	to	TO
randomwalker-info-585	497	6	point	point	VB
randomwalker-info-585	497	7	out	out	RP
randomwalker-info-585	497	8	two	two	CD
randomwalker-info-585	497	9	possibly	possibly	RB
randomwalker-info-585	497	10	salient	salient	NN
randomwalker-info-585	497	11	differences	difference	NNS
randomwalker-info-585	497	12	between	between	IN
randomwalker-info-585	497	13	selfish	selfish	JJ
randomwalker-info-585	497	14	mining	mining	NN
randomwalker-info-585	497	15	in	in	IN
randomwalker-info-585	497	16	the	the	DT
randomwalker-info-585	497	17	two	two	CD
randomwalker-info-585	497	18	models	model	NNS
randomwalker-info-585	497	19	.	.	.
randomwalker-info-585	498	1	First	first	RB
randomwalker-info-585	498	2	,	,	,
randomwalker-info-585	498	3	in	in	IN
randomwalker-info-585	498	4	the	the	DT
randomwalker-info-585	498	5	block	block	NN
randomwalker-info-585	498	6	-	-	HYPH
randomwalker-info-585	498	7	reward	reward	NN
randomwalker-info-585	498	8	model	model	NN
randomwalker-info-585	498	9	,	,	,
randomwalker-info-585	498	10	self-	self-	NNP
randomwalker-info-585	498	11	ish	ish	NNP
randomwalker-info-585	498	12	mining	mining	NN
randomwalker-info-585	498	13	is	be	VBZ
randomwalker-info-585	498	14	actually	actually	RB
randomwalker-info-585	498	15	not	not	RB
randomwalker-info-585	498	16	ever	ever	RB
randomwalker-info-585	498	17	immediately	immediately	RB
randomwalker-info-585	498	18	profitable	profitable	JJ
randomwalker-info-585	498	19	—	—	:
randomwalker-info-585	498	20	it	-PRON-	PRP
randomwalker-info-585	498	21	only	only	RB
randomwalker-info-585	498	22	becomes	become	VBZ
randomwalker-info-585	498	23	profitable	profitable	JJ
randomwalker-info-585	498	24	once	once	IN
randomwalker-info-585	498	25	the	the	DT
randomwalker-info-585	498	26	difficulty	difficulty	NN
randomwalker-info-585	498	27	readjusts	readjust	VBZ
randomwalker-info-585	498	28	to	to	TO
randomwalker-info-585	498	29	ac-	ac-	RB
randomwalker-info-585	498	30	count	count	VB
randomwalker-info-585	498	31	for	for	IN
randomwalker-info-585	498	32	the	the	DT
randomwalker-info-585	498	33	fact	fact	NN
randomwalker-info-585	498	34	that	that	IN
randomwalker-info-585	498	35	the	the	DT
randomwalker-info-585	498	36	effective	effective	JJ
randomwalker-info-585	498	37	mining	mining	NN
randomwalker-info-585	498	38	power	power	NN
randomwalker-info-585	498	39	in	in	IN
randomwalker-info-585	498	40	the	the	DT
randomwalker-info-585	498	41	network	network	NN
randomwalker-info-585	498	42	is	be	VBZ
randomwalker-info-585	498	43	lower	low	JJR
randomwalker-info-585	498	44	.	.	.
randomwalker-info-585	499	1	This	this	DT
randomwalker-info-585	499	2	is	be	VBZ
randomwalker-info-585	499	3	because	because	IN
randomwalker-info-585	499	4	before	before	IN
randomwalker-info-585	499	5	the	the	DT
randomwalker-info-585	499	6	difficulty	difficulty	NN
randomwalker-info-585	499	7	ad-	ad-	CC
randomwalker-info-585	499	8	justs	just	NNS
randomwalker-info-585	499	9	,	,	,
randomwalker-info-585	499	10	the	the	DT
randomwalker-info-585	499	11	selfish	selfish	JJ
randomwalker-info-585	499	12	miner	miner	NN
randomwalker-info-585	499	13	is	be	VBZ
randomwalker-info-585	499	14	literally	literally	RB
randomwalker-info-585	499	15	just	just	RB
randomwalker-info-585	499	16	throwing	throw	VBG
randomwalker-info-585	499	17	blocks	block	NNS
randomwalker-info-585	499	18	away	away	RB
randomwalker-info-585	499	19	,	,	,
randomwalker-info-585	499	20	but	but	CC
randomwalker-info-585	499	21	tricking	trick	VBG
randomwalker-info-585	499	22	the	the	DT
randomwalker-info-585	499	23	rest	rest	NN
randomwalker-info-585	499	24	of	of	IN
randomwalker-info-585	499	25	the	the	DT
randomwalker-info-585	499	26	network	network	NN
randomwalker-info-585	499	27	into	into	IN
randomwalker-info-585	499	28	throwing	throw	VBG
randomwalker-info-585	499	29	blocks	block	NNS
randomwalker-info-585	499	30	away	away	RB
randomwalker-info-585	499	31	at	at	IN
randomwalker-info-585	499	32	a	a	DT
randomwalker-info-585	499	33	higher	high	JJR
randomwalker-info-585	499	34	rate	rate	NN
randomwalker-info-585	499	35	.	.	.
randomwalker-info-585	500	1	In	in	IN
randomwalker-info-585	500	2	the	the	DT
randomwalker-info-585	500	3	transaction	transaction	NN
randomwalker-info-585	500	4	fees	fee	NNS
randomwalker-info-585	500	5	model	model	NN
randomwalker-info-585	500	6	,	,	,
randomwalker-info-585	500	7	selfish	selfish	JJ
randomwalker-info-585	500	8	mining	mining	NN
randomwalker-info-585	500	9	is	be	VBZ
randomwalker-info-585	500	10	immediately	immediately	RB
randomwalker-info-585	500	11	profitable	profitable	JJ
randomwalker-info-585	500	12	—	—	:
randomwalker-info-585	500	13	every	every	DT
randomwalker-info-585	500	14	transaction	transaction	NN
randomwalker-info-585	500	15	that	that	WDT
randomwalker-info-585	500	16	arrives	arrive	VBZ
randomwalker-info-585	500	17	goes	go	VBZ
randomwalker-info-585	500	18	somewhere	somewhere	RB
randomwalker-info-585	500	19	,	,	,
randomwalker-info-585	500	20	so	so	RB
randomwalker-info-585	500	21	neither	neither	CC
randomwalker-info-585	500	22	the	the	DT
randomwalker-info-585	500	23	selfish	selfish	JJ
randomwalker-info-585	500	24	miner	miner	NN
randomwalker-info-585	500	25	nor	nor	CC
randomwalker-info-585	500	26	the	the	DT
randomwalker-info-585	500	27	default	default	NN
randomwalker-info-585	500	28	miners	miner	NNS
randomwalker-info-585	500	29	are	be	VBP
randomwalker-info-585	500	30	throwing	throw	VBG
randomwalker-info-585	500	31	rewards	reward	NNS
randomwalker-info-585	500	32	away	away	RB
randomwalker-info-585	500	33	.	.	.
randomwalker-info-585	501	1	Note	note	VB
randomwalker-info-585	501	2	also	also	RB
randomwalker-info-585	501	3	that	that	IN
randomwalker-info-585	501	4	our	-PRON-	PRP$
randomwalker-info-585	501	5	analysis	analysis	NN
randomwalker-info-585	501	6	in	in	IN
randomwalker-info-585	501	7	no	no	DT
randomwalker-info-585	501	8	way	way	NN
randomwalker-info-585	501	9	requires	require	VBZ
randomwalker-info-585	501	10	the	the	DT
randomwalker-info-585	501	11	difficulty	difficulty	NN
randomwalker-info-585	501	12	to	to	TO
randomwalker-info-585	501	13	adjust	adjust	VB
randomwalker-info-585	501	14	before	before	IN
randomwalker-info-585	501	15	it	-PRON-	PRP
randomwalker-info-585	501	16	becomes	become	VBZ
randomwalker-info-585	501	17	accurate	accurate	JJ
randomwalker-info-585	501	18	—	—	:
randomwalker-info-585	501	19	our	-PRON-	PRP$
randomwalker-info-585	501	20	analysis	analysis	NN
randomwalker-info-585	501	21	would	would	MD
randomwalker-info-585	501	22	hold	hold	VB
randomwalker-info-585	501	23	no	no	RB
randomwalker-info-585	501	24	matter	matter	RB
randomwalker-info-585	501	25	how	how	WRB
randomwalker-info-585	501	26	the	the	DT
randomwalker-info-585	501	27	difficulty	difficulty	NN
randomwalker-info-585	501	28	of	of	IN
randomwalker-info-585	501	29	hash	hash	NN
randomwalker-info-585	501	30	puzzles	puzzle	NNS
randomwalker-info-585	501	31	adjusted	adjust	VBD
randomwalker-info-585	501	32	or	or	CC
randomwalker-info-585	501	33	did	do	VBD
randomwalker-info-585	501	34	n’t	not	RB
randomwalker-info-585	501	35	adjust	adjust	VB
randomwalker-info-585	501	36	over	over	IN
randomwalker-info-585	501	37	time	time	NN
randomwalker-info-585	501	38	.	.	.
randomwalker-info-585	502	1	Moreover	moreover	RB
randomwalker-info-585	502	2	,	,	,
randomwalker-info-585	502	3	if	if	IN
randomwalker-info-585	502	4	some	some	DT
randomwalker-info-585	502	5	of	of	IN
randomwalker-info-585	502	6	the	the	DT
randomwalker-info-585	502	7	rest	rest	NN
randomwalker-info-585	502	8	of	of	IN
randomwalker-info-585	502	9	the	the	DT
randomwalker-info-585	502	10	network	network	NN
randomwalker-info-585	502	11	has	have	VBZ
randomwalker-info-585	502	12	switched	switch	VBN
randomwalker-info-585	502	13	to	to	IN
randomwalker-info-585	502	14	the	the	DT
randomwalker-info-585	502	15	PettyCompliant	PettyCompliant	NNP
randomwalker-info-585	502	16	strategy	strategy	NN
randomwalker-info-585	502	17	,	,	,
randomwalker-info-585	502	18	then	then	RB
randomwalker-info-585	502	19	the	the	DT
randomwalker-info-585	502	20	selfish	selfish	JJ
randomwalker-info-585	502	21	miner	miner	NN
randomwalker-info-585	502	22	’s	’s	POS
randomwalker-info-585	502	23	block	block	NN
randomwalker-info-585	502	24	is	be	VBZ
randomwalker-info-585	502	25	actually	actually	RB
randomwalker-info-585	502	26	more	more	RBR
randomwalker-info-585	502	27	likely	likely	JJ
randomwalker-info-585	502	28	to	to	TO
randomwalker-info-585	502	29	win	win	VB
randomwalker-info-585	502	30	when	when	WRB
randomwalker-info-585	502	31	a	a	DT
randomwalker-info-585	502	32	race	race	NN
randomwalker-info-585	502	33	is	be	VBZ
randomwalker-info-585	502	34	triggered	trigger	VBN
randomwalker-info-585	502	35	(	(	-LRB-
randomwalker-info-585	502	36	because	because	IN
randomwalker-info-585	502	37	it	-PRON-	PRP
randomwalker-info-585	502	38	was	be	VBD
randomwalker-info-585	502	39	mined	mine	VBN
randomwalker-info-585	502	40	earlier	early	RBR
randomwalker-info-585	502	41	and	and	CC
randomwalker-info-585	502	42	therefore	therefore	RB
randomwalker-info-585	502	43	contains	contain	VBZ
randomwalker-info-585	502	44	fewer	few	JJR
randomwalker-info-585	502	45	transactions	transaction	NNS
randomwalker-info-585	502	46	)	)	-RRB-
randomwalker-info-585	502	47	.	.	.
randomwalker-info-585	503	1	So	so	RB
randomwalker-info-585	503	2	the	the	DT
randomwalker-info-585	503	3	existence	existence	NN
randomwalker-info-585	503	4	of	of	IN
randomwalker-info-585	503	5	Petty-	Petty-	NNP
randomwalker-info-585	503	6	Compliant	compliant	JJ
randomwalker-info-585	503	7	miners	miner	NNS
randomwalker-info-585	503	8	in	in	IN
randomwalker-info-585	503	9	the	the	DT
randomwalker-info-585	503	10	transaction	transaction	NN
randomwalker-info-585	503	11	fees	fee	NNS
randomwalker-info-585	503	12	regime	regime	NN
randomwalker-info-585	503	13	indirectly	indirectly	RB
randomwalker-info-585	503	14	improves	improve	VBZ
randomwalker-info-585	503	15	Selfish	Selfish	NNP
randomwalker-info-585	503	16	-	-	HYPH
randomwalker-info-585	503	17	Mine	Mine	NNP
randomwalker-info-585	503	18	’s	’s	POS
randomwalker-info-585	503	19	performance	performance	NN
randomwalker-info-585	503	20	by	by	IN
randomwalker-info-585	503	21	increasing	increase	VBG
randomwalker-info-585	503	22	γ	γ	NNP
randomwalker-info-585	503	23	.	.	.
randomwalker-info-585	504	1	6.2	6.2	CD
randomwalker-info-585	504	2	An	an	DT
randomwalker-info-585	504	3	Improved	Improved	NNP
randomwalker-info-585	504	4	Selfish	Selfish	NNP
randomwalker-info-585	504	5	-	-	HYPH
randomwalker-info-585	504	6	Mine	Mine	NNP
randomwalker-info-585	504	7	Analytical	Analytical	NNP
randomwalker-info-585	504	8	and	and	CC
randomwalker-info-585	504	9	simulation	simulation	NN
randomwalker-info-585	504	10	result	result	NN
randomwalker-info-585	504	11	:	:	:
randomwalker-info-585	504	12	in	in	IN
randomwalker-info-585	504	13	the	the	DT
randomwalker-info-585	504	14	transac-	transac-	NNP
randomwalker-info-585	504	15	tion	tion	NN
randomwalker-info-585	504	16	fee	fee	NN
randomwalker-info-585	504	17	model	model	NN
randomwalker-info-585	504	18	,	,	,
randomwalker-info-585	504	19	selfish	selfish	JJ
randomwalker-info-585	504	20	miners	miner	NNS
randomwalker-info-585	504	21	can	can	MD
randomwalker-info-585	504	22	make	make	VB
randomwalker-info-585	504	23	the	the	DT
randomwalker-info-585	504	24	de-	de-	NN
randomwalker-info-585	504	25	cision	cision	NN
randomwalker-info-585	504	26	whether	whether	IN
randomwalker-info-585	504	27	to	to	TO
randomwalker-info-585	504	28	hide	hide	VB
randomwalker-info-585	504	29	their	-PRON-	PRP$
randomwalker-info-585	504	30	first	first	JJ
randomwalker-info-585	504	31	block	block	NN
randomwalker-info-585	504	32	based	base	VBN
randomwalker-info-585	504	33	on	on	IN
randomwalker-info-585	504	34	the	the	DT
randomwalker-info-585	504	35	value	value	NN
randomwalker-info-585	504	36	of	of	IN
randomwalker-info-585	504	37	the	the	DT
randomwalker-info-585	504	38	block	block	NN
randomwalker-info-585	504	39	.	.	.
randomwalker-info-585	505	1	This	this	DT
randomwalker-info-585	505	2	improved	improve	VBD
randomwalker-info-585	505	3	selfish	selfish	JJ
randomwalker-info-585	505	4	min-	min-	NN
randomwalker-info-585	505	5	ing	ing	NN
randomwalker-info-585	505	6	strictly	strictly	RB
randomwalker-info-585	505	7	and	and	CC
randomwalker-info-585	505	8	always	always	RB
randomwalker-info-585	505	9	outperforms	outperform	VBZ
randomwalker-info-585	505	10	both	both	CC
randomwalker-info-585	505	11	default	default	NN
randomwalker-info-585	505	12	mining	mining	NN
randomwalker-info-585	505	13	and	and	CC
randomwalker-info-585	505	14	traditional	traditional	JJ
randomwalker-info-585	505	15	selfish	selfish	JJ
randomwalker-info-585	505	16	mining	mining	NN
randomwalker-info-585	505	17	.	.	.
randomwalker-info-585	506	1	In	in	IN
randomwalker-info-585	506	2	this	this	DT
randomwalker-info-585	506	3	section	section	NN
randomwalker-info-585	506	4	we	-PRON-	PRP
randomwalker-info-585	506	5	develop	develop	VBP
randomwalker-info-585	506	6	an	an	DT
randomwalker-info-585	506	7	improved	improved	JJ
randomwalker-info-585	506	8	selfish	selfish	JJ
randomwalker-info-585	506	9	mining	mining	NN
randomwalker-info-585	506	10	strategy	strategy	NN
randomwalker-info-585	506	11	.	.	.
randomwalker-info-585	507	1	Essentially	essentially	RB
randomwalker-info-585	507	2	,	,	,
randomwalker-info-585	507	3	we	-PRON-	PRP
randomwalker-info-585	507	4	observe	observe	VBP
randomwalker-info-585	507	5	that	that	IN
randomwalker-info-585	507	6	in	in	IN
randomwalker-info-585	507	7	the	the	DT
randomwalker-info-585	507	8	transaction	transaction	NN
randomwalker-info-585	507	9	fees	fee	NNS
randomwalker-info-585	507	10	model	model	NN
randomwalker-info-585	507	11	,	,	,
randomwalker-info-585	507	12	a	a	DT
randomwalker-info-585	507	13	selfish	selfish	JJ
randomwalker-info-585	507	14	miner	miner	NN
randomwalker-info-585	507	15	has	have	VBZ
randomwalker-info-585	507	16	additional	additional	JJ
randomwalker-info-585	507	17	information	information	NN
randomwalker-info-585	507	18	when	when	WRB
randomwalker-info-585	507	19	de-	de-	RB
randomwalker-info-585	507	20	ciding	cide	VBG
randomwalker-info-585	507	21	whether	whether	IN
randomwalker-info-585	507	22	to	to	TO
randomwalker-info-585	507	23	hide	hide	VB
randomwalker-info-585	507	24	or	or	CC
randomwalker-info-585	507	25	publish	publish	VB
randomwalker-info-585	507	26	their	-PRON-	PRP$
randomwalker-info-585	507	27	private	private	JJ
randomwalker-info-585	507	28	chain	chain	NN
randomwalker-info-585	507	29	(	(	-LRB-
randomwalker-info-585	507	30	namely	namely	RB
randomwalker-info-585	507	31	,	,	,
randomwalker-info-585	507	32	how	how	WRB
randomwalker-info-585	507	33	many	many	JJ
randomwalker-info-585	507	34	transactions	transaction	NNS
randomwalker-info-585	507	35	are	be	VBP
randomwalker-info-585	507	36	included	include	VBN
randomwalker-info-585	507	37	)	)	-RRB-
randomwalker-info-585	507	38	.	.	.
randomwalker-info-585	508	1	We	-PRON-	PRP
randomwalker-info-585	508	2	show	show	VBP
randomwalker-info-585	508	3	that	that	IN
randomwalker-info-585	508	4	,	,	,
randomwalker-info-585	508	5	for	for	IN
randomwalker-info-585	508	6	all	all	DT
randomwalker-info-585	508	7	α	α	XX
randomwalker-info-585	508	8	,	,	,
randomwalker-info-585	508	9	γ	γ	NNP
randomwalker-info-585	508	10	<	<	XX
randomwalker-info-585	508	11	1	1	CD
randomwalker-info-585	508	12	,	,	,
randomwalker-info-585	508	13	our	-PRON-	PRP$
randomwalker-info-585	508	14	strategy	strategy	NN
randomwalker-info-585	508	15	strictly	strictly	RB
randomwalker-info-585	508	16	outperforms	outperform	VBZ
randomwalker-info-585	508	17	both	both	CC
randomwalker-info-585	508	18	default	default	NN
randomwalker-info-585	508	19	mining	mining	NN
randomwalker-info-585	508	20	and	and	CC
randomwalker-info-585	508	21	“	"	``
randomwalker-info-585	508	22	vanilla	vanilla	NN
randomwalker-info-585	508	23	”	"	''
randomwalker-info-585	508	24	selfish	selfish	JJ
randomwalker-info-585	508	25	mining	mining	NN
randomwalker-info-585	508	26	in	in	IN
randomwalker-info-585	508	27	the	the	DT
randomwalker-info-585	508	28	transaction	transaction	NN
randomwalker-info-585	508	29	fees	fee	NNS
randomwalker-info-585	508	30	model	model	NN
randomwalker-info-585	508	31	.	.	.
randomwalker-info-585	509	1	Our	-PRON-	PRP$
randomwalker-info-585	509	2	strategy	strategy	NN
randomwalker-info-585	509	3	will	will	MD
randomwalker-info-585	509	4	decide	decide	VB
randomwalker-info-585	509	5	to	to	TO
randomwalker-info-585	509	6	hide	hide	VB
randomwalker-info-585	509	7	only	only	RB
randomwalker-info-585	509	8	“	"	``
randomwalker-info-585	509	9	small	small	JJ
randomwalker-info-585	509	10	”	"	''
randomwalker-info-585	509	11	blocks	block	NNS
randomwalker-info-585	509	12	,	,	,
randomwalker-info-585	509	13	with	with	IN
randomwalker-info-585	509	14	at	at	IN
randomwalker-info-585	509	15	most	most	JJS
randomwalker-info-585	509	16	β	β	NN
randomwalker-info-585	509	17	(	(	-LRB-
randomwalker-info-585	509	18	some	some	DT
randomwalker-info-585	509	19	cutoff	cutoff	NN
randomwalker-info-585	509	20	parameter	parameter	NN
randomwalker-info-585	509	21	chosen	choose	VBN
randomwalker-info-585	509	22	by	by	IN
randomwalker-info-585	509	23	the	the	DT
randomwalker-info-585	509	24	strat-	strat-	JJ
randomwalker-info-585	509	25	egy	egy	NN
randomwalker-info-585	509	26	as	as	IN
randomwalker-info-585	509	27	a	a	DT
randomwalker-info-585	509	28	function	function	NN
randomwalker-info-585	509	29	of	of	IN
randomwalker-info-585	509	30	α	α	NN
randomwalker-info-585	509	31	,	,	,
randomwalker-info-585	509	32	γ	γ	NNP
randomwalker-info-585	509	33	)	)	-RRB-
randomwalker-info-585	509	34	transaction	transaction	NN
randomwalker-info-585	509	35	fees	fee	NNS
randomwalker-info-585	509	36	included	include	VBD
randomwalker-info-585	509	37	,	,	,
randomwalker-info-585	509	38	but	but	CC
randomwalker-info-585	509	39	will	will	MD
randomwalker-info-585	509	40	immediately	immediately	RB
randomwalker-info-585	509	41	publish	publish	VB
randomwalker-info-585	509	42	any	any	DT
randomwalker-info-585	509	43	“	"	``
randomwalker-info-585	509	44	large	large	JJ
randomwalker-info-585	509	45	”	"	''
randomwalker-info-585	509	46	blocks	block	NNS
randomwalker-info-585	509	47	,	,	,
randomwalker-info-585	509	48	with	with	IN
randomwalker-info-585	509	49	more	more	JJR
randomwalker-info-585	509	50	than	than	IN
randomwalker-info-585	509	51	β	β	NNP
randomwalker-info-585	509	52	transaction	transaction	NN
randomwalker-info-585	509	53	fees	fee	NNS
randomwalker-info-585	509	54	in	in	IN
randomwalker-info-585	509	55	order	order	NN
randomwalker-info-585	509	56	to	to	TO
randomwalker-info-585	509	57	avoid	avoid	VB
randomwalker-info-585	509	58	the	the	DT
randomwalker-info-585	509	59	risk	risk	NN
randomwalker-info-585	509	60	of	of	IN
randomwalker-info-585	509	61	losing	lose	VBG
randomwalker-info-585	509	62	them	-PRON-	PRP
randomwalker-info-585	509	63	.	.	.
randomwalker-info-585	510	1	Selfish	Selfish	NNP
randomwalker-info-585	510	2	-	-	HYPH
randomwalker-info-585	510	3	Mine(β	mine(β	NN
randomwalker-info-585	510	4	)	)	-RRB-
randomwalker-info-585	510	5	:	:	:
randomwalker-info-585	510	6	An	an	DT
randomwalker-info-585	510	7	improvement	improvement	NN
randomwalker-info-585	510	8	to	to	IN
randomwalker-info-585	510	9	the	the	DT
randomwalker-info-585	510	10	selfish	selfish	JJ
randomwalker-info-585	510	11	mining	mining	NN
randomwalker-info-585	510	12	strategy	strategy	NN
randomwalker-info-585	510	13	,	,	,
randomwalker-info-585	510	14	where	where	WRB
randomwalker-info-585	510	15	the	the	DT
randomwalker-info-585	510	16	miner	miner	NN
randomwalker-info-585	510	17	will	will	MD
randomwalker-info-585	510	18	chose	choose	VBD
randomwalker-info-585	510	19	to	to	IN
randomwalker-info-585	510	20	mine	-PRON-	PRP
randomwalker-info-585	510	21	as	as	IN
randomwalker-info-585	510	22	a	a	DT
randomwalker-info-585	510	23	selfish	selfish	JJ
randomwalker-info-585	510	24	miner	miner	NN
randomwalker-info-585	510	25	or	or	CC
randomwalker-info-585	510	26	a	a	DT
randomwalker-info-585	510	27	default	default	NN
randomwalker-info-585	510	28	compliant	compliant	JJ
randomwalker-info-585	510	29	miner	miner	NN
randomwalker-info-585	510	30	based	base	VBN
randomwalker-info-585	510	31	on	on	IN
randomwalker-info-585	510	32	the	the	DT
randomwalker-info-585	510	33	value	value	NN
randomwalker-info-585	510	34	of	of	IN
randomwalker-info-585	510	35	the	the	DT
randomwalker-info-585	510	36	block	block	NN
randomwalker-info-585	510	37	they	-PRON-	PRP
randomwalker-info-585	510	38	risk	risk	VBP
randomwalker-info-585	510	39	losing	lose	VBG
randomwalker-info-585	510	40	.	.	.
randomwalker-info-585	511	1	Which	which	WDT
randomwalker-info-585	511	2	Block	Block	NNP
randomwalker-info-585	511	3	:	:	:
randomwalker-info-585	511	4	OldestmPrivatem	OldestmPrivatem	NNP
randomwalker-info-585	511	5	.	.	.
randomwalker-info-585	512	1	How	how	WRB
randomwalker-info-585	512	2	much	much	JJ
randomwalker-info-585	512	3	:	:	:
randomwalker-info-585	512	4	include	include	VBP
randomwalker-info-585	512	5	Rem(Mining(m	Rem(Mining(m	NNP
randomwalker-info-585	512	6	)	)	-RRB-
randomwalker-info-585	512	7	)	)	-RRB-
randomwalker-info-585	512	8	.	.	.
randomwalker-info-585	513	1	Publish(B	Publish(B	VBN
randomwalker-info-585	513	2	)	)	-RRB-
randomwalker-info-585	513	3	?	?	.
randomwalker-info-585	514	1	if	if	IN
randomwalker-info-585	514	2	Height(B	Height(B	NNP
randomwalker-info-585	514	3	)	)	-RRB-
randomwalker-info-585	514	4	=	=	NFP
randomwalker-info-585	514	5	H	h	NN
randomwalker-info-585	514	6	or	or	CC
randomwalker-info-585	514	7	Tx(B	tx(b	NN
randomwalker-info-585	514	8	)	)	-RRB-
randomwalker-info-585	514	9	≥	≥	UH
randomwalker-info-585	514	10	β	β	NN
randomwalker-info-585	514	11	yes	yes	UH
randomwalker-info-585	514	12	.	.	.
randomwalker-info-585	515	1	elseif	elseif	NNP
randomwalker-info-585	515	2	RacingmH	RacingmH	NNP
randomwalker-info-585	515	3	,	,	,
randomwalker-info-585	515	4	and	and	CC
randomwalker-info-585	515	5	Private	private	JJ
randomwalker-info-585	515	6	m	m	NN
randomwalker-info-585	515	7	=	=	SYM
randomwalker-info-585	515	8	H	h	NN
randomwalker-info-585	515	9	+	+	CC
randomwalker-info-585	515	10	1	1	CD
randomwalker-info-585	515	11	yes	yes	UH
randomwalker-info-585	515	12	.	.	.
randomwalker-info-585	516	1	else	else	RB
randomwalker-info-585	516	2	no	no	UH
randomwalker-info-585	516	3	.	.	.
randomwalker-info-585	517	1	Intuitively	intuitively	RB
randomwalker-info-585	517	2	,	,	,
randomwalker-info-585	517	3	imagine	imagine	VBP
randomwalker-info-585	517	4	you	-PRON-	PRP
randomwalker-info-585	517	5	are	be	VBP
randomwalker-info-585	517	6	mining	mine	VBG
randomwalker-info-585	517	7	and	and	CC
randomwalker-info-585	517	8	find	find	VB
randomwalker-info-585	517	9	yourself	-PRON-	PRP
randomwalker-info-585	517	10	solv-	solv-	JJ
randomwalker-info-585	517	11	ing	e	VBG
randomwalker-info-585	517	12	a	a	DT
randomwalker-info-585	517	13	new	new	JJ
randomwalker-info-585	517	14	block	block	NN
randomwalker-info-585	517	15	immediately	immediately	RB
randomwalker-info-585	517	16	after	after	IN
randomwalker-info-585	517	17	a	a	DT
randomwalker-info-585	517	18	previous	previous	JJ
randomwalker-info-585	517	19	block	block	NN
randomwalker-info-585	517	20	was	be	VBD
randomwalker-info-585	517	21	announced	announce	VBN
randomwalker-info-585	517	22	and	and	CC
randomwalker-info-585	517	23	before	before	IN
randomwalker-info-585	517	24	any	any	DT
randomwalker-info-585	517	25	new	new	JJ
randomwalker-info-585	517	26	transactions	transaction	NNS
randomwalker-info-585	517	27	have	have	VBP
randomwalker-info-585	517	28	been	be	VBN
randomwalker-info-585	517	29	an-	an-	RB
randomwalker-info-585	517	30	nounced	nounce	VBN
randomwalker-info-585	517	31	.	.	.
randomwalker-info-585	518	1	This	this	DT
randomwalker-info-585	518	2	block	block	NN
randomwalker-info-585	518	3	is	be	VBZ
randomwalker-info-585	518	4	literally	literally	RB
randomwalker-info-585	518	5	worthless	worthless	JJ
randomwalker-info-585	518	6	,	,	,
randomwalker-info-585	518	7	so	so	RB
randomwalker-info-585	518	8	instead	instead	RB
randomwalker-info-585	518	9	of	of	IN
randomwalker-info-585	518	10	pub-	pub-	JJ
randomwalker-info-585	518	11	lishing	lishing	NN
randomwalker-info-585	518	12	,	,	,
randomwalker-info-585	518	13	why	why	WRB
randomwalker-info-585	518	14	not	not	RB
randomwalker-info-585	518	15	use	use	VB
randomwalker-info-585	518	16	it	-PRON-	PRP
randomwalker-info-585	518	17	to	to	TO
randomwalker-info-585	518	18	try	try	VB
randomwalker-info-585	518	19	and	and	CC
randomwalker-info-585	518	20	selfish	selfish	VB
randomwalker-info-585	518	21	mine	mine	NN
randomwalker-info-585	518	22	?	?	.
randomwalker-info-585	519	1	There	there	EX
randomwalker-info-585	519	2	is	be	VBZ
randomwalker-info-585	519	3	Figure	figure	NN
randomwalker-info-585	519	4	8	8	CD
randomwalker-info-585	519	5	:	:	:
randomwalker-info-585	519	6	We	-PRON-	PRP
randomwalker-info-585	519	7	show	show	VBP
randomwalker-info-585	519	8	the	the	DT
randomwalker-info-585	519	9	ideal	ideal	JJ
randomwalker-info-585	519	10	cutoff	cutoff	NNP
randomwalker-info-585	519	11	factor	factor	NNP
randomwalker-info-585	519	12	,	,	,
randomwalker-info-585	519	13	β	β	NNP
randomwalker-info-585	519	14	,	,	,
randomwalker-info-585	519	15	for	for	IN
randomwalker-info-585	519	16	a	a	DT
randomwalker-info-585	519	17	selfish	selfish	JJ
randomwalker-info-585	519	18	miner	miner	NN
randomwalker-info-585	519	19	with	with	IN
randomwalker-info-585	519	20	mining	mining	NN
randomwalker-info-585	519	21	power	power	NN
randomwalker-info-585	519	22	α	α	NNP
randomwalker-info-585	519	23	,	,	,
randomwalker-info-585	519	24	and	and	CC
randomwalker-info-585	519	25	γ	γ	NNP
randomwalker-info-585	519	26	=	=	SYM
randomwalker-info-585	519	27	0	0	NFP
randomwalker-info-585	519	28	.	.	.
randomwalker-info-585	519	29	no	no	DT
randomwalker-info-585	519	30	cost	cost	NN
randomwalker-info-585	519	31	,	,	,
randomwalker-info-585	519	32	but	but	CC
randomwalker-info-585	519	33	a	a	DT
randomwalker-info-585	519	34	positive	positive	JJ
randomwalker-info-585	519	35	probability	probability	NN
randomwalker-info-585	519	36	that	that	WDT
randomwalker-info-585	519	37	you	-PRON-	PRP
randomwalker-info-585	519	38	build	build	VBP
randomwalker-info-585	519	39	a	a	DT
randomwalker-info-585	519	40	lead	lead	NN
randomwalker-info-585	519	41	of	of	IN
randomwalker-info-585	519	42	two	two	CD
randomwalker-info-585	519	43	,	,	,
randomwalker-info-585	519	44	no	no	RB
randomwalker-info-585	519	45	matter	matter	RB
randomwalker-info-585	519	46	your	-PRON-	PRP$
randomwalker-info-585	519	47	hash	hash	NN
randomwalker-info-585	519	48	power	power	NN
randomwalker-info-585	519	49	.	.	.
randomwalker-info-585	520	1	Similarly	similarly	RB
randomwalker-info-585	520	2	,	,	,
randomwalker-info-585	520	3	imagine	imagine	VB
randomwalker-info-585	520	4	instead	instead	RB
randomwalker-info-585	520	5	that	that	IN
randomwalker-info-585	520	6	just	just	RB
randomwalker-info-585	520	7	by	by	IN
randomwalker-info-585	520	8	chance	chance	NN
randomwalker-info-585	520	9	an	an	DT
randomwalker-info-585	520	10	hour	hour	NN
randomwalker-info-585	520	11	goes	go	VBZ
randomwalker-info-585	520	12	by	by	RB
randomwalker-info-585	520	13	since	since	IN
randomwalker-info-585	520	14	the	the	DT
randomwalker-info-585	520	15	last	last	JJ
randomwalker-info-585	520	16	block	block	NN
randomwalker-info-585	520	17	was	be	VBD
randomwalker-info-585	520	18	found	find	VBN
randomwalker-info-585	520	19	and	and	CC
randomwalker-info-585	520	20	you	-PRON-	PRP
randomwalker-info-585	520	21	just	just	RB
randomwalker-info-585	520	22	solved	solve	VBD
randomwalker-info-585	520	23	a	a	DT
randomwalker-info-585	520	24	new	new	JJ
randomwalker-info-585	520	25	block	block	NN
randomwalker-info-585	520	26	including	include	VBG
randomwalker-info-585	520	27	all	all	DT
randomwalker-info-585	520	28	trans-	trans-	JJ
randomwalker-info-585	520	29	actions	action	NNS
randomwalker-info-585	520	30	that	that	WDT
randomwalker-info-585	520	31	arrived	arrive	VBD
randomwalker-info-585	520	32	during	during	IN
randomwalker-info-585	520	33	that	that	DT
randomwalker-info-585	520	34	period	period	NN
randomwalker-info-585	520	35	.	.	.
randomwalker-info-585	521	1	This	this	DT
randomwalker-info-585	521	2	block	block	NN
randomwalker-info-585	521	3	is	be	VBZ
randomwalker-info-585	521	4	worth	worth	JJ
randomwalker-info-585	521	5	roughly	roughly	RB
randomwalker-info-585	521	6	six	six	CD
randomwalker-info-585	521	7	“	"	``
randomwalker-info-585	521	8	normal	normal	JJ
randomwalker-info-585	521	9	”	"	''
randomwalker-info-585	521	10	blocks	block	NNS
randomwalker-info-585	521	11	,	,	,
randomwalker-info-585	521	12	so	so	RB
randomwalker-info-585	521	13	why	why	WRB
randomwalker-info-585	521	14	risk	risk	NN
randomwalker-info-585	521	15	losing	lose	VBG
randomwalker-info-585	521	16	it	-PRON-	PRP
randomwalker-info-585	521	17	?	?	.
randomwalker-info-585	522	1	Unless	unless	IN
randomwalker-info-585	522	2	your	-PRON-	PRP$
randomwalker-info-585	522	3	hash	hash	NN
randomwalker-info-585	522	4	power	power	NN
randomwalker-info-585	522	5	is	be	VBZ
randomwalker-info-585	522	6	very	very	RB
randomwalker-info-585	522	7	close	close	JJ
randomwalker-info-585	522	8	to	to	IN
randomwalker-info-585	522	9	50	50	CD
randomwalker-info-585	522	10	%	%	NN
randomwalker-info-585	522	11	,	,	,
randomwalker-info-585	522	12	the	the	DT
randomwalker-info-585	522	13	expected	expect	VBN
randomwalker-info-585	522	14	gains	gain	NNS
randomwalker-info-585	522	15	from	from	IN
randomwalker-info-585	522	16	selfish	selfish	JJ
randomwalker-info-585	522	17	mining	mining	NN
randomwalker-info-585	522	18	are	be	VBP
randomwalker-info-585	522	19	dwarfed	dwarf	VBN
randomwalker-info-585	522	20	by	by	IN
randomwalker-info-585	522	21	the	the	DT
randomwalker-info-585	522	22	possibility	possibility	NN
randomwalker-info-585	522	23	of	of	IN
randomwalker-info-585	522	24	losing	lose	VBG
randomwalker-info-585	522	25	this	this	DT
randomwalker-info-585	522	26	unusually	unusually	RB
randomwalker-info-585	522	27	wealthy	wealthy	JJ
randomwalker-info-585	522	28	block	block	NN
randomwalker-info-585	522	29	.	.	.
randomwalker-info-585	523	1	So	so	RB
randomwalker-info-585	523	2	the	the	DT
randomwalker-info-585	523	3	trick	trick	NN
randomwalker-info-585	523	4	is	be	VBZ
randomwalker-info-585	523	5	just	just	RB
randomwalker-info-585	523	6	choosing	choose	VBG
randomwalker-info-585	523	7	the	the	DT
randomwalker-info-585	523	8	proper	proper	JJ
randomwalker-info-585	523	9	cutoff	cutoff	NN
randomwalker-info-585	523	10	β	β	NNP
randomwalker-info-585	523	11	as	as	IN
randomwalker-info-585	523	12	a	a	DT
randomwalker-info-585	523	13	function	function	NN
randomwalker-info-585	523	14	of	of	IN
randomwalker-info-585	523	15	your	-PRON-	PRP$
randomwalker-info-585	523	16	hash	hash	NN
randomwalker-info-585	523	17	power	power	NN
randomwalker-info-585	523	18	α	α	NNP
randomwalker-info-585	523	19	and	and	CC
randomwalker-info-585	523	20	network	network	NNP
randomwalker-info-585	523	21	connectivity	connectivity	NNP
randomwalker-info-585	523	22	γ	γ	NNP
randomwalker-info-585	523	23	.	.	.
randomwalker-info-585	524	1	Note	note	VB
randomwalker-info-585	524	2	that	that	IN
randomwalker-info-585	524	3	Selfish	Selfish	NNP
randomwalker-info-585	524	4	-	-	HYPH
randomwalker-info-585	524	5	Mine(0	mine(0	NN
randomwalker-info-585	524	6	)	)	-RRB-
randomwalker-info-585	524	7	=	=	NFP
randomwalker-info-585	524	8	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	524	9	,	,	,
randomwalker-info-585	524	10	and	and	CC
randomwalker-info-585	524	11	that	that	IN
randomwalker-info-585	524	12	Selfish	Selfish	NNP
randomwalker-info-585	524	13	-	-	HYPH
randomwalker-info-585	524	14	Mine(∞	Mine(∞	NNP
randomwalker-info-585	524	15	)	)	-RRB-
randomwalker-info-585	524	16	=	=	NFP
randomwalker-info-585	524	17	Selfish	Selfish	NNP
randomwalker-info-585	524	18	-	-	HYPH
randomwalker-info-585	524	19	Mine	mine	NN
randomwalker-info-585	524	20	.	.	.
randomwalker-info-585	525	1	So	so	RB
randomwalker-info-585	525	2	clearly	clearly	RB
randomwalker-info-585	525	3	,	,	,
randomwalker-info-585	525	4	tak-	tak-	NNP
randomwalker-info-585	525	5	ing	e	VBG
randomwalker-info-585	525	6	the	the	DT
randomwalker-info-585	525	7	optimal	optimal	JJ
randomwalker-info-585	525	8	choice	choice	NN
randomwalker-info-585	525	9	of	of	IN
randomwalker-info-585	525	10	β	β	NNP
randomwalker-info-585	525	11	will	will	MD
randomwalker-info-585	525	12	result	result	VB
randomwalker-info-585	525	13	in	in	IN
randomwalker-info-585	525	14	a	a	DT
randomwalker-info-585	525	15	strategy	strategy	NN
randomwalker-info-585	525	16	that	that	WDT
randomwalker-info-585	525	17	equals	equal	VBZ
randomwalker-info-585	525	18	or	or	CC
randomwalker-info-585	525	19	outperforms	outperform	VBZ
randomwalker-info-585	525	20	both	both	DT
randomwalker-info-585	525	21	.	.	.
randomwalker-info-585	526	1	Using	use	VBG
randomwalker-info-585	526	2	an	an	DT
randomwalker-info-585	526	3	analysis	analysis	NN
randomwalker-info-585	526	4	similar	similar	JJ
randomwalker-info-585	526	5	to	to	IN
randomwalker-info-585	526	6	that	that	DT
randomwalker-info-585	526	7	of	of	IN
randomwalker-info-585	526	8	Section	section	NN
randomwalker-info-585	526	9	6.1	6.1	CD
randomwalker-info-585	526	10	,	,	,
randomwalker-info-585	526	11	we	-PRON-	PRP
randomwalker-info-585	526	12	are	be	VBP
randomwalker-info-585	526	13	able	able	JJ
randomwalker-info-585	526	14	to	to	TO
randomwalker-info-585	526	15	compute	compute	VB
randomwalker-info-585	526	16	the	the	DT
randomwalker-info-585	526	17	expected	expected	JJ
randomwalker-info-585	526	18	reward	reward	NN
randomwalker-info-585	526	19	achieved	achieve	VBN
randomwalker-info-585	526	20	by	by	IN
randomwalker-info-585	526	21	a	a	DT
randomwalker-info-585	526	22	miner	miner	NN
randomwalker-info-585	526	23	with	with	IN
randomwalker-info-585	526	24	an	an	DT
randomwalker-info-585	526	25	α	α	NNP
randomwalker-info-585	526	26	fraction	fraction	NN
randomwalker-info-585	526	27	of	of	IN
randomwalker-info-585	526	28	the	the	DT
randomwalker-info-585	526	29	min-	min-	JJ
randomwalker-info-585	526	30	ing	ing	NNP
randomwalker-info-585	526	31	power	power	NN
randomwalker-info-585	526	32	,	,	,
randomwalker-info-585	526	33	a	a	DT
randomwalker-info-585	526	34	γ	γ	JJ
randomwalker-info-585	526	35	success	success	JJ
randomwalker-info-585	526	36	probability	probability	NN
randomwalker-info-585	526	37	of	of	IN
randomwalker-info-585	526	38	winning	win	VBG
randomwalker-info-585	526	39	a	a	DT
randomwalker-info-585	526	40	race	race	NN
randomwalker-info-585	526	41	,	,	,
randomwalker-info-585	526	42	and	and	CC
randomwalker-info-585	526	43	using	use	VBG
randomwalker-info-585	526	44	strategy	strategy	NN
randomwalker-info-585	526	45	Selfish	selfish	JJ
randomwalker-info-585	526	46	-	-	HYPH
randomwalker-info-585	526	47	Mine(β	mine(β	NN
randomwalker-info-585	526	48	)	)	-RRB-
randomwalker-info-585	526	49	.	.	.
randomwalker-info-585	527	1	A	a	DT
randomwalker-info-585	527	2	derivation	derivation	NN
randomwalker-info-585	527	3	is	be	VBZ
randomwalker-info-585	527	4	included	include	VBN
randomwalker-info-585	527	5	in	in	IN
randomwalker-info-585	527	6	Appendix	Appendix	NNP
randomwalker-info-585	527	7	E.2	E.2	NNP
randomwalker-info-585	527	8	.	.	.
randomwalker-info-585	528	1	Reward(α	Reward(α	NNP
randomwalker-info-585	528	2	,	,	,
randomwalker-info-585	528	3	γ	γ	NNP
randomwalker-info-585	528	4	,	,	,
randomwalker-info-585	528	5	β	β	NNP
randomwalker-info-585	528	6	)	)	-RRB-
randomwalker-info-585	528	7	=(	=(	NNP
randomwalker-info-585	528	8	1	1	CD
randomwalker-info-585	528	9	+	+	SYM
randomwalker-info-585	528	10	β(1	β(1	NNS
randomwalker-info-585	528	11	−α)2(1	−α)2(1	NNP
randomwalker-info-585	528	12	−γ	−γ	NNP
randomwalker-info-585	528	13	)	)	-RRB-
randomwalker-info-585	528	14	eβ	eβ	NNP
randomwalker-info-585	528	15	−	−	NNP
randomwalker-info-585	528	16	1	1	CD
randomwalker-info-585	528	17	+	+	SYM
randomwalker-info-585	528	18	5α	5α	CD
randomwalker-info-585	528	19	+	+	SYM
randomwalker-info-585	528	20	(	(	-LRB-
randomwalker-info-585	528	21	1	1	CD
randomwalker-info-585	528	22	−α)2γ	−α)2γ	SYM
randomwalker-info-585	528	23	+	+	CD
randomwalker-info-585	528	24	2α2	2α2	CD
randomwalker-info-585	528	25	1	1	CD
randomwalker-info-585	528	26	−	−	NNP
randomwalker-info-585	528	27	2α	2α	CD
randomwalker-info-585	528	28	−	−	NNP
randomwalker-info-585	528	29	2α2	2α2	CD
randomwalker-info-585	528	30	)	)	-RRB-
randomwalker-info-585	528	31	×	×	NFP
randomwalker-info-585	528	32	(	(	-LRB-
randomwalker-info-585	528	33	α(1	α(1	NFP
randomwalker-info-585	528	34	−	−	NNP
randomwalker-info-585	528	35	2α)(1	2α)(1	CD
randomwalker-info-585	528	36	−e−β	−e−β	NN
randomwalker-info-585	528	37	)	)	-RRB-
randomwalker-info-585	528	38	1	1	CD
randomwalker-info-585	528	39	−	−	NNP
randomwalker-info-585	528	40	2e−βα−	2e−βα−	CD
randomwalker-info-585	528	41	3(1	3(1	NN
randomwalker-info-585	528	42	−e−β)α2	−e−β)α2	NN
randomwalker-info-585	528	43	)	)	-RRB-
randomwalker-info-585	528	44	Figure	figure	NN
randomwalker-info-585	528	45	8	8	CD
randomwalker-info-585	528	46	contains	contain	VBZ
randomwalker-info-585	528	47	a	a	DT
randomwalker-info-585	528	48	plot	plot	NN
randomwalker-info-585	528	49	showing	show	VBG
randomwalker-info-585	528	50	the	the	DT
randomwalker-info-585	528	51	optimal	optimal	JJ
randomwalker-info-585	528	52	choice	choice	NN
randomwalker-info-585	528	53	of	of	IN
randomwalker-info-585	528	54	β	β	NNP
randomwalker-info-585	528	55	as	as	IN
randomwalker-info-585	528	56	a	a	DT
randomwalker-info-585	528	57	function	function	NN
randomwalker-info-585	528	58	of	of	IN
randomwalker-info-585	528	59	α	α	NN
randomwalker-info-585	528	60	when	when	WRB
randomwalker-info-585	528	61	γ	γ	NNP
randomwalker-info-585	528	62	=	=	SYM
randomwalker-info-585	528	63	0	0	NFP
randomwalker-info-585	528	64	.	.	.
randomwalker-info-585	529	1	A	a	DT
randomwalker-info-585	529	2	few	few	JJ
randomwalker-info-585	529	3	noteworthy	noteworthy	JJ
randomwalker-info-585	529	4	points	point	NNS
randomwalker-info-585	529	5	from	from	IN
randomwalker-info-585	529	6	this	this	DT
randomwalker-info-585	529	7	plot	plot	NN
randomwalker-info-585	529	8	:	:	:
randomwalker-info-585	529	9	as	as	IN
randomwalker-info-585	529	10	α	α	XX
randomwalker-info-585	529	11	→	→	SYM
randomwalker-info-585	529	12	0	0	CD
randomwalker-info-585	529	13	,	,	,
randomwalker-info-585	529	14	so	so	RB
randomwalker-info-585	529	15	does	do	VBZ
randomwalker-info-585	529	16	the	the	DT
randomwalker-info-585	529	17	optimal	optimal	JJ
randomwalker-info-585	529	18	β	β	NN
randomwalker-info-585	529	19	.	.	.
randomwalker-info-585	530	1	As	as	IN
randomwalker-info-585	530	2	α	α	XX
randomwalker-info-585	530	3	→	→	SYM
randomwalker-info-585	530	4	1/2	1/2	CD
randomwalker-info-585	530	5	,	,	,
randomwalker-info-585	530	6	the	the	DT
randomwalker-info-585	530	7	optimal	optimal	JJ
randomwalker-info-585	530	8	β	β	NNP
randomwalker-info-585	530	9	approaches	approaches	NNP
randomwalker-info-585	530	10	∞.	∞.	XX
randomwalker-info-585	531	1	Figure	figure	NN
randomwalker-info-585	531	2	9	9	CD
randomwalker-info-585	531	3	plots	plot	NNS
randomwalker-info-585	531	4	our	-PRON-	PRP$
randomwalker-info-585	531	5	theoretical	theoretical	JJ
randomwalker-info-585	531	6	predictions	prediction	NNS
randomwalker-info-585	531	7	against	against	IN
randomwalker-info-585	531	8	simulation	simulation	NN
randomwalker-info-585	531	9	results	result	NNS
randomwalker-info-585	531	10	,	,	,
randomwalker-info-585	531	11	confirming	confirm	VBG
randomwalker-info-585	531	12	that	that	IN
randomwalker-info-585	531	13	the	the	DT
randomwalker-info-585	531	14	analysis	analysis	NN
randomwalker-info-585	531	15	is	be	VBZ
randomwalker-info-585	531	16	correct	correct	JJ
randomwalker-info-585	531	17	.	.	.
randomwalker-info-585	532	1	We	-PRON-	PRP
randomwalker-info-585	532	2	conclude	conclude	VBP
randomwalker-info-585	532	3	this	this	DT
randomwalker-info-585	532	4	section	section	NN
randomwalker-info-585	532	5	with	with	IN
randomwalker-info-585	532	6	Figure	Figure	NNP
randomwalker-info-585	532	7	10	10	CD
randomwalker-info-585	532	8	plotting	plot	VBG
randomwalker-info-585	532	9	the	the	DT
randomwalker-info-585	532	10	(	(	-LRB-
randomwalker-info-585	532	11	the-	the-	DT
randomwalker-info-585	532	12	oretical	oretical	JJ
randomwalker-info-585	532	13	)	)	-RRB-
randomwalker-info-585	532	14	performance	performance	NN
randomwalker-info-585	532	15	of	of	IN
randomwalker-info-585	532	16	default	default	NN
randomwalker-info-585	532	17	mining	mining	NN
randomwalker-info-585	532	18	,	,	,
randomwalker-info-585	532	19	selfish	selfish	JJ
randomwalker-info-585	532	20	mining	mining	NN
randomwalker-info-585	532	21	,	,	,
randomwalker-info-585	532	22	and	and	CC
randomwalker-info-585	532	23	selfish	selfish	JJ
randomwalker-info-585	532	24	mining	mining	NN
randomwalker-info-585	532	25	with	with	IN
randomwalker-info-585	532	26	the	the	DT
randomwalker-info-585	532	27	optimal	optimal	JJ
randomwalker-info-585	532	28	cutoff	cutoff	NN
randomwalker-info-585	532	29	for	for	IN
randomwalker-info-585	532	30	a	a	DT
randomwalker-info-585	532	31	range	range	NN
randomwalker-info-585	532	32	of	of	IN
randomwalker-info-585	532	33	α	α	NN
randomwalker-info-585	532	34	and	and	CC
randomwalker-info-585	532	35	γ	γ	NNP
randomwalker-info-585	532	36	=	=	SYM
randomwalker-info-585	532	37	0	0	CD
randomwalker-info-585	532	38	.	.	.
randomwalker-info-585	533	1	Note	note	VB
randomwalker-info-585	533	2	that	that	IN
randomwalker-info-585	533	3	in	in	IN
randomwalker-info-585	533	4	some	some	DT
randomwalker-info-585	533	5	ranges	range	NNS
randomwalker-info-585	533	6	,	,	,
randomwalker-info-585	533	7	the	the	DT
randomwalker-info-585	533	8	gains	gain	NNS
randomwalker-info-585	533	9	are	be	VBP
randomwalker-info-585	533	10	quite	quite	RB
randomwalker-info-585	533	11	signif-	signif-	JJ
randomwalker-info-585	533	12	icant	icant	NN
randomwalker-info-585	533	13	.	.	.
randomwalker-info-585	534	1	Specifically	specifically	RB
randomwalker-info-585	534	2	,	,	,
randomwalker-info-585	534	3	when	when	WRB
randomwalker-info-585	534	4	α	α	XX
randomwalker-info-585	534	5	=	=	SYM
randomwalker-info-585	534	6	1/3	1/3	CD
randomwalker-info-585	534	7	,	,	,
randomwalker-info-585	534	8	both	both	DT
randomwalker-info-585	534	9	selfish	selfish	JJ
randomwalker-info-585	534	10	mining	mining	NN
randomwalker-info-585	534	11	and	and	CC
randomwalker-info-585	534	12	default	default	NN
randomwalker-info-585	534	13	mining	mining	NN
randomwalker-info-585	534	14	achieve	achieve	VBP
randomwalker-info-585	534	15	expected	expect	VBN
randomwalker-info-585	534	16	reward	reward	NN
randomwalker-info-585	534	17	of	of	IN
randomwalker-info-585	534	18	≈	≈	NNP
randomwalker-info-585	534	19	1/3	1/3	CD
randomwalker-info-585	534	20	,	,	,
randomwalker-info-585	534	21	but	but	CC
randomwalker-info-585	534	22	selfish	selfish	JJ
randomwalker-info-585	534	23	mining	mining	NN
randomwalker-info-585	534	24	with	with	IN
randomwalker-info-585	534	25	the	the	DT
randomwalker-info-585	534	26	optimal	optimal	JJ
randomwalker-info-585	534	27	cutoff	cutoff	NN
randomwalker-info-585	534	28	achieves	achieve	VBZ
randomwalker-info-585	534	29	an	an	DT
randomwalker-info-585	534	30	expected	expected	JJ
randomwalker-info-585	534	31	reward	reward	NN
randomwalker-info-585	534	32	of	of	IN
randomwalker-info-585	534	33	≈	≈	NNP
randomwalker-info-585	534	34	.38	.38	NNS
randomwalker-info-585	534	35	,	,	,
randomwalker-info-585	534	36	a	a	DT
randomwalker-info-585	534	37	13.6	13.6	CD
randomwalker-info-585	534	38	%	%	NN
randomwalker-info-585	534	39	increase	increase	NN
randomwalker-info-585	534	40	!	!	.
randomwalker-info-585	535	1	Test	Test	NNP
randomwalker-info-585	535	2	Figure	figure	NN
randomwalker-info-585	535	3	9	9	CD
randomwalker-info-585	535	4	:	:	:
randomwalker-info-585	535	5	Theory	theory	NN
randomwalker-info-585	535	6	matching	match	VBG
randomwalker-info-585	535	7	simulation	simulation	NN
randomwalker-info-585	535	8	for	for	IN
randomwalker-info-585	535	9	a	a	DT
randomwalker-info-585	535	10	variety	variety	NN
randomwalker-info-585	535	11	of	of	IN
randomwalker-info-585	535	12	cutoff	cutoff	NN
randomwalker-info-585	535	13	thresholds	threshold	NNS
randomwalker-info-585	535	14	for	for	IN
randomwalker-info-585	535	15	selfish	selfish	JJ
randomwalker-info-585	535	16	mining	mining	NN
randomwalker-info-585	535	17	,	,	,
randomwalker-info-585	535	18	all	all	RB
randomwalker-info-585	535	19	with	with	IN
randomwalker-info-585	535	20	γ	γ	NNP
randomwalker-info-585	535	21	=	=	SYM
randomwalker-info-585	535	22	0	0	CD
randomwalker-info-585	535	23	.	.	.
randomwalker-info-585	536	1	The	the	DT
randomwalker-info-585	536	2	smaller	small	JJR
randomwalker-info-585	536	3	cutoffs	cutoff	NNS
randomwalker-info-585	536	4	do	do	VBP
randomwalker-info-585	536	5	better	well	RBR
randomwalker-info-585	536	6	for	for	IN
randomwalker-info-585	536	7	a	a	DT
randomwalker-info-585	536	8	miner	miner	NN
randomwalker-info-585	536	9	with	with	IN
randomwalker-info-585	536	10	a	a	DT
randomwalker-info-585	536	11	smaller	small	JJR
randomwalker-info-585	536	12	hash	hash	NN
randomwalker-info-585	536	13	-	-	HYPH
randomwalker-info-585	536	14	power	power	NN
randomwalker-info-585	536	15	(	(	-LRB-
randomwalker-info-585	536	16	α	α	NN
randomwalker-info-585	536	17	)	)	-RRB-
randomwalker-info-585	536	18	and	and	CC
randomwalker-info-585	536	19	the	the	DT
randomwalker-info-585	536	20	larger	large	JJR
randomwalker-info-585	536	21	cutoffs	cutoff	NNS
randomwalker-info-585	536	22	do	do	VBP
randomwalker-info-585	536	23	better	better	RB
randomwalker-info-585	536	24	with	with	IN
randomwalker-info-585	536	25	a	a	DT
randomwalker-info-585	536	26	larger	large	JJR
randomwalker-info-585	536	27	hash	hash	NN
randomwalker-info-585	536	28	-	-	HYPH
randomwalker-info-585	536	29	power	power	NN
randomwalker-info-585	536	30	.	.	.
randomwalker-info-585	537	1	Intuitively	intuitively	RB
randomwalker-info-585	537	2	,	,	,
randomwalker-info-585	537	3	this	this	DT
randomwalker-info-585	537	4	makes	make	VBZ
randomwalker-info-585	537	5	sense	sense	NN
randomwalker-info-585	537	6	as	as	IN
randomwalker-info-585	537	7	a	a	DT
randomwalker-info-585	537	8	more	more	RBR
randomwalker-info-585	537	9	powerful	powerful	JJ
randomwalker-info-585	537	10	miner	miner	NN
randomwalker-info-585	537	11	should	should	MD
randomwalker-info-585	537	12	be	be	VB
randomwalker-info-585	537	13	willing	willing	JJ
randomwalker-info-585	537	14	to	to	TO
randomwalker-info-585	537	15	risk	risk	VB
randomwalker-info-585	537	16	a	a	DT
randomwalker-info-585	537	17	larger	large	JJR
randomwalker-info-585	537	18	block	block	NN
randomwalker-info-585	537	19	to	to	TO
randomwalker-info-585	537	20	try	try	VB
randomwalker-info-585	537	21	to	to	TO
randomwalker-info-585	537	22	selfishly	selfishly	RB
randomwalker-info-585	537	23	mine	-PRON-	PRP
randomwalker-info-585	537	24	.	.	.
randomwalker-info-585	538	1	Figure	figure	NN
randomwalker-info-585	538	2	10	10	CD
randomwalker-info-585	538	3	:	:	:
randomwalker-info-585	538	4	A	a	DT
randomwalker-info-585	538	5	selfish	selfish	JJ
randomwalker-info-585	538	6	miner	miner	NN
randomwalker-info-585	538	7	using	use	VBG
randomwalker-info-585	538	8	the	the	DT
randomwalker-info-585	538	9	optimal	optimal	NNP
randomwalker-info-585	538	10	cutoff	cutoff	NN
randomwalker-info-585	538	11	outperforms	outperform	VBZ
randomwalker-info-585	538	12	both	both	CC
randomwalker-info-585	538	13	the	the	DT
randomwalker-info-585	538	14	original	original	JJ
randomwalker-info-585	538	15	selfish	selfish	JJ
randomwalker-info-585	538	16	mining	mining	NN
randomwalker-info-585	538	17	proto-	proto-	FW
randomwalker-info-585	538	18	col	col	NN
randomwalker-info-585	538	19	and	and	CC
randomwalker-info-585	538	20	default	default	NN
randomwalker-info-585	538	21	mining	mining	NN
randomwalker-info-585	538	22	for	for	IN
randomwalker-info-585	538	23	all	all	DT
randomwalker-info-585	538	24	values	value	NNS
randomwalker-info-585	538	25	of	of	IN
randomwalker-info-585	538	26	α	α	XX
randomwalker-info-585	538	27	,	,	,
randomwalker-info-585	538	28	with	with	IN
randomwalker-info-585	538	29	γ	γ	NNP
randomwalker-info-585	538	30	=	=	SYM
randomwalker-info-585	538	31	0	0	CD
randomwalker-info-585	538	32	.	.	.
randomwalker-info-585	539	1	The	the	DT
randomwalker-info-585	539	2	simulation	simulation	NN
randomwalker-info-585	539	3	points	point	NNS
randomwalker-info-585	539	4	confirm	confirm	VBP
randomwalker-info-585	539	5	that	that	IN
randomwalker-info-585	539	6	the	the	DT
randomwalker-info-585	539	7	theory	theory	NN
randomwalker-info-585	539	8	is	be	VBZ
randomwalker-info-585	539	9	ac-	ac-	RB
randomwalker-info-585	539	10	curate	curate	NN
randomwalker-info-585	539	11	.	.	.
randomwalker-info-585	540	1	7	7	LS
randomwalker-info-585	540	2	.	.	.
randomwalker-info-585	541	1	IMPACT	IMPACT	NNP
randomwalker-info-585	541	2	ON	on	IN
randomwalker-info-585	541	3	BITCOIN	BITCOIN	NNS
randomwalker-info-585	541	4	AND	and	CC
randomwalker-info-585	541	5	LESSONS	lessons	NN
randomwalker-info-585	541	6	FOR	for	IN
randomwalker-info-585	541	7	CRYPTOCURRENCY	cryptocurrency	NN
randomwalker-info-585	541	8	DESIGN	design	NN
randomwalker-info-585	541	9	We	-PRON-	PRP
randomwalker-info-585	541	10	have	have	VBP
randomwalker-info-585	541	11	argued	argue	VBN
randomwalker-info-585	541	12	that	that	IN
randomwalker-info-585	541	13	deviant	deviant	NN
randomwalker-info-585	541	14	mining	mining	NN
randomwalker-info-585	541	15	strategies	strategy	NNS
randomwalker-info-585	541	16	in	in	IN
randomwalker-info-585	541	17	a	a	DT
randomwalker-info-585	541	18	transaction-	transaction-	NN
randomwalker-info-585	541	19	fee	fee	NN
randomwalker-info-585	541	20	regime	regime	NN
randomwalker-info-585	541	21	could	could	MD
randomwalker-info-585	541	22	hurt	hurt	VB
randomwalker-info-585	541	23	the	the	DT
randomwalker-info-585	541	24	stability	stability	NN
randomwalker-info-585	541	25	of	of	IN
randomwalker-info-585	541	26	Bitcoin	Bitcoin	NNP
randomwalker-info-585	541	27	mining	mining	NN
randomwalker-info-585	541	28	and	and	CC
randomwalker-info-585	541	29	harm	harm	VB
randomwalker-info-585	541	30	the	the	DT
randomwalker-info-585	541	31	ecosystem	ecosystem	NN
randomwalker-info-585	541	32	.	.	.
randomwalker-info-585	542	1	In	in	IN
randomwalker-info-585	542	2	a	a	DT
randomwalker-info-585	542	3	block	block	NN
randomwalker-info-585	542	4	chain	chain	NN
randomwalker-info-585	542	5	with	with	IN
randomwalker-info-585	542	6	constant	constant	JJ
randomwalker-info-585	542	7	forks	fork	NNS
randomwalker-info-585	542	8	caused	cause	VBN
randomwalker-info-585	542	9	by	by	IN
randomwalker-info-585	542	10	undercutting	undercutting	NN
randomwalker-info-585	542	11	,	,	,
randomwalker-info-585	542	12	an	an	DT
randomwalker-info-585	542	13	attacker	attacker	NN
randomwalker-info-585	542	14	’s	’s	POS
randomwalker-info-585	542	15	effective	effective	JJ
randomwalker-info-585	542	16	hash	hash	NN
randomwalker-info-585	542	17	power	power	NN
randomwalker-info-585	542	18	is	be	VBZ
randomwalker-info-585	542	19	magnified	magnify	VBN
randomwalker-info-585	542	20	because	because	IN
randomwalker-info-585	542	21	he	-PRON-	PRP
randomwalker-info-585	542	22	will	will	MD
randomwalker-info-585	542	23	always	always	RB
randomwalker-info-585	542	24	mine	mine	VB
randomwalker-info-585	542	25	to	to	TO
randomwalker-info-585	542	26	extend	extend	VB
randomwalker-info-585	542	27	his	-PRON-	PRP$
randomwalker-info-585	542	28	own	own	JJ
randomwalker-info-585	542	29	blocks	block	NNS
randomwalker-info-585	542	30	whereas	whereas	IN
randomwalker-info-585	542	31	other	other	JJ
randomwalker-info-585	542	32	miners	miner	NNS
randomwalker-info-585	542	33	are	be	VBP
randomwalker-info-585	542	34	not	not	RB
randomwalker-info-585	542	35	unified	unify	VBN
randomwalker-info-585	542	36	.	.	.
randomwalker-info-585	543	1	This	this	DT
randomwalker-info-585	543	2	would	would	MD
randomwalker-info-585	543	3	make	make	VB
randomwalker-info-585	543	4	a	a	DT
randomwalker-info-585	543	5	“	"	``
randomwalker-info-585	543	6	51	51	CD
randomwalker-info-585	543	7	%	%	NN
randomwalker-info-585	543	8	”	"	''
randomwalker-info-585	543	9	attack	attack	NN
randomwalker-info-585	543	10	possible	possible	JJ
randomwalker-info-585	543	11	with	with	IN
randomwalker-info-585	543	12	much	much	RB
randomwalker-info-585	543	13	less	less	JJR
randomwalker-info-585	543	14	than	than	IN
randomwalker-info-585	543	15	51	51	CD
randomwalker-info-585	543	16	%	%	NN
randomwalker-info-585	543	17	of	of	IN
randomwalker-info-585	543	18	the	the	DT
randomwalker-info-585	543	19	hash	hash	NN
randomwalker-info-585	543	20	power	power	NN
randomwalker-info-585	543	21	.	.	.
randomwalker-info-585	544	1	Many	many	JJ
randomwalker-info-585	544	2	other	other	JJ
randomwalker-info-585	544	3	unanticipated	unanticipated	JJ
randomwalker-info-585	544	4	side	side	NN
randomwalker-info-585	544	5	-	-	HYPH
randomwalker-info-585	544	6	effects	effect	NNS
randomwalker-info-585	544	7	may	may	MD
randomwalker-info-585	544	8	arise	arise	VB
randomwalker-info-585	544	9	.	.	.
randomwalker-info-585	545	1	In	in	IN
randomwalker-info-585	545	2	the	the	DT
randomwalker-info-585	545	3	block	block	NN
randomwalker-info-585	545	4	size	size	NN
randomwalker-info-585	545	5	debate	debate	NN
randomwalker-info-585	545	6	,	,	,
randomwalker-info-585	545	7	it	-PRON-	PRP
randomwalker-info-585	545	8	is	be	VBZ
randomwalker-info-585	545	9	frequently	frequently	RB
randomwalker-info-585	545	10	argued	argue	VBN
randomwalker-info-585	545	11	or	or	CC
randomwalker-info-585	545	12	assumed	assume	VBN
randomwalker-info-585	545	13	that	that	DT
randomwalker-info-585	545	14	space	space	NN
randomwalker-info-585	545	15	in	in	IN
randomwalker-info-585	545	16	the	the	DT
randomwalker-info-585	545	17	block	block	NN
randomwalker-info-585	545	18	chain	chain	NN
randomwalker-info-585	545	19	will	will	MD
randomwalker-info-585	545	20	be	be	VB
randomwalker-info-585	545	21	a	a	DT
randomwalker-info-585	545	22	scarce	scarce	JJ
randomwalker-info-585	545	23	resource	resource	NN
randomwalker-info-585	545	24	and	and	CC
randomwalker-info-585	545	25	a	a	DT
randomwalker-info-585	545	26	market	market	NN
randomwalker-info-585	545	27	will	will	MD
randomwalker-info-585	545	28	emerge	emerge	VB
randomwalker-info-585	545	29	,	,	,
randomwalker-info-585	545	30	with	with	IN
randomwalker-info-585	545	31	users	user	NNS
randomwalker-info-585	545	32	being	be	VBG
randomwalker-info-585	545	33	able	able	JJ
randomwalker-info-585	545	34	to	to	TO
randomwalker-info-585	545	35	speed	speed	VB
randomwalker-info-585	545	36	up	up	RP
randomwalker-info-585	545	37	the	the	DT
randomwalker-info-585	545	38	confirmation	confirmation	NN
randomwalker-info-585	545	39	of	of	IN
randomwalker-info-585	545	40	a	a	DT
randomwalker-info-585	545	41	transaction	transaction	NN
randomwalker-info-585	545	42	by	by	IN
randomwalker-info-585	545	43	paying	pay	VBG
randomwalker-info-585	545	44	a	a	DT
randomwalker-info-585	545	45	sufficiently	sufficiently	RB
randomwalker-info-585	545	46	large	large	JJ
randomwalker-info-585	545	47	transaction	transaction	NN
randomwalker-info-585	545	48	fee	fee	NN
randomwalker-info-585	545	49	.	.	.
randomwalker-info-585	546	1	But	but	CC
randomwalker-info-585	546	2	if	if	IN
randomwalker-info-585	546	3	miners	miner	NNS
randomwalker-info-585	546	4	intentionally	intentionally	RB
randomwalker-info-585	546	5	“	"	``
randomwalker-info-585	546	6	leave	leave	VB
randomwalker-info-585	546	7	money	money	NN
randomwalker-info-585	546	8	on	on	IN
randomwalker-info-585	546	9	the	the	DT
randomwalker-info-585	546	10	table	table	NN
randomwalker-info-585	546	11	”	"	''
randomwalker-info-585	546	12	when	when	WRB
randomwalker-info-585	546	13	solving	solve	VBG
randomwalker-info-585	546	14	blocks	block	NNS
randomwalker-info-585	546	15	,	,	,
randomwalker-info-585	546	16	as	as	IN
randomwalker-info-585	546	17	is	be	VBZ
randomwalker-info-585	546	18	the	the	DT
randomwalker-info-585	546	19	case	case	NN
randomwalker-info-585	546	20	in	in	IN
randomwalker-info-585	546	21	undercutting	undercut	VBG
randomwalker-info-585	546	22	attacks	attack	NNS
randomwalker-info-585	546	23	,	,	,
randomwalker-info-585	546	24	it	-PRON-	PRP
randomwalker-info-585	546	25	breaks	break	VBZ
randomwalker-info-585	546	26	this	this	DT
randomwalker-info-585	546	27	assumption	assumption	NN
randomwalker-info-585	546	28	.	.	.
randomwalker-info-585	547	1	That	that	DT
randomwalker-info-585	547	2	is	be	VBZ
randomwalker-info-585	547	3	because	because	IN
randomwalker-info-585	547	4	under-	under-	JJ
randomwalker-info-585	547	5	cutting	cut	VBG
randomwalker-info-585	547	6	miners	miner	NNS
randomwalker-info-585	547	7	are	be	VBP
randomwalker-info-585	547	8	not	not	RB
randomwalker-info-585	547	9	looking	look	VBG
randomwalker-info-585	547	10	to	to	TO
randomwalker-info-585	547	11	maximize	maximize	VB
randomwalker-info-585	547	12	the	the	DT
randomwalker-info-585	547	13	transaction	transaction	NN
randomwalker-info-585	547	14	fee	fee	NN
randomwalker-info-585	547	15	that	that	WDT
randomwalker-info-585	547	16	they	-PRON-	PRP
randomwalker-info-585	547	17	can	can	MD
randomwalker-info-585	547	18	claim	claim	VB
randomwalker-info-585	547	19	,	,	,
randomwalker-info-585	547	20	and	and	CC
randomwalker-info-585	547	21	do	do	VBP
randomwalker-info-585	547	22	n’t	not	RB
randomwalker-info-585	547	23	have	have	VB
randomwalker-info-585	547	24	a	a	DT
randomwalker-info-585	547	25	strong	strong	JJ
randomwalker-info-585	547	26	reason	reason	NN
randomwalker-info-585	547	27	to	to	TO
randomwalker-info-585	547	28	prioritize	prioritize	VB
randomwalker-info-585	547	29	a	a	DT
randomwalker-info-585	547	30	transaction	transaction	NN
randomwalker-info-585	547	31	with	with	IN
randomwalker-info-585	547	32	a	a	DT
randomwalker-info-585	547	33	high	high	JJ
randomwalker-info-585	547	34	fee.9	fee.9	NN
randomwalker-info-585	547	35	Put	put	VB
randomwalker-info-585	547	36	another	another	DT
randomwalker-info-585	547	37	way	way	NN
randomwalker-info-585	547	38	,	,	,
randomwalker-info-585	547	39	the	the	DT
randomwalker-info-585	547	40	block	block	NN
randomwalker-info-585	547	41	size	size	NN
randomwalker-info-585	547	42	imposes	impose	VBZ
randomwalker-info-585	547	43	a	a	DT
randomwalker-info-585	547	44	constraint	constraint	NN
randomwalker-info-585	547	45	on	on	IN
randomwalker-info-585	547	46	the	the	DT
randomwalker-info-585	547	47	total	total	JJ
randomwalker-info-585	547	48	size	size	NN
randomwalker-info-585	547	49	of	of	IN
randomwalker-info-585	547	50	trans-	trans-	JJ
randomwalker-info-585	547	51	actions	action	NNS
randomwalker-info-585	547	52	in	in	IN
randomwalker-info-585	547	53	a	a	DT
randomwalker-info-585	547	54	block	block	NN
randomwalker-info-585	547	55	and	and	CC
randomwalker-info-585	547	56	the	the	DT
randomwalker-info-585	547	57	threat	threat	NN
randomwalker-info-585	547	58	of	of	IN
randomwalker-info-585	547	59	being	be	VBG
randomwalker-info-585	547	60	undercut	undercut	JJ
randomwalker-info-585	547	61	imposes	impose	VBZ
randomwalker-info-585	547	62	another	another	DT
randomwalker-info-585	547	63	constraint	constraint	NN
randomwalker-info-585	547	64	on	on	IN
randomwalker-info-585	547	65	the	the	DT
randomwalker-info-585	547	66	total	total	JJ
randomwalker-info-585	547	67	fee	fee	NN
randomwalker-info-585	547	68	.	.	.
randomwalker-info-585	548	1	The	the	DT
randomwalker-info-585	548	2	two	two	CD
randomwalker-info-585	548	3	interact	interact	NN
randomwalker-info-585	548	4	in	in	IN
randomwalker-info-585	548	5	complex	complex	JJ
randomwalker-info-585	548	6	ways	way	NNS
randomwalker-info-585	548	7	.	.	.
randomwalker-info-585	549	1	We	-PRON-	PRP
randomwalker-info-585	549	2	believe	believe	VBP
randomwalker-info-585	549	3	that	that	IN
randomwalker-info-585	549	4	qualitatively	qualitatively	RB
randomwalker-info-585	549	5	our	-PRON-	PRP$
randomwalker-info-585	549	6	results	result	NNS
randomwalker-info-585	549	7	will	will	MD
randomwalker-info-585	549	8	continue	continue	VB
randomwalker-info-585	549	9	to	to	TO
randomwalker-info-585	549	10	hold	hold	VB
randomwalker-info-585	549	11	in	in	RP
randomwalker-info-585	549	12	a	a	DT
randomwalker-info-585	549	13	world	world	NN
randomwalker-info-585	549	14	where	where	WRB
randomwalker-info-585	549	15	the	the	DT
randomwalker-info-585	549	16	available	available	JJ
randomwalker-info-585	549	17	block	block	NN
randomwalker-info-585	549	18	size	size	NN
randomwalker-info-585	549	19	is	be	VBZ
randomwalker-info-585	549	20	much	much	RB
randomwalker-info-585	549	21	smaller	small	JJR
randomwalker-info-585	549	22	than	than	IN
randomwalker-info-585	549	23	the	the	DT
randomwalker-info-585	549	24	demand	demand	NN
randomwalker-info-585	549	25	,	,	,
randomwalker-info-585	549	26	but	but	CC
randomwalker-info-585	549	27	quantitatively	quantitatively	RB
randomwalker-info-585	549	28	the	the	DT
randomwalker-info-585	549	29	im-	im-	JJ
randomwalker-info-585	549	30	pact	pact	NN
randomwalker-info-585	549	31	of	of	IN
randomwalker-info-585	549	32	undercutting	undercutting	NN
randomwalker-info-585	549	33	will	will	MD
randomwalker-info-585	549	34	be	be	VB
randomwalker-info-585	549	35	mitigated	mitigate	VBN
randomwalker-info-585	549	36	(	(	-LRB-
randomwalker-info-585	549	37	see	see	VB
randomwalker-info-585	549	38	end	end	NN
randomwalker-info-585	549	39	of	of	IN
randomwalker-info-585	549	40	Section	section	NN
randomwalker-info-585	549	41	3.1	3.1	CD
randomwalker-info-585	549	42	)	)	-RRB-
randomwalker-info-585	549	43	.	.	.
randomwalker-info-585	550	1	Still	still	RB
randomwalker-info-585	550	2	,	,	,
randomwalker-info-585	550	3	it	-PRON-	PRP
randomwalker-info-585	550	4	is	be	VBZ
randomwalker-info-585	550	5	an	an	DT
randomwalker-info-585	550	6	important	important	JJ
randomwalker-info-585	550	7	direction	direction	NN
randomwalker-info-585	550	8	for	for	IN
randomwalker-info-585	550	9	future	future	JJ
randomwalker-info-585	550	10	research	research	NN
randomwalker-info-585	550	11	to	to	TO
randomwalker-info-585	550	12	understand	understand	VB
randomwalker-info-585	550	13	this	this	DT
randomwalker-info-585	550	14	connection	connection	NN
randomwalker-info-585	550	15	more	more	RBR
randomwalker-info-585	550	16	rigorously	rigorously	RB
randomwalker-info-585	550	17	.	.	.
randomwalker-info-585	551	1	Despite	despite	IN
randomwalker-info-585	551	2	the	the	DT
randomwalker-info-585	551	3	variety	variety	NN
randomwalker-info-585	551	4	of	of	IN
randomwalker-info-585	551	5	our	-PRON-	PRP$
randomwalker-info-585	551	6	results	result	NNS
randomwalker-info-585	551	7	,	,	,
randomwalker-info-585	551	8	we	-PRON-	PRP
randomwalker-info-585	551	9	believe	believe	VBP
randomwalker-info-585	551	10	we	-PRON-	PRP
randomwalker-info-585	551	11	have	have	VBP
randomwalker-info-585	551	12	only	only	RB
randomwalker-info-585	551	13	scratched	scratch	VBN
randomwalker-info-585	551	14	the	the	DT
randomwalker-info-585	551	15	surface	surface	NN
randomwalker-info-585	551	16	of	of	IN
randomwalker-info-585	551	17	what	what	WP
randomwalker-info-585	551	18	can	can	MD
randomwalker-info-585	551	19	go	go	VB
randomwalker-info-585	551	20	wrong	wrong	JJ
randomwalker-info-585	551	21	in	in	IN
randomwalker-info-585	551	22	a	a	DT
randomwalker-info-585	551	23	transaction-	transaction-	NN
randomwalker-info-585	551	24	fee	fee	NN
randomwalker-info-585	551	25	regime	regime	NN
randomwalker-info-585	551	26	.	.	.
randomwalker-info-585	552	1	To	to	IN
randomwalker-info-585	552	2	wit	wit	NN
randomwalker-info-585	552	3	:	:	:
randomwalker-info-585	552	4	we	-PRON-	PRP
randomwalker-info-585	552	5	have	have	VBP
randomwalker-info-585	552	6	not	not	RB
randomwalker-info-585	552	7	presented	present	VBN
randomwalker-info-585	552	8	an	an	DT
randomwalker-info-585	552	9	analysis	analysis	NN
randomwalker-info-585	552	10	of	of	IN
randomwalker-info-585	552	11	miners	miner	NNS
randomwalker-info-585	552	12	whose	whose	WP$
randomwalker-info-585	552	13	strategy	strategy	NN
randomwalker-info-585	552	14	space	space	NN
randomwalker-info-585	552	15	includes	include	VBZ
randomwalker-info-585	552	16	both	both	DT
randomwalker-info-585	552	17	undercutting	undercutting	NN
randomwalker-info-585	552	18	and	and	CC
randomwalker-info-585	552	19	selfish	selfish	JJ
randomwalker-info-585	552	20	mining	mining	NN
randomwalker-info-585	552	21	,	,	,
randomwalker-info-585	552	22	primarily	primarily	RB
randomwalker-info-585	552	23	due	due	IN
randomwalker-info-585	552	24	to	to	IN
randomwalker-info-585	552	25	the	the	DT
randomwalker-info-585	552	26	complexity	complexity	NN
randomwalker-info-585	552	27	of	of	IN
randomwalker-info-585	552	28	the	the	DT
randomwalker-info-585	552	29	result-	result-	NN
randomwalker-info-585	552	30	ing	ing	NN
randomwalker-info-585	552	31	models	model	NNS
randomwalker-info-585	552	32	.	.	.
randomwalker-info-585	553	1	There	there	EX
randomwalker-info-585	553	2	has	have	VBZ
randomwalker-info-585	553	3	been	be	VBN
randomwalker-info-585	553	4	scant	scant	JJ
randomwalker-info-585	553	5	attention	attention	NN
randomwalker-info-585	553	6	paid	pay	VBN
randomwalker-info-585	553	7	to	to	IN
randomwalker-info-585	553	8	the	the	DT
randomwalker-info-585	553	9	transition	transition	NN
randomwalker-info-585	553	10	to	to	IN
randomwalker-info-585	553	11	a	a	DT
randomwalker-info-585	553	12	transaction	transaction	NN
randomwalker-info-585	553	13	-	-	HYPH
randomwalker-info-585	553	14	fee	fee	NN
randomwalker-info-585	553	15	regime	regime	NN
randomwalker-info-585	553	16	.	.	.
randomwalker-info-585	554	1	The	the	DT
randomwalker-info-585	554	2	Nakamoto	Nakamoto	NNP
randomwalker-info-585	554	3	paper	paper	NN
randomwalker-info-585	554	4	addresses	address	VBZ
randomwalker-info-585	554	5	it	-PRON-	PRP
randomwalker-info-585	554	6	briefly	briefly	RB
randomwalker-info-585	554	7	:	:	:
randomwalker-info-585	554	8	“	"	``
randomwalker-info-585	554	9	The	the	DT
randomwalker-info-585	554	10	incentive	incentive	NN
randomwalker-info-585	554	11	can	can	MD
randomwalker-info-585	554	12	also	also	RB
randomwalker-info-585	554	13	be	be	VB
randomwalker-info-585	554	14	funded	fund	VBN
randomwalker-info-585	554	15	with	with	IN
randomwalker-info-585	554	16	transaction	transaction	NN
randomwalker-info-585	554	17	fees	fee	NNS
randomwalker-info-585	554	18	...	...	:
randomwalker-info-585	554	19	Once	once	IN
randomwalker-info-585	554	20	a	a	DT
randomwalker-info-585	554	21	predetermined	predetermined	JJ
randomwalker-info-585	554	22	number	number	NN
randomwalker-info-585	554	23	of	of	IN
randomwalker-info-585	554	24	coins	coin	NNS
randomwalker-info-585	554	25	have	have	VBP
randomwalker-info-585	554	26	entered	enter	VBN
randomwalker-info-585	554	27	circulation	circulation	NN
randomwalker-info-585	554	28	,	,	,
randomwalker-info-585	554	29	the	the	DT
randomwalker-info-585	554	30	incentive	incentive	NN
randomwalker-info-585	554	31	can	can	MD
randomwalker-info-585	554	32	transition	transition	VB
randomwalker-info-585	554	33	entirely	entirely	RB
randomwalker-info-585	554	34	to	to	IN
randomwalker-info-585	554	35	transac-	transac-	NNP
randomwalker-info-585	554	36	tion	tion	NN
randomwalker-info-585	554	37	fees	fee	NNS
randomwalker-info-585	554	38	and	and	CC
randomwalker-info-585	554	39	be	be	VB
randomwalker-info-585	554	40	completely	completely	RB
randomwalker-info-585	554	41	inflation	inflation	NN
randomwalker-info-585	554	42	free	free	JJ
randomwalker-info-585	554	43	”	"	''
randomwalker-info-585	554	44	[	[	-LRB-
randomwalker-info-585	554	45	19	19	CD
randomwalker-info-585	554	46	]	]	-RRB-
randomwalker-info-585	554	47	.	.	.
randomwalker-info-585	555	1	Similar	similar	JJ
randomwalker-info-585	555	2	com-	com-	NN
randomwalker-info-585	555	3	ments	ment	NNS
randomwalker-info-585	555	4	on	on	IN
randomwalker-info-585	555	5	the	the	DT
randomwalker-info-585	555	6	Bitcoin	Bitcoin	NNP
randomwalker-info-585	555	7	Wiki	Wiki	NNP
randomwalker-info-585	555	8	and	and	CC
randomwalker-info-585	555	9	other	other	JJ
randomwalker-info-585	555	10	places	place	NNS
randomwalker-info-585	555	11	suggest	suggest	VBP
randomwalker-info-585	555	12	that	that	IN
randomwalker-info-585	555	13	the	the	DT
randomwalker-info-585	555	14	community	community	NN
randomwalker-info-585	555	15	views	view	VBZ
randomwalker-info-585	555	16	the	the	DT
randomwalker-info-585	555	17	transition	transition	NN
randomwalker-info-585	555	18	as	as	IN
randomwalker-info-585	555	19	unremarkable	unremarkable	JJ
randomwalker-info-585	555	20	.	.	.
randomwalker-info-585	556	1	Some	some	DT
randomwalker-info-585	556	2	altcoins	altcoin	NNS
randomwalker-info-585	556	3	(	(	-LRB-
randomwalker-info-585	556	4	Monero	Monero	NNP
randomwalker-info-585	556	5	,	,	,
randomwalker-info-585	556	6	Dogecoin	Dogecoin	NNP
randomwalker-info-585	556	7	)	)	-RRB-
randomwalker-info-585	556	8	have	have	VBP
randomwalker-info-585	556	9	even	even	RB
randomwalker-info-585	556	10	opted	opt	VBN
randomwalker-info-585	556	11	to	to	TO
randomwalker-info-585	556	12	hasten	hasten	VB
randomwalker-info-585	556	13	the	the	DT
randomwalker-info-585	556	14	block	block	NN
randomwalker-info-585	556	15	reward	reward	NN
randomwalker-info-585	556	16	halving	halving	NNP
randomwalker-info-585	556	17	time	time	NN
randomwalker-info-585	556	18	.	.	.
randomwalker-info-585	557	1	Our	-PRON-	PRP$
randomwalker-info-585	557	2	results	result	NNS
randomwalker-info-585	557	3	suggest	suggest	VBP
randomwalker-info-585	557	4	a	a	DT
randomwalker-info-585	557	5	different	different	JJ
randomwalker-info-585	557	6	view	view	NN
randomwalker-info-585	557	7	.	.	.
randomwalker-info-585	558	1	We	-PRON-	PRP
randomwalker-info-585	558	2	see	see	VBP
randomwalker-info-585	558	3	the	the	DT
randomwalker-info-585	558	4	block	block	NN
randomwalker-info-585	558	5	re-	re-	RB
randomwalker-info-585	558	6	ward	ward	RB
randomwalker-info-585	558	7	as	as	IN
randomwalker-info-585	558	8	integral	integral	JJ
randomwalker-info-585	558	9	to	to	IN
randomwalker-info-585	558	10	the	the	DT
randomwalker-info-585	558	11	stability	stability	NN
randomwalker-info-585	558	12	of	of	IN
randomwalker-info-585	558	13	the	the	DT
randomwalker-info-585	558	14	mining	mining	NN
randomwalker-info-585	558	15	game	game	NN
randomwalker-info-585	558	16	.	.	.
randomwalker-info-585	559	1	At	at	IN
randomwalker-info-585	559	2	a	a	DT
randomwalker-info-585	559	3	minimum	minimum	NN
randomwalker-info-585	559	4	,	,	,
randomwalker-info-585	559	5	analyzing	analyze	VBG
randomwalker-info-585	559	6	equilibria	equilibria	NN
randomwalker-info-585	559	7	in	in	IN
randomwalker-info-585	559	8	the	the	DT
randomwalker-info-585	559	9	transaction	transaction	NN
randomwalker-info-585	559	10	-	-	HYPH
randomwalker-info-585	559	11	fee	fee	NN
randomwalker-info-585	559	12	regime	regime	NN
randomwalker-info-585	559	13	appears	appear	VBZ
randomwalker-info-585	559	14	dramatically	dramatically	RB
randomwalker-info-585	559	15	harder	hard	JJR
randomwalker-info-585	559	16	than	than	IN
randomwalker-info-585	559	17	in	in	IN
randomwalker-info-585	559	18	the	the	DT
randomwalker-info-585	559	19	block	block	NN
randomwalker-info-585	559	20	-	-	HYPH
randomwalker-info-585	559	21	reward	reward	NN
randomwalker-info-585	559	22	regime	regime	NN
randomwalker-info-585	559	23	,	,	,
randomwalker-info-585	559	24	which	which	WDT
randomwalker-info-585	559	25	is	be	VBZ
randomwalker-info-585	559	26	a	a	DT
randomwalker-info-585	559	27	cause	cause	NN
randomwalker-info-585	559	28	for	for	IN
randomwalker-info-585	559	29	concern	concern	NN
randomwalker-info-585	559	30	by	by	IN
randomwalker-info-585	559	31	itself	-PRON-	PRP
randomwalker-info-585	559	32	.	.	.
randomwalker-info-585	560	1	The	the	DT
randomwalker-info-585	560	2	monetary	monetary	JJ
randomwalker-info-585	560	3	infla-	infla-	NN
randomwalker-info-585	560	4	tion	tion	NN
randomwalker-info-585	560	5	resulting	result	VBG
randomwalker-info-585	560	6	from	from	IN
randomwalker-info-585	560	7	making	make	VBG
randomwalker-info-585	560	8	the	the	DT
randomwalker-info-585	560	9	block	block	NN
randomwalker-info-585	560	10	reward	reward	NN
randomwalker-info-585	560	11	permanent	permanent	JJ
randomwalker-info-585	560	12	,	,	,
randomwalker-info-585	560	13	as	as	IN
randomwalker-info-585	560	14	Ethereum	Ethereum	NNP
randomwalker-info-585	560	15	does	do	VBZ
randomwalker-info-585	560	16	,	,	,
randomwalker-info-585	560	17	may	may	MD
randomwalker-info-585	560	18	be	be	VB
randomwalker-info-585	560	19	a	a	DT
randomwalker-info-585	560	20	small	small	JJ
randomwalker-info-585	560	21	price	price	NN
randomwalker-info-585	560	22	to	to	TO
randomwalker-info-585	560	23	pay	pay	VB
randomwalker-info-585	560	24	to	to	TO
randomwalker-info-585	560	25	ensure	ensure	VB
randomwalker-info-585	560	26	the	the	DT
randomwalker-info-585	560	27	stability	stability	NN
randomwalker-info-585	560	28	of	of	IN
randomwalker-info-585	560	29	a	a	DT
randomwalker-info-585	560	30	cryptocurrency	cryptocurrency	NN
randomwalker-info-585	560	31	.	.	.
randomwalker-info-585	561	1	8	8	LS
randomwalker-info-585	561	2	.	.	.
randomwalker-info-585	562	1	ACKNOWLEDGMENTS	acknowledgment	NNS
randomwalker-info-585	562	2	We	-PRON-	PRP
randomwalker-info-585	562	3	are	be	VBP
randomwalker-info-585	562	4	extremely	extremely	RB
randomwalker-info-585	562	5	grateful	grateful	JJ
randomwalker-info-585	562	6	to	to	IN
randomwalker-info-585	562	7	Jiechen	Jiechen	NNP
randomwalker-info-585	562	8	Chen	Chen	NNP
randomwalker-info-585	562	9	,	,	,
randomwalker-info-585	562	10	Kira	Kira	NNP
randomwalker-info-585	562	11	Goldner	Goldner	NNP
randomwalker-info-585	562	12	,	,	,
randomwalker-info-585	562	13	9They	9they	PRP
randomwalker-info-585	562	14	do	do	VBP
randomwalker-info-585	562	15	have	have	VB
randomwalker-info-585	562	16	a	a	DT
randomwalker-info-585	562	17	weak	weak	JJ
randomwalker-info-585	562	18	reason	reason	NN
randomwalker-info-585	562	19	:	:	:
randomwalker-info-585	562	20	miners	miner	NNS
randomwalker-info-585	562	21	benefit	benefit	VBP
randomwalker-info-585	562	22	from	from	IN
randomwalker-info-585	562	23	creat-	creat-	NNP
randomwalker-info-585	562	24	ing	ing	NNP
randomwalker-info-585	562	25	the	the	DT
randomwalker-info-585	562	26	smallest	small	JJS
randomwalker-info-585	562	27	possible	possible	JJ
randomwalker-info-585	562	28	block	block	NN
randomwalker-info-585	562	29	for	for	IN
randomwalker-info-585	562	30	a	a	DT
randomwalker-info-585	562	31	given	give	VBN
randomwalker-info-585	562	32	value	value	NN
randomwalker-info-585	562	33	of	of	IN
randomwalker-info-585	562	34	the	the	DT
randomwalker-info-585	562	35	to-	to-	XX
randomwalker-info-585	562	36	tal	tal	NNP
randomwalker-info-585	562	37	transaction	transaction	NNP
randomwalker-info-585	562	38	fee	fee	NN
randomwalker-info-585	562	39	they	-PRON-	PRP
randomwalker-info-585	562	40	seek	seek	VBP
randomwalker-info-585	562	41	to	to	TO
randomwalker-info-585	562	42	claim	claim	VB
randomwalker-info-585	562	43	,	,	,
randomwalker-info-585	562	44	since	since	IN
randomwalker-info-585	562	45	smaller	small	JJR
randomwalker-info-585	562	46	blocks	block	NNS
randomwalker-info-585	562	47	propagate	propagate	VBP
randomwalker-info-585	562	48	faster	fast	RBR
randomwalker-info-585	562	49	through	through	IN
randomwalker-info-585	562	50	the	the	DT
randomwalker-info-585	562	51	network	network	NN
randomwalker-info-585	562	52	and	and	CC
randomwalker-info-585	562	53	are	be	VBP
randomwalker-info-585	562	54	less	less	RBR
randomwalker-info-585	562	55	likely	likely	JJ
randomwalker-info-585	562	56	to	to	TO
randomwalker-info-585	562	57	be	be	VB
randomwalker-info-585	562	58	orphaned	orphan	VBN
randomwalker-info-585	562	59	.	.	.
randomwalker-info-585	563	1	Anna	Anna	NNP
randomwalker-info-585	563	2	Karlin	Karlin	NNP
randomwalker-info-585	563	3	,	,	,
randomwalker-info-585	563	4	and	and	CC
randomwalker-info-585	563	5	Rainer	Rainer	NNP
randomwalker-info-585	563	6	Böhme	Böhme	NNP
randomwalker-info-585	563	7	for	for	IN
randomwalker-info-585	563	8	very	very	RB
randomwalker-info-585	563	9	detailed	detailed	JJ
randomwalker-info-585	563	10	feedback	feedback	NN
randomwalker-info-585	563	11	on	on	IN
randomwalker-info-585	563	12	an	an	DT
randomwalker-info-585	563	13	earlier	early	JJR
randomwalker-info-585	563	14	draft	draft	NN
randomwalker-info-585	563	15	of	of	IN
randomwalker-info-585	563	16	this	this	DT
randomwalker-info-585	563	17	paper	paper	NN
randomwalker-info-585	563	18	.	.	.
randomwalker-info-585	564	1	9	9	CD
randomwalker-info-585	564	2	.	.	.
randomwalker-info-585	565	1	REFERENCES	reference	NNS
randomwalker-info-585	565	2	[	[	-LRB-
randomwalker-info-585	565	3	1	1	CD
randomwalker-info-585	565	4	]	]	-RRB-
randomwalker-info-585	565	5	Calibrated	calibrate	VBN
randomwalker-info-585	565	6	learning	learning	NN
randomwalker-info-585	565	7	and	and	CC
randomwalker-info-585	565	8	correlated	correlate	VBD
randomwalker-info-585	565	9	equilibrium	equilibrium	NN
randomwalker-info-585	565	10	.	.	.
randomwalker-info-585	566	1	Games	Games	NNPS
randomwalker-info-585	566	2	and	and	CC
randomwalker-info-585	566	3	Economic	Economic	NNP
randomwalker-info-585	566	4	Behavior	Behavior	NNP
randomwalker-info-585	566	5	,	,	,
randomwalker-info-585	566	6	21(1):40–55	21(1):40–55	CD
randomwalker-info-585	566	7	,	,	,
randomwalker-info-585	566	8	1997	1997	CD
randomwalker-info-585	566	9	.	.	.
randomwalker-info-585	567	1	[	[	-LRB-
randomwalker-info-585	567	2	2	2	LS
randomwalker-info-585	567	3	]	]	-RRB-
randomwalker-info-585	567	4	A	a	DT
randomwalker-info-585	567	5	simple	simple	JJ
randomwalker-info-585	567	6	adaptive	adaptive	JJ
randomwalker-info-585	567	7	procedure	procedure	NN
randomwalker-info-585	567	8	leading	lead	VBG
randomwalker-info-585	567	9	to	to	IN
randomwalker-info-585	567	10	correlated	correlate	VBN
randomwalker-info-585	567	11	equilibrium	equilibrium	NN
randomwalker-info-585	567	12	.	.	.
randomwalker-info-585	568	1	Econometrica	Econometrica	NNP
randomwalker-info-585	568	2	,	,	,
randomwalker-info-585	568	3	68(5):1127–1150	68(5):1127–1150	CD
randomwalker-info-585	568	4	,	,	,
randomwalker-info-585	568	5	2000	2000	CD
randomwalker-info-585	568	6	.	.	.
randomwalker-info-585	569	1	[	[	-LRB-
randomwalker-info-585	569	2	3	3	LS
randomwalker-info-585	569	3	]	]	-RRB-
randomwalker-info-585	569	4	E.	E.	NNP
randomwalker-info-585	569	5	Androulaki	Androulaki	NNP
randomwalker-info-585	569	6	,	,	,
randomwalker-info-585	569	7	G.	G.	NNP
randomwalker-info-585	569	8	O.	O.	NNP
randomwalker-info-585	569	9	Karame	Karame	NNP
randomwalker-info-585	569	10	,	,	,
randomwalker-info-585	569	11	M.	M.	NNP
randomwalker-info-585	569	12	Roeschlin	Roeschlin	NNP
randomwalker-info-585	569	13	,	,	,
randomwalker-info-585	569	14	T.	T.	NNP
randomwalker-info-585	569	15	Scherer	Scherer	NNP
randomwalker-info-585	569	16	,	,	,
randomwalker-info-585	569	17	and	and	CC
randomwalker-info-585	569	18	S.	S.	NNP
randomwalker-info-585	569	19	Capkun	Capkun	NNP
randomwalker-info-585	569	20	.	.	.
randomwalker-info-585	570	1	Evaluating	evaluate	VBG
randomwalker-info-585	570	2	user	user	NN
randomwalker-info-585	570	3	privacy	privacy	NN
randomwalker-info-585	570	4	in	in	IN
randomwalker-info-585	570	5	bitcoin	bitcoin	NN
randomwalker-info-585	570	6	.	.	.
randomwalker-info-585	571	1	In	in	IN
randomwalker-info-585	571	2	Proceedings	Proceedings	NNP
randomwalker-info-585	571	3	of	of	IN
randomwalker-info-585	571	4	Financial	Financial	NNP
randomwalker-info-585	571	5	Cryptography	Cryptography	NNP
randomwalker-info-585	571	6	,	,	,
randomwalker-info-585	571	7	2013	2013	CD
randomwalker-info-585	571	8	.	.	.
randomwalker-info-585	572	1	[	[	-LRB-
randomwalker-info-585	572	2	4	4	CD
randomwalker-info-585	572	3	]	]	-RRB-
randomwalker-info-585	572	4	S.	S.	NNP
randomwalker-info-585	572	5	Arora	Arora	NNP
randomwalker-info-585	572	6	,	,	,
randomwalker-info-585	572	7	E.	E.	NNP
randomwalker-info-585	572	8	Hazan	Hazan	NNP
randomwalker-info-585	572	9	,	,	,
randomwalker-info-585	572	10	and	and	CC
randomwalker-info-585	572	11	S.	S.	NNP
randomwalker-info-585	572	12	Kale	Kale	NNP
randomwalker-info-585	572	13	.	.	.
randomwalker-info-585	573	1	The	the	DT
randomwalker-info-585	573	2	multiplicative	multiplicative	JJ
randomwalker-info-585	573	3	weights	weight	NNS
randomwalker-info-585	573	4	update	update	NN
randomwalker-info-585	573	5	method	method	NN
randomwalker-info-585	573	6	:	:	:
randomwalker-info-585	573	7	a	a	DT
randomwalker-info-585	573	8	meta	meta	JJ
randomwalker-info-585	573	9	-	-	HYPH
randomwalker-info-585	573	10	algorithm	algorithm	NN
randomwalker-info-585	573	11	and	and	CC
randomwalker-info-585	573	12	applications	application	NNS
randomwalker-info-585	573	13	.	.	.
randomwalker-info-585	574	1	Theory	theory	NN
randomwalker-info-585	574	2	of	of	IN
randomwalker-info-585	574	3	Computing	Computing	NNP
randomwalker-info-585	574	4	,	,	,
randomwalker-info-585	574	5	8(1):121–164	8(1):121–164	NNP
randomwalker-info-585	574	6	,	,	,
randomwalker-info-585	574	7	2012	2012	CD
randomwalker-info-585	574	8	.	.	.
randomwalker-info-585	575	1	[	[	-LRB-
randomwalker-info-585	575	2	5	5	CD
randomwalker-info-585	575	3	]	]	-RRB-
randomwalker-info-585	575	4	P.	P.	NNP
randomwalker-info-585	575	5	Auer	Auer	NNP
randomwalker-info-585	575	6	,	,	,
randomwalker-info-585	575	7	N.	N.	NNP
randomwalker-info-585	575	8	Cesa	Cesa	NNP
randomwalker-info-585	575	9	-	-	HYPH
randomwalker-info-585	575	10	Bianchi	Bianchi	NNP
randomwalker-info-585	575	11	,	,	,
randomwalker-info-585	575	12	Y.	Y.	NNP
randomwalker-info-585	575	13	Freund	Freund	NNP
randomwalker-info-585	575	14	,	,	,
randomwalker-info-585	575	15	and	and	CC
randomwalker-info-585	575	16	R.	R.	NNP
randomwalker-info-585	575	17	E.	E.	NNP
randomwalker-info-585	575	18	Schapire	Schapire	NNP
randomwalker-info-585	575	19	.	.	.
randomwalker-info-585	576	1	The	the	DT
randomwalker-info-585	576	2	nonstochastic	nonstochastic	JJ
randomwalker-info-585	576	3	multiarmed	multiarme	VBD
randomwalker-info-585	576	4	bandit	bandit	NN
randomwalker-info-585	576	5	problem	problem	NN
randomwalker-info-585	576	6	.	.	.
randomwalker-info-585	577	1	SIAM	SIAM	NNP
randomwalker-info-585	577	2	Journal	Journal	NNP
randomwalker-info-585	577	3	of	of	IN
randomwalker-info-585	577	4	Computing	Computing	NNP
randomwalker-info-585	577	5	,	,	,
randomwalker-info-585	577	6	32(1):48–77	32(1):48–77	CD
randomwalker-info-585	577	7	,	,	,
randomwalker-info-585	577	8	2002	2002	CD
randomwalker-info-585	577	9	.	.	.
randomwalker-info-585	578	1	[	[	-LRB-
randomwalker-info-585	578	2	6	6	CD
randomwalker-info-585	578	3	]	]	-RRB-
randomwalker-info-585	578	4	A.	a.	NN
randomwalker-info-585	578	5	Blum	Blum	NNP
randomwalker-info-585	578	6	and	and	CC
randomwalker-info-585	578	7	Y.	Y.	NNP
randomwalker-info-585	578	8	Mansour	Mansour	NNP
randomwalker-info-585	578	9	.	.	.
randomwalker-info-585	579	1	From	from	IN
randomwalker-info-585	579	2	external	external	JJ
randomwalker-info-585	579	3	to	to	IN
randomwalker-info-585	579	4	internal	internal	JJ
randomwalker-info-585	579	5	regret	regret	NN
randomwalker-info-585	579	6	.	.	.
randomwalker-info-585	580	1	Journal	Journal	NNP
randomwalker-info-585	580	2	of	of	IN
randomwalker-info-585	580	3	Machine	Machine	NNP
randomwalker-info-585	580	4	Learning	Learning	NNP
randomwalker-info-585	580	5	Research	Research	NNP
randomwalker-info-585	580	6	,	,	,
randomwalker-info-585	580	7	8:1307–1324	8:1307–1324	CD
randomwalker-info-585	580	8	,	,	,
randomwalker-info-585	580	9	2007	2007	CD
randomwalker-info-585	580	10	.	.	.
randomwalker-info-585	581	1	[	[	-LRB-
randomwalker-info-585	581	2	7	7	CD
randomwalker-info-585	581	3	]	]	-RRB-
randomwalker-info-585	581	4	N.	N.	NNP
randomwalker-info-585	581	5	T.	T.	NNP
randomwalker-info-585	581	6	Courtois	Courtois	NNP
randomwalker-info-585	581	7	and	and	CC
randomwalker-info-585	581	8	L.	L.	NNP
randomwalker-info-585	581	9	Bahack	Bahack	NNP
randomwalker-info-585	581	10	.	.	.
randomwalker-info-585	582	1	On	on	IN
randomwalker-info-585	582	2	subversive	subversive	JJ
randomwalker-info-585	582	3	miner	miner	NN
randomwalker-info-585	582	4	strategies	strategy	NNS
randomwalker-info-585	582	5	and	and	CC
randomwalker-info-585	582	6	block	block	NN
randomwalker-info-585	582	7	withholding	withholding	NN
randomwalker-info-585	582	8	attack	attack	NN
randomwalker-info-585	582	9	in	in	IN
randomwalker-info-585	582	10	bitcoin	bitcoin	NNP
randomwalker-info-585	582	11	digital	digital	NNP
randomwalker-info-585	582	12	currency	currency	NN
randomwalker-info-585	582	13	.	.	.
randomwalker-info-585	583	1	CoRR	CoRR	NNP
randomwalker-info-585	583	2	,	,	,
randomwalker-info-585	583	3	abs/1402.1718	abs/1402.1718	JJS
randomwalker-info-585	583	4	,	,	,
randomwalker-info-585	583	5	2014	2014	CD
randomwalker-info-585	583	6	.	.	.
randomwalker-info-585	584	1	[	[	-LRB-
randomwalker-info-585	584	2	8	8	CD
randomwalker-info-585	584	3	]	]	-RRB-
randomwalker-info-585	584	4	I.	I.	NNP
randomwalker-info-585	584	5	Eyal	Eyal	NNP
randomwalker-info-585	584	6	.	.	.
randomwalker-info-585	585	1	The	the	DT
randomwalker-info-585	585	2	miner	miner	NN
randomwalker-info-585	585	3	’s	’s	POS
randomwalker-info-585	585	4	dilemma	dilemma	NN
randomwalker-info-585	585	5	.	.	.
randomwalker-info-585	586	1	In	in	IN
randomwalker-info-585	586	2	Security	Security	NNP
randomwalker-info-585	586	3	and	and	CC
randomwalker-info-585	586	4	Privacy	Privacy	NNP
randomwalker-info-585	586	5	(	(	-LRB-
randomwalker-info-585	586	6	SP	SP	NNP
randomwalker-info-585	586	7	)	)	-RRB-
randomwalker-info-585	586	8	,	,	,
randomwalker-info-585	586	9	2015	2015	CD
randomwalker-info-585	586	10	IEEE	IEEE	NNP
randomwalker-info-585	586	11	Symposium	Symposium	NNP
randomwalker-info-585	586	12	on	on	RB
randomwalker-info-585	586	13	,	,	,
randomwalker-info-585	586	14	pages	page	NNS
randomwalker-info-585	586	15	89–103	89–103	NNP
randomwalker-info-585	586	16	.	.	.
randomwalker-info-585	587	1	IEEE	IEEE	NNP
randomwalker-info-585	587	2	,	,	,
randomwalker-info-585	587	3	2015	2015	CD
randomwalker-info-585	587	4	.	.	.
randomwalker-info-585	588	1	[	[	-LRB-
randomwalker-info-585	588	2	9	9	CD
randomwalker-info-585	588	3	]	]	-RRB-
randomwalker-info-585	588	4	I.	I.	NNP
randomwalker-info-585	588	5	Eyal	Eyal	NNP
randomwalker-info-585	588	6	and	and	CC
randomwalker-info-585	588	7	E.	E.	NNP
randomwalker-info-585	588	8	G.	G.	NNP
randomwalker-info-585	588	9	Sirer	Sirer	NNP
randomwalker-info-585	588	10	.	.	.
randomwalker-info-585	589	1	Majority	majority	NN
randomwalker-info-585	589	2	is	be	VBZ
randomwalker-info-585	589	3	not	not	RB
randomwalker-info-585	589	4	enough	enough	JJ
randomwalker-info-585	589	5	:	:	:
randomwalker-info-585	589	6	Bitcoin	Bitcoin	NNP
randomwalker-info-585	589	7	mining	mining	NN
randomwalker-info-585	589	8	is	be	VBZ
randomwalker-info-585	589	9	vulnerable	vulnerable	JJ
randomwalker-info-585	589	10	.	.	.
randomwalker-info-585	590	1	In	in	IN
randomwalker-info-585	590	2	Financial	Financial	NNP
randomwalker-info-585	590	3	Cryptography	Cryptography	NNP
randomwalker-info-585	590	4	and	and	CC
randomwalker-info-585	590	5	Data	Data	NNPS
randomwalker-info-585	590	6	Security	Security	NNP
randomwalker-info-585	590	7	,	,	,
randomwalker-info-585	590	8	pages	page	VBZ
randomwalker-info-585	590	9	436–454	436–454	CD
randomwalker-info-585	590	10	.	.	.
randomwalker-info-585	591	1	Springer	Springer	NNP
randomwalker-info-585	591	2	,	,	,
randomwalker-info-585	591	3	2014	2014	CD
randomwalker-info-585	591	4	.	.	.
randomwalker-info-585	592	1	[	[	-LRB-
randomwalker-info-585	592	2	10	10	CD
randomwalker-info-585	592	3	]	]	-RRB-
randomwalker-info-585	592	4	K.	K.	NNP
randomwalker-info-585	592	5	Hill	Hill	NNP
randomwalker-info-585	592	6	.	.	.
randomwalker-info-585	593	1	Bitcoin	Bitcoin	NNP
randomwalker-info-585	593	2	is	be	VBZ
randomwalker-info-585	593	3	not	not	RB
randomwalker-info-585	593	4	broken	break	VBN
randomwalker-info-585	593	5	.	.	.
randomwalker-info-585	594	1	Forbes	Forbes	NNP
randomwalker-info-585	594	2	,	,	,
randomwalker-info-585	594	3	2013	2013	CD
randomwalker-info-585	594	4	.	.	.
randomwalker-info-585	594	5	http://www.forbes.com/sites/kashmirhill/2013/11/	http://www.forbes.com/sites/kashmirhill/2013/11/	JJS
randomwalker-info-585	594	6	06	06	NNP
randomwalker-info-585	594	7	/	/	SYM
randomwalker-info-585	594	8	bitcoin	bitcoin	NN
randomwalker-info-585	594	9	-	-	HYPH
randomwalker-info-585	594	10	is	be	VBZ
randomwalker-info-585	594	11	-	-	HYPH
randomwalker-info-585	594	12	not	not	RB
randomwalker-info-585	594	13	-	-	HYPH
randomwalker-info-585	594	14	broken/#55d4a8812568	broken/#55d4a8812568	NNP
randomwalker-info-585	594	15	.	.	.
randomwalker-info-585	595	1	[	[	-LRB-
randomwalker-info-585	595	2	11	11	CD
randomwalker-info-585	595	3	]	]	-RRB-
randomwalker-info-585	595	4	N.	N.	NNP
randomwalker-info-585	595	5	Houy	Houy	NNP
randomwalker-info-585	595	6	.	.	.
randomwalker-info-585	596	1	The	the	DT
randomwalker-info-585	596	2	economics	economic	NNS
randomwalker-info-585	596	3	of	of	IN
randomwalker-info-585	596	4	bitcoin	bitcoin	NN
randomwalker-info-585	596	5	transaction	transaction	NN
randomwalker-info-585	596	6	fees	fee	NNS
randomwalker-info-585	596	7	.	.	.
randomwalker-info-585	597	1	Working	Working	NNP
randomwalker-info-585	597	2	Paper	Paper	NNP
randomwalker-info-585	597	3	GATE	GATE	NNP
randomwalker-info-585	597	4	2014	2014	CD
randomwalker-info-585	597	5	-	-	SYM
randomwalker-info-585	597	6	07	07	CD
randomwalker-info-585	597	7	.	.	.
randomwalker-info-585	598	1	halshs-00951358	halshs-00951358	NNP
randomwalker-info-585	598	2	.	.	.
randomwalker-info-585	598	3	,	,	,
randomwalker-info-585	598	4	2014	2014	CD
randomwalker-info-585	598	5	.	.	.
randomwalker-info-585	599	1	[	[	-LRB-
randomwalker-info-585	599	2	12	12	CD
randomwalker-info-585	599	3	]	]	-RRB-
randomwalker-info-585	599	4	B.	B.	NNP
randomwalker-info-585	599	5	Johnson	Johnson	NNP
randomwalker-info-585	599	6	,	,	,
randomwalker-info-585	599	7	A.	A.	NNP
randomwalker-info-585	599	8	Laszka	Laszka	NNP
randomwalker-info-585	599	9	,	,	,
randomwalker-info-585	599	10	J.	J.	NNP
randomwalker-info-585	599	11	Grossklags	Grossklags	NNP
randomwalker-info-585	599	12	,	,	,
randomwalker-info-585	599	13	M.	M.	NNP
randomwalker-info-585	599	14	Vasek	Vasek	NNP
randomwalker-info-585	599	15	,	,	,
randomwalker-info-585	599	16	and	and	CC
randomwalker-info-585	599	17	T.	T.	NNP
randomwalker-info-585	599	18	Moore	Moore	NNP
randomwalker-info-585	599	19	.	.	.
randomwalker-info-585	600	1	Game	game	NN
randomwalker-info-585	600	2	-	-	HYPH
randomwalker-info-585	600	3	theoretic	theoretic	JJ
randomwalker-info-585	600	4	analysis	analysis	NN
randomwalker-info-585	600	5	of	of	IN
randomwalker-info-585	600	6	ddos	ddos	NNP
randomwalker-info-585	600	7	attacks	attack	NNS
randomwalker-info-585	600	8	against	against	IN
randomwalker-info-585	600	9	bitcoin	bitcoin	NN
randomwalker-info-585	600	10	mining	mining	NN
randomwalker-info-585	600	11	pools	pool	NNS
randomwalker-info-585	600	12	.	.	.
randomwalker-info-585	601	1	In	in	IN
randomwalker-info-585	601	2	Proceedings	Proceedings	NNP
randomwalker-info-585	601	3	of	of	IN
randomwalker-info-585	601	4	the	the	DT
randomwalker-info-585	601	5	First	First	NNP
randomwalker-info-585	601	6	Workshop	Workshop	NNP
randomwalker-info-585	601	7	on	on	IN
randomwalker-info-585	601	8	Bitcoin	Bitcoin	NNP
randomwalker-info-585	601	9	Research	Research	NNP
randomwalker-info-585	601	10	,	,	,
randomwalker-info-585	601	11	2014	2014	CD
randomwalker-info-585	601	12	.	.	.
randomwalker-info-585	602	1	[	[	-LRB-
randomwalker-info-585	602	2	13	13	CD
randomwalker-info-585	602	3	]	]	-RRB-
randomwalker-info-585	602	4	A.	a.	NN
randomwalker-info-585	602	5	Kiayias	Kiayias	NNP
randomwalker-info-585	602	6	,	,	,
randomwalker-info-585	602	7	E.	E.	NNP
randomwalker-info-585	602	8	Koutsoupias	Koutsoupias	NNP
randomwalker-info-585	602	9	,	,	,
randomwalker-info-585	602	10	M.	M.	NNP
randomwalker-info-585	602	11	Kyropoulou	Kyropoulou	NNP
randomwalker-info-585	602	12	,	,	,
randomwalker-info-585	602	13	and	and	CC
randomwalker-info-585	602	14	Y.	Y.	NNP
randomwalker-info-585	602	15	Tselekounis	Tselekounis	NNP
randomwalker-info-585	602	16	.	.	.
randomwalker-info-585	603	1	Blockchain	Blockchain	NNP
randomwalker-info-585	603	2	mining	mining	NN
randomwalker-info-585	603	3	games	game	NNS
randomwalker-info-585	603	4	.	.	.
randomwalker-info-585	604	1	In	in	IN
randomwalker-info-585	604	2	ACM	ACM	NNP
randomwalker-info-585	604	3	Conference	Conference	NNP
randomwalker-info-585	604	4	on	on	IN
randomwalker-info-585	604	5	Economics	Economics	NNP
randomwalker-info-585	604	6	and	and	CC
randomwalker-info-585	604	7	Computation	Computation	NNP
randomwalker-info-585	604	8	(	(	-LRB-
randomwalker-info-585	604	9	EC	EC	NNP
randomwalker-info-585	604	10	)	)	-RRB-
randomwalker-info-585	604	11	,	,	,
randomwalker-info-585	604	12	2016	2016	CD
randomwalker-info-585	604	13	.	.	.
randomwalker-info-585	605	1	[	[	-LRB-
randomwalker-info-585	605	2	14	14	CD
randomwalker-info-585	605	3	]	]	-RRB-
randomwalker-info-585	605	4	J.	J.	NNP
randomwalker-info-585	606	1	A.	A.	NNP
randomwalker-info-585	606	2	Kroll	Kroll	NNP
randomwalker-info-585	606	3	,	,	,
randomwalker-info-585	606	4	I.	I.	NNP
randomwalker-info-585	606	5	C.	C.	NNP
randomwalker-info-585	606	6	Davey	Davey	NNP
randomwalker-info-585	606	7	,	,	,
randomwalker-info-585	606	8	and	and	CC
randomwalker-info-585	606	9	E.	E.	NNP
randomwalker-info-585	606	10	W.	W.	NNP
randomwalker-info-585	606	11	Felten	Felten	NNP
randomwalker-info-585	606	12	.	.	.
randomwalker-info-585	607	1	The	the	DT
randomwalker-info-585	607	2	economics	economic	NNS
randomwalker-info-585	607	3	of	of	IN
randomwalker-info-585	607	4	bitcoin	bitcoin	NN
randomwalker-info-585	607	5	mining	mining	NN
randomwalker-info-585	607	6	,	,	,
randomwalker-info-585	607	7	or	or	CC
randomwalker-info-585	607	8	bitcoin	bitcoin	NN
randomwalker-info-585	607	9	in	in	IN
randomwalker-info-585	607	10	the	the	DT
randomwalker-info-585	607	11	presence	presence	NN
randomwalker-info-585	607	12	of	of	IN
randomwalker-info-585	607	13	adversaries	adversary	NNS
randomwalker-info-585	607	14	.	.	.
randomwalker-info-585	608	1	In	in	IN
randomwalker-info-585	608	2	Proceedings	Proceedings	NNP
randomwalker-info-585	608	3	of	of	IN
randomwalker-info-585	608	4	the	the	DT
randomwalker-info-585	608	5	Twelfth	Twelfth	NNP
randomwalker-info-585	608	6	Annual	Annual	NNP
randomwalker-info-585	608	7	Workshop	Workshop	NNP
randomwalker-info-585	608	8	on	on	IN
randomwalker-info-585	608	9	the	the	DT
randomwalker-info-585	608	10	Economics	Economics	NNP
randomwalker-info-585	608	11	of	of	IN
randomwalker-info-585	608	12	Information	Information	NNP
randomwalker-info-585	608	13	Security	Security	NNP
randomwalker-info-585	608	14	(	(	-LRB-
randomwalker-info-585	608	15	WEIS	WEIS	NNP
randomwalker-info-585	608	16	)	)	-RRB-
randomwalker-info-585	608	17	,	,	,
randomwalker-info-585	608	18	2013	2013	CD
randomwalker-info-585	608	19	.	.	.
randomwalker-info-585	609	1	[	[	-LRB-
randomwalker-info-585	609	2	15	15	CD
randomwalker-info-585	609	3	]	]	-RRB-
randomwalker-info-585	609	4	N.	N.	NNP
randomwalker-info-585	609	5	Littlestone	Littlestone	NNP
randomwalker-info-585	609	6	and	and	CC
randomwalker-info-585	609	7	M.	M.	NNP
randomwalker-info-585	609	8	K.	K.	NNP
randomwalker-info-585	609	9	Warmuth	Warmuth	NNP
randomwalker-info-585	609	10	.	.	.
randomwalker-info-585	610	1	The	the	DT
randomwalker-info-585	610	2	weighted	weighted	JJ
randomwalker-info-585	610	3	majority	majority	NN
randomwalker-info-585	610	4	algorithm	algorithm	NN
randomwalker-info-585	610	5	.	.	.
randomwalker-info-585	611	1	Inf	inf	NN
randomwalker-info-585	611	2	.	.	.
randomwalker-info-585	612	1	Comput	comput	NN
randomwalker-info-585	612	2	.	.	.
randomwalker-info-585	612	3	,	,	,
randomwalker-info-585	612	4	108(2):212–261	108(2):212–261	CD
randomwalker-info-585	612	5	,	,	,
randomwalker-info-585	612	6	1994	1994	CD
randomwalker-info-585	612	7	.	.	.
randomwalker-info-585	613	1	[	[	-LRB-
randomwalker-info-585	613	2	16	16	CD
randomwalker-info-585	613	3	]	]	-RRB-
randomwalker-info-585	613	4	L.	L.	NNP
randomwalker-info-585	613	5	Luu	Luu	NNP
randomwalker-info-585	613	6	,	,	,
randomwalker-info-585	613	7	J.	J.	NNP
randomwalker-info-585	613	8	Teutsch	Teutsch	NNP
randomwalker-info-585	613	9	,	,	,
randomwalker-info-585	613	10	R.	R.	NNP
randomwalker-info-585	613	11	Kulkarni	Kulkarni	NNP
randomwalker-info-585	613	12	,	,	,
randomwalker-info-585	613	13	and	and	CC
randomwalker-info-585	613	14	P.	P.	NNP
randomwalker-info-585	613	15	Saxena	Saxena	NNP
randomwalker-info-585	613	16	.	.	.
randomwalker-info-585	614	1	Demystifying	Demystifying	NNP
randomwalker-info-585	614	2	incentives	incentive	NNS
randomwalker-info-585	614	3	in	in	IN
randomwalker-info-585	614	4	the	the	DT
randomwalker-info-585	614	5	consensus	consensus	NN
randomwalker-info-585	614	6	computer	computer	NN
randomwalker-info-585	614	7	.	.	.
randomwalker-info-585	615	1	In	in	IN
randomwalker-info-585	615	2	Proceedings	Proceedings	NNP
randomwalker-info-585	615	3	of	of	IN
randomwalker-info-585	615	4	the	the	DT
randomwalker-info-585	615	5	ACM	ACM	NNP
randomwalker-info-585	615	6	Conference	Conference	NNP
randomwalker-info-585	615	7	on	on	IN
randomwalker-info-585	615	8	Computer	Computer	NNP
randomwalker-info-585	615	9	and	and	CC
randomwalker-info-585	615	10	Communications	Communications	NNPS
randomwalker-info-585	615	11	Security	Security	NNP
randomwalker-info-585	615	12	(	(	-LRB-
randomwalker-info-585	615	13	CCS	CCS	NNP
randomwalker-info-585	615	14	)	)	-RRB-
randomwalker-info-585	615	15	,	,	,
randomwalker-info-585	615	16	2015	2015	CD
randomwalker-info-585	615	17	.	.	.
randomwalker-info-585	616	1	[	[	-LRB-
randomwalker-info-585	616	2	17	17	CD
randomwalker-info-585	616	3	]	]	-RRB-
randomwalker-info-585	616	4	A.	a.	NN
randomwalker-info-585	616	5	Miller	Miller	NNP
randomwalker-info-585	616	6	and	and	CC
randomwalker-info-585	616	7	R.	R.	NNP
randomwalker-info-585	616	8	Jansen	Jansen	NNP
randomwalker-info-585	616	9	.	.	.
randomwalker-info-585	617	1	Shadow	Shadow	NNP
randomwalker-info-585	617	2	-	-	HYPH
randomwalker-info-585	617	3	bitcoin	bitcoin	NNP
randomwalker-info-585	617	4	:	:	:
randomwalker-info-585	617	5	scalable	scalable	JJ
randomwalker-info-585	617	6	simulation	simulation	NN
randomwalker-info-585	617	7	via	via	IN
randomwalker-info-585	617	8	direct	direct	JJ
randomwalker-info-585	617	9	execution	execution	NN
randomwalker-info-585	617	10	of	of	IN
randomwalker-info-585	617	11	multithreaded	multithreaded	JJ
randomwalker-info-585	617	12	applications	application	NNS
randomwalker-info-585	617	13	.	.	.
randomwalker-info-585	618	1	In	in	IN
randomwalker-info-585	618	2	Proceedings	proceeding	NNS
randomwalker-info-585	618	3	of	of	IN
randomwalker-info-585	618	4	the	the	DT
randomwalker-info-585	618	5	eighth	eighth	JJ
randomwalker-info-585	618	6	workshop	workshop	NN
randomwalker-info-585	618	7	on	on	IN
randomwalker-info-585	618	8	Cybersecurity	Cybersecurity	NNP
randomwalker-info-585	618	9	Experimentations	Experimentations	NNP
randomwalker-info-585	618	10	and	and	CC
randomwalker-info-585	618	11	Test	Test	NNP
randomwalker-info-585	618	12	(	(	-LRB-
randomwalker-info-585	618	13	CSET	cset	NN
randomwalker-info-585	618	14	)	)	-RRB-
randomwalker-info-585	618	15	,	,	,
randomwalker-info-585	618	16	2015	2015	CD
randomwalker-info-585	618	17	.	.	.
randomwalker-info-585	619	1	[	[	-LRB-
randomwalker-info-585	619	2	18	18	CD
randomwalker-info-585	619	3	]	]	-RRB-
randomwalker-info-585	619	4	M.	M.	NNP
randomwalker-info-585	619	5	Möser	Möser	NNP
randomwalker-info-585	619	6	and	and	CC
randomwalker-info-585	619	7	R.	R.	NNP
randomwalker-info-585	619	8	Böhme	Böhme	NNP
randomwalker-info-585	619	9	.	.	.
randomwalker-info-585	620	1	Trends	trend	NNS
randomwalker-info-585	620	2	,	,	,
randomwalker-info-585	620	3	tips	tip	NNS
randomwalker-info-585	620	4	,	,	,
randomwalker-info-585	620	5	tolls	toll	NNS
randomwalker-info-585	620	6	:	:	:
randomwalker-info-585	620	7	A	a	DT
randomwalker-info-585	620	8	longitudinal	longitudinal	JJ
randomwalker-info-585	620	9	study	study	NN
randomwalker-info-585	620	10	of	of	IN
randomwalker-info-585	620	11	bitcoin	bitcoin	NN
randomwalker-info-585	620	12	transaction	transaction	NN
randomwalker-info-585	620	13	fees	fee	NNS
randomwalker-info-585	620	14	.	.	.
randomwalker-info-585	621	1	In	in	IN
randomwalker-info-585	621	2	Workshop	Workshop	NNP
randomwalker-info-585	621	3	on	on	IN
randomwalker-info-585	621	4	Bitcoin	Bitcoin	NNP
randomwalker-info-585	621	5	Research	Research	NNP
randomwalker-info-585	621	6	,	,	,
randomwalker-info-585	621	7	pages	page	VBZ
randomwalker-info-585	621	8	19–33	19–33	CD
randomwalker-info-585	621	9	,	,	,
randomwalker-info-585	621	10	2015	2015	CD
randomwalker-info-585	621	11	.	.	.
randomwalker-info-585	622	1	[	[	-LRB-
randomwalker-info-585	622	2	19	19	CD
randomwalker-info-585	622	3	]	]	-RRB-
randomwalker-info-585	622	4	S.	S.	NNP
randomwalker-info-585	622	5	Nakamoto	Nakamoto	NNP
randomwalker-info-585	622	6	.	.	.
randomwalker-info-585	623	1	Bitcoin	Bitcoin	NNP
randomwalker-info-585	623	2	:	:	:
randomwalker-info-585	623	3	A	a	DT
randomwalker-info-585	623	4	peer	peer	NN
randomwalker-info-585	623	5	-	-	HYPH
randomwalker-info-585	623	6	to	to	IN
randomwalker-info-585	623	7	-	-	HYPH
randomwalker-info-585	623	8	peer	peer	NN
randomwalker-info-585	623	9	electronic	electronic	JJ
randomwalker-info-585	623	10	cash	cash	NN
randomwalker-info-585	623	11	system	system	NN
randomwalker-info-585	623	12	,	,	,
randomwalker-info-585	623	13	2008	2008	CD
randomwalker-info-585	623	14	.	.	.
randomwalker-info-585	624	1	[	[	-LRB-
randomwalker-info-585	624	2	20	20	CD
randomwalker-info-585	624	3	]	]	-RRB-
randomwalker-info-585	624	4	K.	K.	NNP
randomwalker-info-585	624	5	Nayak	Nayak	NNP
randomwalker-info-585	624	6	,	,	,
randomwalker-info-585	624	7	S.	S.	NNP
randomwalker-info-585	624	8	Kumar	Kumar	NNP
randomwalker-info-585	624	9	,	,	,
randomwalker-info-585	624	10	A.	a.	NN
randomwalker-info-585	624	11	Miller	Miller	NNP
randomwalker-info-585	624	12	,	,	,
randomwalker-info-585	624	13	and	and	CC
randomwalker-info-585	624	14	E.	E.	NNP
randomwalker-info-585	624	15	Shi	Shi	NNP
randomwalker-info-585	624	16	.	.	.
randomwalker-info-585	625	1	Stubborn	stubborn	JJ
randomwalker-info-585	625	2	mining	mining	NN
randomwalker-info-585	625	3	:	:	:
randomwalker-info-585	625	4	Generalizing	generalize	VBG
randomwalker-info-585	625	5	selfish	selfish	JJ
randomwalker-info-585	625	6	mining	mining	NN
randomwalker-info-585	625	7	and	and	CC
randomwalker-info-585	625	8	combining	combine	VBG
randomwalker-info-585	625	9	with	with	IN
randomwalker-info-585	625	10	an	an	DT
randomwalker-info-585	625	11	eclipse	eclipse	NN
randomwalker-info-585	625	12	attack	attack	NN
randomwalker-info-585	625	13	.	.	.
randomwalker-info-585	626	1	In	in	IN
randomwalker-info-585	626	2	IEEE	IEEE	NNP
randomwalker-info-585	626	3	European	European	NNP
randomwalker-info-585	626	4	Symposium	Symposium	NNP
randomwalker-info-585	626	5	on	on	IN
randomwalker-info-585	626	6	Security	Security	NNP
randomwalker-info-585	626	7	and	and	CC
randomwalker-info-585	626	8	Privacy	Privacy	NNP
randomwalker-info-585	626	9	(	(	-LRB-
randomwalker-info-585	626	10	EuroS&P	EuroS&P	NNP
randomwalker-info-585	626	11	)	)	-RRB-
randomwalker-info-585	626	12	,	,	,
randomwalker-info-585	626	13	2016	2016	CD
randomwalker-info-585	626	14	.	.	.
randomwalker-info-585	627	1	[	[	-LRB-
randomwalker-info-585	627	2	21	21	CD
randomwalker-info-585	627	3	]	]	-RRB-
randomwalker-info-585	627	4	R.	R.	NNP
randomwalker-info-585	627	5	Peter	Peter	NNP
randomwalker-info-585	627	6	.	.	.
randomwalker-info-585	628	1	A	a	DT
randomwalker-info-585	628	2	transaction	transaction	NN
randomwalker-info-585	628	3	fee	fee	NN
randomwalker-info-585	628	4	market	market	NN
randomwalker-info-585	628	5	exists	exist	VBZ
randomwalker-info-585	628	6	without	without	IN
randomwalker-info-585	628	7	a	a	DT
randomwalker-info-585	628	8	block	block	NN
randomwalker-info-585	628	9	size	size	NN
randomwalker-info-585	628	10	limit	limit	NN
randomwalker-info-585	628	11	.	.	.
randomwalker-info-585	629	1	2015	2015	CD
randomwalker-info-585	629	2	.	.	.
randomwalker-info-585	630	1	[	[	-LRB-
randomwalker-info-585	630	2	22	22	CD
randomwalker-info-585	630	3	]	]	-RRB-
randomwalker-info-585	630	4	M.	M.	NNP
randomwalker-info-585	630	5	Rosenfeld	Rosenfeld	NNP
randomwalker-info-585	630	6	.	.	.
randomwalker-info-585	631	1	Analysis	analysis	NN
randomwalker-info-585	631	2	of	of	IN
randomwalker-info-585	631	3	bitcoin	bitcoin	NN
randomwalker-info-585	631	4	pooled	pool	VBN
randomwalker-info-585	631	5	mining	mining	NN
randomwalker-info-585	631	6	reward	reward	NN
randomwalker-info-585	631	7	systems	system	NNS
randomwalker-info-585	631	8	.	.	.
randomwalker-info-585	632	1	CoRR	CoRR	NNP
randomwalker-info-585	632	2	,	,	,
randomwalker-info-585	632	3	abs/1112.4980	abs/1112.4980	NNP
randomwalker-info-585	632	4	,	,	,
randomwalker-info-585	632	5	2011	2011	CD
randomwalker-info-585	632	6	.	.	.
randomwalker-info-585	633	1	[	[	-LRB-
randomwalker-info-585	633	2	23	23	CD
randomwalker-info-585	633	3	]	]	-RRB-
randomwalker-info-585	633	4	A.	a.	NN
randomwalker-info-585	633	5	Sapirshtein	Sapirshtein	NNP
randomwalker-info-585	633	6	,	,	,
randomwalker-info-585	633	7	Y.	Y.	NNP
randomwalker-info-585	633	8	Sompolinsky	Sompolinsky	NNP
randomwalker-info-585	633	9	,	,	,
randomwalker-info-585	633	10	and	and	CC
randomwalker-info-585	633	11	A.	A.	NNP
randomwalker-info-585	633	12	Zohar	Zohar	NNP
randomwalker-info-585	633	13	.	.	.
randomwalker-info-585	634	1	Optimal	optimal	JJ
randomwalker-info-585	634	2	selfish	selfish	JJ
randomwalker-info-585	634	3	mining	mining	NN
randomwalker-info-585	634	4	strategies	strategy	NNS
randomwalker-info-585	634	5	in	in	IN
randomwalker-info-585	634	6	bitcoin	bitcoin	NN
randomwalker-info-585	634	7	.	.	.
randomwalker-info-585	635	1	In	in	IN
randomwalker-info-585	635	2	Financial	Financial	NNP
randomwalker-info-585	635	3	Cryptography	Cryptography	NNP
randomwalker-info-585	635	4	and	and	CC
randomwalker-info-585	635	5	Data	Data	NNPS
randomwalker-info-585	635	6	Security	Security	NNP
randomwalker-info-585	635	7	,	,	,
randomwalker-info-585	635	8	2016	2016	CD
randomwalker-info-585	635	9	.	.	.
randomwalker-info-585	636	1	[	[	-LRB-
randomwalker-info-585	636	2	24	24	CD
randomwalker-info-585	636	3	]	]	-RRB-
randomwalker-info-585	636	4	M.	M.	NNP
randomwalker-info-585	636	5	Vasek	Vasek	NNP
randomwalker-info-585	636	6	,	,	,
randomwalker-info-585	636	7	M.	M.	NNP
randomwalker-info-585	636	8	Thornton	Thornton	NNP
randomwalker-info-585	636	9	,	,	,
randomwalker-info-585	636	10	and	and	CC
randomwalker-info-585	636	11	T.	T.	NNP
randomwalker-info-585	636	12	Moore	Moore	NNP
randomwalker-info-585	636	13	.	.	.
randomwalker-info-585	637	1	Empirical	empirical	JJ
randomwalker-info-585	637	2	analysis	analysis	NN
randomwalker-info-585	637	3	of	of	IN
randomwalker-info-585	637	4	denial	denial	JJ
randomwalker-info-585	637	5	-	-	HYPH
randomwalker-info-585	637	6	of	of	IN
randomwalker-info-585	637	7	-	-	HYPH
randomwalker-info-585	637	8	service	service	NN
randomwalker-info-585	637	9	attacks	attack	NNS
randomwalker-info-585	637	10	in	in	IN
randomwalker-info-585	637	11	the	the	DT
randomwalker-info-585	637	12	bitcoin	bitcoin	NN
randomwalker-info-585	637	13	ecosystem	ecosystem	NN
randomwalker-info-585	637	14	.	.	.
randomwalker-info-585	638	1	In	in	IN
randomwalker-info-585	638	2	Proceedings	Proceedings	NNP
randomwalker-info-585	638	3	of	of	IN
randomwalker-info-585	638	4	the	the	DT
randomwalker-info-585	638	5	First	First	NNP
randomwalker-info-585	638	6	Workshop	Workshop	NNP
randomwalker-info-585	638	7	on	on	IN
randomwalker-info-585	638	8	Bitcoin	Bitcoin	NNP
randomwalker-info-585	638	9	Research	Research	NNP
randomwalker-info-585	638	10	,	,	,
randomwalker-info-585	638	11	2014	2014	CD
randomwalker-info-585	638	12	.	.	.
randomwalker-info-585	639	1	APPENDIX	APPENDIX	NNP
randomwalker-info-585	639	2	A.	A.	NNP
randomwalker-info-585	640	1	MINING	MINING	NNP
randomwalker-info-585	640	2	GAP	GAP	NNP
randomwalker-info-585	640	3	This	this	DT
randomwalker-info-585	640	4	appendix	appendix	NNP
randomwalker-info-585	640	5	contains	contain	VBZ
randomwalker-info-585	640	6	a	a	DT
randomwalker-info-585	640	7	theoretical	theoretical	JJ
randomwalker-info-585	640	8	analysis	analysis	NN
randomwalker-info-585	640	9	of	of	IN
randomwalker-info-585	640	10	the	the	DT
randomwalker-info-585	640	11	mining	mining	NN
randomwalker-info-585	640	12	gaps	gap	NNS
randomwalker-info-585	640	13	referenced	reference	VBD
randomwalker-info-585	640	14	in	in	IN
randomwalker-info-585	640	15	Section	section	NN
randomwalker-info-585	640	16	3.2	3.2	CD
randomwalker-info-585	640	17	.	.	.
randomwalker-info-585	641	1	Let	let	VB
randomwalker-info-585	641	2	’s	-PRON-	PRP
randomwalker-info-585	641	3	consider	consider	VB
randomwalker-info-585	641	4	the	the	DT
randomwalker-info-585	641	5	following	follow	VBG
randomwalker-info-585	641	6	simplified	simplified	JJ
randomwalker-info-585	641	7	model	model	NN
randomwalker-info-585	641	8	:	:	:
randomwalker-info-585	641	9	there	there	EX
randomwalker-info-585	641	10	is	be	VBZ
randomwalker-info-585	641	11	one	one	CD
randomwalker-info-585	641	12	style	style	NN
randomwalker-info-585	641	13	of	of	IN
randomwalker-info-585	641	14	“	"	``
randomwalker-info-585	641	15	rig	rig	NN
randomwalker-info-585	641	16	”	"	''
randomwalker-info-585	641	17	available	available	JJ
randomwalker-info-585	641	18	to	to	IN
randomwalker-info-585	641	19	miners	miner	NNS
randomwalker-info-585	641	20	,	,	,
randomwalker-info-585	641	21	which	which	WDT
randomwalker-info-585	641	22	costs	cost	VBZ
randomwalker-info-585	641	23	p	p	NN
randomwalker-info-585	641	24	BTC	btc	NN
randomwalker-info-585	641	25	per	per	IN
randomwalker-info-585	641	26	time	time	NN
randomwalker-info-585	641	27	unit	unit	NN
randomwalker-info-585	641	28	in	in	IN
randomwalker-info-585	641	29	electricity	electricity	NN
randomwalker-info-585	641	30	to	to	TO
randomwalker-info-585	641	31	run	run	VB
randomwalker-info-585	641	32	.	.	.
randomwalker-info-585	642	1	Let	let	VB
randomwalker-info-585	642	2	’s	-PRON-	PRP
randomwalker-info-585	642	3	first	first	RB
randomwalker-info-585	642	4	analyze	analyze	VB
randomwalker-info-585	642	5	what	what	WDT
randomwalker-info-585	642	6	effect	effect	NN
randomwalker-info-585	642	7	this	this	DT
randomwalker-info-585	642	8	has	have	VBZ
randomwalker-info-585	642	9	in	in	IN
randomwalker-info-585	642	10	the	the	DT
randomwalker-info-585	642	11	fixed	fixed	JJ
randomwalker-info-585	642	12	reward	reward	NN
randomwalker-info-585	642	13	model	model	NN
randomwalker-info-585	642	14	,	,	,
randomwalker-info-585	642	15	where	where	WRB
randomwalker-info-585	642	16	each	each	DT
randomwalker-info-585	642	17	block	block	NN
randomwalker-info-585	642	18	found	find	VBD
randomwalker-info-585	642	19	is	be	VBZ
randomwalker-info-585	642	20	worth	worth	JJ
randomwalker-info-585	642	21	one	one	CD
randomwalker-info-585	642	22	BTC	BTC	NNP
randomwalker-info-585	642	23	,	,	,
randomwalker-info-585	642	24	and	and	CC
randomwalker-info-585	642	25	the	the	DT
randomwalker-info-585	642	26	difficulty	difficulty	NN
randomwalker-info-585	642	27	is	be	VBZ
randomwalker-info-585	642	28	adjusted	adjust	VBN
randomwalker-info-585	642	29	so	so	IN
randomwalker-info-585	642	30	that	that	IN
randomwalker-info-585	642	31	the	the	DT
randomwalker-info-585	642	32	time	time	NN
randomwalker-info-585	642	33	between	between	IN
randomwalker-info-585	642	34	successive	successive	JJ
randomwalker-info-585	642	35	blocks	block	NNS
randomwalker-info-585	642	36	is	be	VBZ
randomwalker-info-585	642	37	one	one	CD
randomwalker-info-585	642	38	unit	unit	NN
randomwalker-info-585	642	39	in	in	IN
randomwalker-info-585	642	40	expectation	expectation	NN
randomwalker-info-585	642	41	.	.	.
randomwalker-info-585	643	1	Then	then	RB
randomwalker-info-585	643	2	if	if	IN
randomwalker-info-585	643	3	there	there	EX
randomwalker-info-585	643	4	are	be	VBP
randomwalker-info-585	643	5	k	k	NN
randomwalker-info-585	643	6	rigs	rig	NNS
randomwalker-info-585	643	7	in	in	IN
randomwalker-info-585	643	8	the	the	DT
randomwalker-info-585	643	9	network	network	NN
randomwalker-info-585	643	10	,	,	,
randomwalker-info-585	643	11	the	the	DT
randomwalker-info-585	643	12	expected	expected	JJ
randomwalker-info-585	643	13	reward	reward	NN
randomwalker-info-585	643	14	from	from	IN
randomwalker-info-585	643	15	running	run	VBG
randomwalker-info-585	643	16	a	a	DT
randomwalker-info-585	643	17	rig	rig	NN
randomwalker-info-585	643	18	for	for	IN
randomwalker-info-585	643	19	one	one	CD
randomwalker-info-585	643	20	time	time	NN
randomwalker-info-585	643	21	unit	unit	NN
randomwalker-info-585	643	22	is	be	VBZ
randomwalker-info-585	643	23	exactly	exactly	RB
randomwalker-info-585	643	24	1	1	CD
randomwalker-info-585	643	25	/	/	SYM
randomwalker-info-585	643	26	k	k	NNS
randomwalker-info-585	643	27	,	,	,
randomwalker-info-585	643	28	whereas	whereas	IN
randomwalker-info-585	643	29	the	the	DT
randomwalker-info-585	643	30	cost	cost	NN
randomwalker-info-585	643	31	in	in	IN
randomwalker-info-585	643	32	electricity	electricity	NN
randomwalker-info-585	643	33	is	be	VBZ
randomwalker-info-585	643	34	p.	p.	NN
randomwalker-info-585	643	35	So	so	RB
randomwalker-info-585	643	36	the	the	DT
randomwalker-info-585	643	37	network	network	NN
randomwalker-info-585	643	38	is	be	VBZ
randomwalker-info-585	643	39	sustainable	sustainable	JJ
randomwalker-info-585	643	40	as	as	RB
randomwalker-info-585	643	41	long	long	RB
randomwalker-info-585	643	42	as	as	IN
randomwalker-info-585	643	43	1	1	CD
randomwalker-info-585	643	44	/	/	SYM
randomwalker-info-585	643	45	k	k	NN
randomwalker-info-585	643	46	≥	≥	NNP
randomwalker-info-585	643	47	p	p	NN
randomwalker-info-585	643	48	,	,	,
randomwalker-info-585	643	49	or	or	CC
randomwalker-info-585	643	50	k	k	NNP
randomwalker-info-585	643	51	≤	≤	NNP
randomwalker-info-585	643	52	1	1	CD
randomwalker-info-585	643	53	/	/	SYM
randomwalker-info-585	643	54	p	p	NN
randomwalker-info-585	643	55	.	.	.
randomwalker-info-585	644	1	In	in	IN
randomwalker-info-585	644	2	other	other	JJ
randomwalker-info-585	644	3	words	word	NNS
randomwalker-info-585	644	4	,	,	,
randomwalker-info-585	644	5	the	the	DT
randomwalker-info-585	644	6	cost	cost	NN
randomwalker-info-585	644	7	of	of	IN
randomwalker-info-585	644	8	electricity	electricity	NN
randomwalker-info-585	644	9	imposes	impose	VBZ
randomwalker-info-585	644	10	a	a	DT
randomwalker-info-585	644	11	hard	hard	JJ
randomwalker-info-585	644	12	cap	cap	NN
randomwalker-info-585	644	13	on	on	IN
randomwalker-info-585	644	14	the	the	DT
randomwalker-info-585	644	15	total	total	JJ
randomwalker-info-585	644	16	effective	effective	JJ
randomwalker-info-585	644	17	mining	mining	NN
randomwalker-info-585	644	18	power	power	NN
randomwalker-info-585	644	19	of	of	IN
randomwalker-info-585	644	20	1	1	CD
randomwalker-info-585	644	21	/	/	SYM
randomwalker-info-585	644	22	p	p	NNP
randomwalker-info-585	644	23	rigs	rig	NNS
randomwalker-info-585	644	24	worth	worth	JJ
randomwalker-info-585	644	25	.	.	.
randomwalker-info-585	645	1	Of	of	RB
randomwalker-info-585	645	2	course	course	RB
randomwalker-info-585	645	3	,	,	,
randomwalker-info-585	645	4	this	this	DT
randomwalker-info-585	645	5	can	can	MD
randomwalker-info-585	645	6	always	always	RB
randomwalker-info-585	645	7	be	be	VB
randomwalker-info-585	645	8	adjusted	adjust	VBN
randomwalker-info-585	645	9	if	if	IN
randomwalker-info-585	645	10	necessary	necessary	JJ
randomwalker-info-585	645	11	by	by	IN
randomwalker-info-585	645	12	changing	change	VBG
randomwalker-info-585	645	13	the	the	DT
randomwalker-info-585	645	14	fixed	fix	VBN
randomwalker-info-585	645	15	reward	reward	NN
randomwalker-info-585	645	16	per	per	IN
randomwalker-info-585	645	17	block	block	NN
randomwalker-info-585	645	18	.	.	.
randomwalker-info-585	646	1	Also	also	RB
randomwalker-info-585	646	2	,	,	,
randomwalker-info-585	646	3	it	-PRON-	PRP
randomwalker-info-585	646	4	is	be	VBZ
randomwalker-info-585	646	5	important	important	JJ
randomwalker-info-585	646	6	to	to	TO
randomwalker-info-585	646	7	point	point	VB
randomwalker-info-585	646	8	out	out	RP
randomwalker-info-585	646	9	that	that	IN
randomwalker-info-585	646	10	as	as	RB
randomwalker-info-585	646	11	long	long	RB
randomwalker-info-585	646	12	as	as	IN
randomwalker-info-585	646	13	k	k	NNP
randomwalker-info-585	646	14	≤	≤	NNP
randomwalker-info-585	646	15	1	1	CD
randomwalker-info-585	646	16	/	/	SYM
randomwalker-info-585	646	17	p	p	NNP
randomwalker-info-585	646	18	,	,	,
randomwalker-info-585	646	19	the	the	DT
randomwalker-info-585	646	20	effective	effective	JJ
randomwalker-info-585	646	21	hash	hash	NN
randomwalker-info-585	646	22	power	power	NN
randomwalker-info-585	646	23	in	in	IN
randomwalker-info-585	646	24	the	the	DT
randomwalker-info-585	646	25	network	network	NN
randomwalker-info-585	646	26	will	will	MD
randomwalker-info-585	646	27	be	be	VB
randomwalker-info-585	646	28	k	k	NNP
randomwalker-info-585	646	29	rigs	rig	NNS
randomwalker-info-585	646	30	worth	worth	JJ
randomwalker-info-585	646	31	.	.	.
randomwalker-info-585	647	1	Now	now	RB
randomwalker-info-585	647	2	let	let	VB
randomwalker-info-585	647	3	’s	-PRON-	PRP
randomwalker-info-585	647	4	consider	consider	VB
randomwalker-info-585	647	5	what	what	WP
randomwalker-info-585	647	6	happens	happen	VBZ
randomwalker-info-585	647	7	in	in	IN
randomwalker-info-585	647	8	the	the	DT
randomwalker-info-585	647	9	transaction	transaction	NN
randomwalker-info-585	647	10	fee	fee	NN
randomwalker-info-585	647	11	model	model	NN
randomwalker-info-585	647	12	,	,	,
randomwalker-info-585	647	13	where	where	WRB
randomwalker-info-585	647	14	transaction	transaction	NN
randomwalker-info-585	647	15	fees	fee	NNS
randomwalker-info-585	647	16	arrive	arrive	VBP
randomwalker-info-585	647	17	continuously	continuously	RB
randomwalker-info-585	647	18	at	at	IN
randomwalker-info-585	647	19	a	a	DT
randomwalker-info-585	647	20	rate	rate	NN
randomwalker-info-585	647	21	of	of	IN
randomwalker-info-585	647	22	1	1	CD
randomwalker-info-585	647	23	per	per	IN
randomwalker-info-585	647	24	time	time	NN
randomwalker-info-585	647	25	unit	unit	NN
randomwalker-info-585	647	26	.	.	.
randomwalker-info-585	648	1	Miners	miner	NNS
randomwalker-info-585	648	2	will	will	MD
randomwalker-info-585	648	3	always	always	RB
randomwalker-info-585	648	4	turn	turn	VB
randomwalker-info-585	648	5	off	off	RP
randomwalker-info-585	648	6	their	-PRON-	PRP$
randomwalker-info-585	648	7	rigs	rig	NNS
randomwalker-info-585	648	8	(	(	-LRB-
randomwalker-info-585	648	9	/coin	/coin	NN
randomwalker-info-585	648	10	-	-	HYPH
randomwalker-info-585	648	11	hop	hop	NN
randomwalker-info-585	648	12	)	)	-RRB-
randomwalker-info-585	648	13	immediately	immediately	RB
randomwalker-info-585	648	14	after	after	IN
randomwalker-info-585	648	15	a	a	DT
randomwalker-info-585	648	16	block	block	NN
randomwalker-info-585	648	17	is	be	VBZ
randomwalker-info-585	648	18	found	find	VBN
randomwalker-info-585	648	19	,	,	,
randomwalker-info-585	648	20	because	because	IN
randomwalker-info-585	648	21	the	the	DT
randomwalker-info-585	648	22	instantaneous	instantaneous	JJ
randomwalker-info-585	648	23	expected	expected	JJ
randomwalker-info-585	648	24	reward	reward	NN
randomwalker-info-585	648	25	of	of	IN
randomwalker-info-585	648	26	running	run	VBG
randomwalker-info-585	648	27	a	a	DT
randomwalker-info-585	648	28	rig	rig	NN
randomwalker-info-585	648	29	is	be	VBZ
randomwalker-info-585	648	30	0	0	CD
randomwalker-info-585	648	31	,	,	,
randomwalker-info-585	648	32	but	but	CC
randomwalker-info-585	648	33	the	the	DT
randomwalker-info-585	648	34	cost	cost	NN
randomwalker-info-585	648	35	is	be	VBZ
randomwalker-info-585	648	36	non	non	JJ
randomwalker-info-585	648	37	-	-	JJ
randomwalker-info-585	648	38	zero	zero	CD
randomwalker-info-585	648	39	.	.	.
randomwalker-info-585	649	1	If	if	IN
randomwalker-info-585	649	2	the	the	DT
randomwalker-info-585	649	3	current	current	JJ
randomwalker-info-585	649	4	effective	effective	JJ
randomwalker-info-585	649	5	hash	hash	NN
randomwalker-info-585	649	6	power	power	NN
randomwalker-info-585	649	7	in	in	IN
randomwalker-info-585	649	8	the	the	DT
randomwalker-info-585	649	9	network	network	NN
randomwalker-info-585	649	10	is	be	VBZ
randomwalker-info-585	649	11	c	c	NN
randomwalker-info-585	649	12	rigs	rig	NNS
randomwalker-info-585	649	13	worth	worth	JJ
randomwalker-info-585	649	14	,	,	,
randomwalker-info-585	649	15	then	then	RB
randomwalker-info-585	649	16	the	the	DT
randomwalker-info-585	649	17	miner	miner	NN
randomwalker-info-585	649	18	needs	need	VBZ
randomwalker-info-585	649	19	to	to	TO
randomwalker-info-585	649	20	wait	wait	VB
randomwalker-info-585	649	21	until	until	IN
randomwalker-info-585	649	22	x	x	SYM
randomwalker-info-585	649	23	=	=	SYM
randomwalker-info-585	649	24	cp	cp	NNP
randomwalker-info-585	649	25	transaction	transaction	NN
randomwalker-info-585	649	26	fees	fee	NNS
randomwalker-info-585	649	27	have	have	VBP
randomwalker-info-585	649	28	arrived	arrive	VBN
randomwalker-info-585	649	29	in	in	IN
randomwalker-info-585	649	30	order	order	NN
randomwalker-info-585	649	31	for	for	IN
randomwalker-info-585	649	32	mining	mining	NN
randomwalker-info-585	649	33	to	to	TO
randomwalker-info-585	649	34	be	be	VB
randomwalker-info-585	649	35	profitable	profitable	JJ
randomwalker-info-585	649	36	.	.	.
randomwalker-info-585	650	1	Now	now	RB
randomwalker-info-585	650	2	,	,	,
randomwalker-info-585	650	3	assuming	assume	VBG
randomwalker-info-585	650	4	that	that	IN
randomwalker-info-585	650	5	miners	miner	NNS
randomwalker-info-585	650	6	are	be	VBP
randomwalker-info-585	650	7	cleverly	cleverly	RB
randomwalker-info-585	650	8	turning	turn	VBG
randomwalker-info-585	650	9	their	-PRON-	PRP$
randomwalker-info-585	650	10	rigs	rig	NNS
randomwalker-info-585	650	11	on	on	IN
randomwalker-info-585	650	12	and	and	CC
randomwalker-info-585	650	13	off	off	RB
randomwalker-info-585	650	14	at	at	IN
randomwalker-info-585	650	15	the	the	DT
randomwalker-info-585	650	16	right	right	JJ
randomwalker-info-585	650	17	times	time	NNS
randomwalker-info-585	650	18	,	,	,
randomwalker-info-585	650	19	how	how	WRB
randomwalker-info-585	650	20	many	many	JJ
randomwalker-info-585	650	21	rigs	rig	NNS
randomwalker-info-585	650	22	must	must	MD
randomwalker-info-585	650	23	be	be	VB
randomwalker-info-585	650	24	in	in	IN
randomwalker-info-585	650	25	the	the	DT
randomwalker-info-585	650	26	network	network	NN
randomwalker-info-585	650	27	in	in	IN
randomwalker-info-585	650	28	order	order	NN
randomwalker-info-585	650	29	to	to	TO
randomwalker-info-585	650	30	attain	attain	VB
randomwalker-info-585	650	31	an	an	DT
randomwalker-info-585	650	32	effective	effective	JJ
randomwalker-info-585	650	33	hash	hash	NN
randomwalker-info-585	650	34	power	power	NN
randomwalker-info-585	650	35	of	of	IN
randomwalker-info-585	650	36	c	c	NNP
randomwalker-info-585	650	37	?	?	.
randomwalker-info-585	651	1	The	the	DT
randomwalker-info-585	651	2	rigs	rig	NNS
randomwalker-info-585	651	3	are	be	VBP
randomwalker-info-585	651	4	all	all	RB
randomwalker-info-585	651	5	off	off	RB
randomwalker-info-585	651	6	for	for	IN
randomwalker-info-585	651	7	cp	cp	NNP
randomwalker-info-585	651	8	units	unit	NNS
randomwalker-info-585	651	9	of	of	IN
randomwalker-info-585	651	10	time	time	NN
randomwalker-info-585	651	11	,	,	,
randomwalker-info-585	651	12	and	and	CC
randomwalker-info-585	651	13	then	then	RB
randomwalker-info-585	651	14	all	all	DT
randomwalker-info-585	651	15	k	k	XX
randomwalker-info-585	651	16	of	of	IN
randomwalker-info-585	651	17	them	-PRON-	PRP
randomwalker-info-585	651	18	are	be	VBP
randomwalker-info-585	651	19	turned	turn	VBN
randomwalker-info-585	651	20	on	on	RP
randomwalker-info-585	651	21	,	,	,
randomwalker-info-585	651	22	and	and	CC
randomwalker-info-585	651	23	the	the	DT
randomwalker-info-585	651	24	expected	expect	VBN
randomwalker-info-585	651	25	time	time	NN
randomwalker-info-585	651	26	to	to	TO
randomwalker-info-585	651	27	find	find	VB
randomwalker-info-585	651	28	a	a	DT
randomwalker-info-585	651	29	block	block	NN
randomwalker-info-585	651	30	is	be	VBZ
randomwalker-info-585	651	31	1	1	CD
randomwalker-info-585	651	32	unit	unit	NN
randomwalker-info-585	651	33	of	of	IN
randomwalker-info-585	651	34	time	time	NN
randomwalker-info-585	651	35	.	.	.
randomwalker-info-585	652	1	This	this	DT
randomwalker-info-585	652	2	means	mean	VBZ
randomwalker-info-585	652	3	that	that	IN
randomwalker-info-585	652	4	the	the	DT
randomwalker-info-585	652	5	expected	expect	VBN
randomwalker-info-585	652	6	time	time	NN
randomwalker-info-585	652	7	to	to	TO
randomwalker-info-585	652	8	find	find	VB
randomwalker-info-585	652	9	a	a	DT
randomwalker-info-585	652	10	block	block	NN
randomwalker-info-585	652	11	with	with	IN
randomwalker-info-585	652	12	all	all	DT
randomwalker-info-585	652	13	k	k	NN
randomwalker-info-585	652	14	units	unit	NNS
randomwalker-info-585	652	15	running	running	NN
randomwalker-info-585	652	16	must	must	MD
randomwalker-info-585	652	17	be	be	VB
randomwalker-info-585	652	18	1−cp	1−cp	NNS
randomwalker-info-585	652	19	(	(	-LRB-
randomwalker-info-585	652	20	due	due	JJ
randomwalker-info-585	652	21	to	to	IN
randomwalker-info-585	652	22	difficulty	difficulty	NN
randomwalker-info-585	652	23	adjustment	adjustment	NN
randomwalker-info-585	652	24	)	)	-RRB-
randomwalker-info-585	652	25	,	,	,
randomwalker-info-585	652	26	whereas	whereas	IN
randomwalker-info-585	652	27	the	the	DT
randomwalker-info-585	652	28	expected	expect	VBN
randomwalker-info-585	652	29	time	time	NN
randomwalker-info-585	652	30	to	to	TO
randomwalker-info-585	652	31	find	find	VB
randomwalker-info-585	652	32	a	a	DT
randomwalker-info-585	652	33	block	block	NN
randomwalker-info-585	652	34	with	with	IN
randomwalker-info-585	652	35	c	c	NNP
randomwalker-info-585	652	36	units	unit	NNS
randomwalker-info-585	652	37	running	run	VBG
randomwalker-info-585	652	38	is	be	VBZ
randomwalker-info-585	652	39	1	1	CD
randomwalker-info-585	652	40	(	(	-LRB-
randomwalker-info-585	652	41	because	because	IN
randomwalker-info-585	652	42	the	the	DT
randomwalker-info-585	652	43	effective	effective	JJ
randomwalker-info-585	652	44	hash	hash	NN
randomwalker-info-585	652	45	power	power	NN
randomwalker-info-585	652	46	is	be	VBZ
randomwalker-info-585	652	47	c	c	NN
randomwalker-info-585	652	48	)	)	-RRB-
randomwalker-info-585	652	49	.	.	.
randomwalker-info-585	653	1	Finally	finally	RB
randomwalker-info-585	653	2	,	,	,
randomwalker-info-585	653	3	we	-PRON-	PRP
randomwalker-info-585	653	4	observe	observe	VBP
randomwalker-info-585	653	5	that	that	IN
randomwalker-info-585	653	6	for	for	IN
randomwalker-info-585	653	7	a	a	DT
randomwalker-info-585	653	8	fixed	fix	VBN
randomwalker-info-585	653	9	difficulty	difficulty	NN
randomwalker-info-585	653	10	,	,	,
randomwalker-info-585	653	11	if	if	IN
randomwalker-info-585	653	12	x	x	DT
randomwalker-info-585	653	13	denotes	denote	VBZ
randomwalker-info-585	653	14	the	the	DT
randomwalker-info-585	653	15	number	number	NN
randomwalker-info-585	653	16	of	of	IN
randomwalker-info-585	653	17	rigs	rig	NNS
randomwalker-info-585	653	18	running	run	VBG
randomwalker-info-585	653	19	,	,	,
randomwalker-info-585	653	20	and	and	CC
randomwalker-info-585	653	21	yx	yx	NNP
randomwalker-info-585	653	22	denotes	denote	VBZ
randomwalker-info-585	653	23	the	the	DT
randomwalker-info-585	653	24	expected	expect	VBN
randomwalker-info-585	653	25	time	time	NN
randomwalker-info-585	653	26	for	for	IN
randomwalker-info-585	653	27	x	x	NN
randomwalker-info-585	653	28	rigs	rig	NNS
randomwalker-info-585	653	29	to	to	TO
randomwalker-info-585	653	30	find	find	VB
randomwalker-info-585	653	31	a	a	DT
randomwalker-info-585	653	32	block	block	NN
randomwalker-info-585	653	33	,	,	,
randomwalker-info-585	653	34	then	then	RB
randomwalker-info-585	653	35	x1	x1	NNP
randomwalker-info-585	653	36	·	·	NFP
randomwalker-info-585	653	37	yx1	yx1	NNP
randomwalker-info-585	653	38	=	=	SYM
randomwalker-info-585	653	39	x2	x2	NNP
randomwalker-info-585	653	40	·	·	NFP
randomwalker-info-585	653	41	yx2	yx2	NN
randomwalker-info-585	653	42	for	for	IN
randomwalker-info-585	653	43	all	all	DT
randomwalker-info-585	653	44	possible	possible	JJ
randomwalker-info-585	653	45	number	number	NN
randomwalker-info-585	653	46	of	of	IN
randomwalker-info-585	653	47	rigs	rig	NNS
randomwalker-info-585	653	48	x1,x2	x1,x2	NN
randomwalker-info-585	653	49	.	.	.
randomwalker-info-585	654	1	Together	together	RB
randomwalker-info-585	654	2	,	,	,
randomwalker-info-585	654	3	this	this	DT
randomwalker-info-585	654	4	yields	yield	VBZ
randomwalker-info-585	654	5	the	the	DT
randomwalker-info-585	654	6	following	following	JJ
randomwalker-info-585	654	7	equation	equation	NN
randomwalker-info-585	654	8	:	:	:
randomwalker-info-585	654	9	k	k	NNP
randomwalker-info-585	654	10	·	·	NFP
randomwalker-info-585	654	11	(	(	-LRB-
randomwalker-info-585	654	12	1	1	CD
randomwalker-info-585	654	13	−	−	NNP
randomwalker-info-585	654	14	cp	cp	NNP
randomwalker-info-585	654	15	)	)	-RRB-
randomwalker-info-585	654	16	=	=	NFP
randomwalker-info-585	654	17	c	c	NN
randomwalker-info-585	654	18	·	·	NFP
randomwalker-info-585	654	19	1	1	CD
randomwalker-info-585	654	20	⇒	⇒	CD
randomwalker-info-585	654	21	k	k	NN
randomwalker-info-585	654	22	=	=	SYM
randomwalker-info-585	654	23	c	c	NN
randomwalker-info-585	654	24	1	1	CD
randomwalker-info-585	654	25	−	−	NNP
randomwalker-info-585	654	26	cp	cp	NNP
randomwalker-info-585	654	27	.	.	.
randomwalker-info-585	655	1	What	what	WP
randomwalker-info-585	655	2	do	do	VBP
randomwalker-info-585	655	3	we	-PRON-	PRP
randomwalker-info-585	655	4	learn	learn	VB
randomwalker-info-585	655	5	from	from	IN
randomwalker-info-585	655	6	this	this	DT
randomwalker-info-585	655	7	?	?	.
randomwalker-info-585	656	1	First	first	RB
randomwalker-info-585	656	2	,	,	,
randomwalker-info-585	656	3	we	-PRON-	PRP
randomwalker-info-585	656	4	see	see	VBP
randomwalker-info-585	656	5	that	that	IN
randomwalker-info-585	656	6	no	no	UH
randomwalker-info-585	656	7	c	c	NN
randomwalker-info-585	656	8	≥	≥	CD
randomwalker-info-585	656	9	1	1	CD
randomwalker-info-585	656	10	/	/	SYM
randomwalker-info-585	656	11	p	p	NN
randomwalker-info-585	656	12	can	can	MD
randomwalker-info-585	656	13	possibly	possibly	RB
randomwalker-info-585	656	14	be	be	VB
randomwalker-info-585	656	15	supported	support	VBN
randomwalker-info-585	656	16	,	,	,
randomwalker-info-585	656	17	just	just	RB
randomwalker-info-585	656	18	like	like	IN
randomwalker-info-585	656	19	in	in	IN
randomwalker-info-585	656	20	the	the	DT
randomwalker-info-585	656	21	fixed	fix	VBN
randomwalker-info-585	656	22	-	-	HYPH
randomwalker-info-585	656	23	reward	reward	NN
randomwalker-info-585	656	24	model	model	NN
randomwalker-info-585	656	25	.	.	.
randomwalker-info-585	657	1	On	on	IN
randomwalker-info-585	657	2	the	the	DT
randomwalker-info-585	657	3	other	other	JJ
randomwalker-info-585	657	4	hand	hand	NN
randomwalker-info-585	657	5	,	,	,
randomwalker-info-585	657	6	we	-PRON-	PRP
randomwalker-info-585	657	7	see	see	VBP
randomwalker-info-585	657	8	that	that	IN
randomwalker-info-585	657	9	it	-PRON-	PRP
randomwalker-info-585	657	10	takes	take	VBZ
randomwalker-info-585	657	11	an	an	DT
randomwalker-info-585	657	12	additional	additional	JJ
randomwalker-info-585	657	13	factor	factor	NN
randomwalker-info-585	657	14	of	of	IN
randomwalker-info-585	657	15	1	1	CD
randomwalker-info-585	657	16	1−cp	1−cp	CD
randomwalker-info-585	657	17	rigs	rig	NNS
randomwalker-info-585	657	18	in	in	IN
randomwalker-info-585	657	19	order	order	NN
randomwalker-info-585	657	20	to	to	TO
randomwalker-info-585	657	21	get	get	VB
randomwalker-info-585	657	22	the	the	DT
randomwalker-info-585	657	23	effective	effective	JJ
randomwalker-info-585	657	24	hash	hash	NN
randomwalker-info-585	657	25	power	power	NN
randomwalker-info-585	657	26	of	of	IN
randomwalker-info-585	657	27	c	c	NNP
randomwalker-info-585	657	28	≤	≤	NNP
randomwalker-info-585	657	29	p	p	NNP
randomwalker-info-585	657	30	rigs	rig	NNS
randomwalker-info-585	657	31	.	.	.
randomwalker-info-585	658	1	As	as	IN
randomwalker-info-585	658	2	c	c	NN
randomwalker-info-585	658	3	→	→	SYM
randomwalker-info-585	658	4	1	1	CD
randomwalker-info-585	658	5	/	/	SYM
randomwalker-info-585	658	6	p	p	NN
randomwalker-info-585	658	7	,	,	,
randomwalker-info-585	658	8	the	the	DT
randomwalker-info-585	658	9	maximum	maximum	JJ
randomwalker-info-585	658	10	possible	possible	JJ
randomwalker-info-585	658	11	effective	effective	JJ
randomwalker-info-585	658	12	hash	hash	NN
randomwalker-info-585	658	13	power	power	NN
randomwalker-info-585	658	14	,	,	,
randomwalker-info-585	658	15	this	this	DT
randomwalker-info-585	658	16	ratio	ratio	NN
randomwalker-info-585	658	17	approaches	approach	VBZ
randomwalker-info-585	658	18	∞	∞	XX
randomwalker-info-585	658	19	!	!	.
randomwalker-info-585	659	1	More	more	RBR
randomwalker-info-585	659	2	quantitatively	quantitatively	RB
randomwalker-info-585	659	3	,	,	,
randomwalker-info-585	659	4	if	if	IN
randomwalker-info-585	659	5	we	-PRON-	PRP
randomwalker-info-585	659	6	plug	plug	VBP
randomwalker-info-585	659	7	in	in	RP
randomwalker-info-585	659	8	c	c	NN
randomwalker-info-585	659	9	=	=	SYM
randomwalker-info-585	659	10	x	x	NNP
randomwalker-info-585	659	11	/	/	SYM
randomwalker-info-585	659	12	p	p	NN
randomwalker-info-585	659	13	for	for	IN
randomwalker-info-585	659	14	x	x	NN
randomwalker-info-585	659	15	<	<	XX
randomwalker-info-585	659	16	1	1	CD
randomwalker-info-585	659	17	,	,	,
randomwalker-info-585	659	18	we	-PRON-	PRP
randomwalker-info-585	659	19	see	see	VBP
randomwalker-info-585	659	20	that	that	IN
randomwalker-info-585	659	21	the	the	DT
randomwalker-info-585	659	22	blow	blow	NN
randomwalker-info-585	659	23	-	-	HYPH
randomwalker-info-585	659	24	up	up	NN
randomwalker-info-585	659	25	is	be	VBZ
randomwalker-info-585	659	26	1	1	CD
randomwalker-info-585	659	27	1−x	1−x	CD
randomwalker-info-585	659	28	.	.	.
randomwalker-info-585	660	1	This	this	DT
randomwalker-info-585	660	2	means	mean	VBZ
randomwalker-info-585	660	3	the	the	DT
randomwalker-info-585	660	4	following	following	NN
randomwalker-info-585	660	5	:	:	:
randomwalker-info-585	660	6	In	in	IN
randomwalker-info-585	660	7	the	the	DT
randomwalker-info-585	660	8	transaction	transaction	NN
randomwalker-info-585	660	9	fees	fee	NNS
randomwalker-info-585	660	10	model	model	NN
randomwalker-info-585	660	11	,	,	,
randomwalker-info-585	660	12	to	to	TO
randomwalker-info-585	660	13	obtain	obtain	VB
randomwalker-info-585	660	14	an	an	DT
randomwalker-info-585	660	15	x	x	NN
randomwalker-info-585	660	16	fraction	fraction	NN
randomwalker-info-585	660	17	of	of	IN
randomwalker-info-585	660	18	the	the	DT
randomwalker-info-585	660	19	maximum	maximum	JJ
randomwalker-info-585	660	20	possible	possible	JJ
randomwalker-info-585	660	21	effective	effective	JJ
randomwalker-info-585	660	22	hash	hash	NN
randomwalker-info-585	660	23	power	power	NN
randomwalker-info-585	660	24	,	,	,
randomwalker-info-585	660	25	a	a	DT
randomwalker-info-585	660	26	multiplicative	multiplicative	JJ
randomwalker-info-585	660	27	blow	blow	NN
randomwalker-info-585	660	28	-	-	HYPH
randomwalker-info-585	660	29	up	up	NN
randomwalker-info-585	660	30	of	of	IN
randomwalker-info-585	660	31	1	1	CD
randomwalker-info-585	660	32	1−x	1−x	CD
randomwalker-info-585	660	33	rigs	rig	NNS
randomwalker-info-585	660	34	are	be	VBP
randomwalker-info-585	660	35	necessary	necessary	JJ
randomwalker-info-585	660	36	.	.	.
randomwalker-info-585	661	1	Recall	recall	VB
randomwalker-info-585	661	2	that	that	IN
randomwalker-info-585	661	3	in	in	IN
randomwalker-info-585	661	4	the	the	DT
randomwalker-info-585	661	5	fixed	fix	VBN
randomwalker-info-585	661	6	-	-	HYPH
randomwalker-info-585	661	7	reward	reward	NN
randomwalker-info-585	661	8	model	model	NN
randomwalker-info-585	661	9	,	,	,
randomwalker-info-585	661	10	no	no	DT
randomwalker-info-585	661	11	blow	blow	NN
randomwalker-info-585	661	12	-	-	HYPH
randomwalker-info-585	661	13	up	up	NN
randomwalker-info-585	661	14	is	be	VBZ
randomwalker-info-585	661	15	necessary	necessary	JJ
randomwalker-info-585	661	16	.	.	.
randomwalker-info-585	662	1	We	-PRON-	PRP
randomwalker-info-585	662	2	can	can	MD
randomwalker-info-585	662	3	also	also	RB
randomwalker-info-585	662	4	reason	reason	VB
randomwalker-info-585	662	5	in	in	IN
randomwalker-info-585	662	6	the	the	DT
randomwalker-info-585	662	7	other	other	JJ
randomwalker-info-585	662	8	direction	direction	NN
randomwalker-info-585	662	9	:	:	:
randomwalker-info-585	662	10	for	for	IN
randomwalker-info-585	662	11	a	a	DT
randomwalker-info-585	662	12	fixed	fix	VBN
randomwalker-info-585	662	13	k	k	NN
randomwalker-info-585	662	14	number	number	NN
randomwalker-info-585	662	15	of	of	IN
randomwalker-info-585	662	16	rigs	rig	NNS
randomwalker-info-585	662	17	in	in	IN
randomwalker-info-585	662	18	the	the	DT
randomwalker-info-585	662	19	network	network	NN
randomwalker-info-585	662	20	,	,	,
randomwalker-info-585	662	21	what	what	WP
randomwalker-info-585	662	22	is	be	VBZ
randomwalker-info-585	662	23	the	the	DT
randomwalker-info-585	662	24	effective	effective	JJ
randomwalker-info-585	662	25	hash	hash	NN
randomwalker-info-585	662	26	rate	rate	NN
randomwalker-info-585	662	27	in	in	IN
randomwalker-info-585	662	28	the	the	DT
randomwalker-info-585	662	29	fixed	fix	VBN
randomwalker-info-585	662	30	reward	reward	NN
randomwalker-info-585	662	31	model	model	NN
randomwalker-info-585	662	32	versus	versus	IN
randomwalker-info-585	662	33	the	the	DT
randomwalker-info-585	662	34	transaction	transaction	NN
randomwalker-info-585	662	35	fees	fee	NNS
randomwalker-info-585	662	36	model	model	NN
randomwalker-info-585	662	37	with	with	IN
randomwalker-info-585	662	38	mining	mining	NN
randomwalker-info-585	662	39	gaps	gap	NNS
randomwalker-info-585	662	40	?	?	.
randomwalker-info-585	663	1	In	in	IN
randomwalker-info-585	663	2	the	the	DT
randomwalker-info-585	663	3	fixed	fixed	JJ
randomwalker-info-585	663	4	reward	reward	NN
randomwalker-info-585	663	5	model	model	NN
randomwalker-info-585	663	6	,	,	,
randomwalker-info-585	663	7	this	this	DT
randomwalker-info-585	663	8	is	be	VBZ
randomwalker-info-585	663	9	easy	easy	JJ
randomwalker-info-585	663	10	:	:	:
randomwalker-info-585	663	11	it	-PRON-	PRP
randomwalker-info-585	663	12	’s	’	VBZ
randomwalker-info-585	663	13	just	just	RB
randomwalker-info-585	663	14	min{k	min{k	NNP
randomwalker-info-585	663	15	,	,	,
randomwalker-info-585	663	16	1	1	CD
randomwalker-info-585	663	17	/	/	SYM
randomwalker-info-585	663	18	p	p	NN
randomwalker-info-585	663	19	}	}	-RRB-
randomwalker-info-585	663	20	.	.	.
randomwalker-info-585	664	1	In	in	IN
randomwalker-info-585	664	2	the	the	DT
randomwalker-info-585	664	3	transaction	transaction	NN
randomwalker-info-585	664	4	fees	fee	NNS
randomwalker-info-585	664	5	model	model	NN
randomwalker-info-585	664	6	,	,	,
randomwalker-info-585	664	7	for	for	IN
randomwalker-info-585	664	8	a	a	DT
randomwalker-info-585	664	9	fixed	fix	VBN
randomwalker-info-585	664	10	k	k	NN
randomwalker-info-585	664	11	,	,	,
randomwalker-info-585	664	12	we	-PRON-	PRP
randomwalker-info-585	664	13	need	need	VBP
randomwalker-info-585	664	14	to	to	TO
randomwalker-info-585	664	15	solve	solve	VB
randomwalker-info-585	664	16	for	for	IN
randomwalker-info-585	664	17	the	the	DT
randomwalker-info-585	664	18	c	c	NN
randomwalker-info-585	664	19	such	such	JJ
randomwalker-info-585	664	20	that	that	IN
randomwalker-info-585	664	21	k	k	NN
randomwalker-info-585	664	22	=	=	SYM
randomwalker-info-585	664	23	c	c	NN
randomwalker-info-585	664	24	1−cp	1−cp	NNS
randomwalker-info-585	664	25	.	.	.
randomwalker-info-585	665	1	This	this	DT
randomwalker-info-585	665	2	is	be	VBZ
randomwalker-info-585	665	3	:	:	:
randomwalker-info-585	665	4	k	k	NNP
randomwalker-info-585	665	5	−kcp	−kcp	NNP
randomwalker-info-585	665	6	=	=	SYM
randomwalker-info-585	665	7	c	c	NNP
randomwalker-info-585	665	8	⇒	⇒	CD
randomwalker-info-585	665	9	c	c	NN
randomwalker-info-585	665	10	=	=	SYM
randomwalker-info-585	665	11	k	k	NN
randomwalker-info-585	665	12	1	1	CD
randomwalker-info-585	665	13	+	+	SYM
randomwalker-info-585	665	14	pk	pk	NN
randomwalker-info-585	665	15	So	so	RB
randomwalker-info-585	665	16	for	for	IN
randomwalker-info-585	665	17	fixed	fix	VBN
randomwalker-info-585	665	18	k	k	NN
randomwalker-info-585	665	19	,	,	,
randomwalker-info-585	665	20	the	the	DT
randomwalker-info-585	665	21	effective	effective	JJ
randomwalker-info-585	665	22	mining	mining	NN
randomwalker-info-585	665	23	power	power	NN
randomwalker-info-585	665	24	of	of	IN
randomwalker-info-585	665	25	k	k	NNP
randomwalker-info-585	665	26	rigs	rig	NNS
randomwalker-info-585	665	27	degrades	degrade	NNS
randomwalker-info-585	665	28	by	by	IN
randomwalker-info-585	665	29	a	a	DT
randomwalker-info-585	665	30	factor	factor	NN
randomwalker-info-585	665	31	of	of	IN
randomwalker-info-585	665	32	1	1	CD
randomwalker-info-585	665	33	1+pk	1+pk	CD
randomwalker-info-585	665	34	,	,	,
randomwalker-info-585	665	35	which	which	WDT
randomwalker-info-585	665	36	is	be	VBZ
randomwalker-info-585	665	37	always	always	RB
randomwalker-info-585	665	38	<	<	XX
randomwalker-info-585	665	39	1	1	CD
randomwalker-info-585	665	40	.	.	.
randomwalker-info-585	666	1	Note	note	VB
randomwalker-info-585	666	2	that	that	IN
randomwalker-info-585	666	3	at	at	IN
randomwalker-info-585	666	4	k	k	NN
randomwalker-info-585	666	5	=	=	SYM
randomwalker-info-585	666	6	1	1	CD
randomwalker-info-585	666	7	/	/	SYM
randomwalker-info-585	666	8	p	p	NN
randomwalker-info-585	666	9	,	,	,
randomwalker-info-585	666	10	every	every	DT
randomwalker-info-585	666	11	rig	rig	NN
randomwalker-info-585	666	12	is	be	VBZ
randomwalker-info-585	666	13	100	100	CD
randomwalker-info-585	666	14	%	%	NN
randomwalker-info-585	666	15	effective	effective	JJ
randomwalker-info-585	666	16	in	in	IN
randomwalker-info-585	666	17	the	the	DT
randomwalker-info-585	666	18	fixed	fixed	JJ
randomwalker-info-585	666	19	reward	reward	NN
randomwalker-info-585	666	20	model	model	NN
randomwalker-info-585	666	21	,	,	,
randomwalker-info-585	666	22	whereas	whereas	IN
randomwalker-info-585	666	23	the	the	DT
randomwalker-info-585	666	24	effective	effective	JJ
randomwalker-info-585	666	25	mining	mining	NN
randomwalker-info-585	666	26	power	power	NN
randomwalker-info-585	666	27	is	be	VBZ
randomwalker-info-585	666	28	just	just	RB
randomwalker-info-585	666	29	k/2	k/2	NNS
randomwalker-info-585	666	30	in	in	IN
randomwalker-info-585	666	31	the	the	DT
randomwalker-info-585	666	32	transaction	transaction	NN
randomwalker-info-585	666	33	fees	fee	NNS
randomwalker-info-585	666	34	model	model	NN
randomwalker-info-585	666	35	.	.	.
randomwalker-info-585	667	1	We	-PRON-	PRP
randomwalker-info-585	667	2	can	can	MD
randomwalker-info-585	667	3	again	again	RB
randomwalker-info-585	667	4	make	make	VB
randomwalker-info-585	667	5	a	a	DT
randomwalker-info-585	667	6	quantitative	quantitative	JJ
randomwalker-info-585	667	7	statement	statement	NN
randomwalker-info-585	667	8	:	:	:
randomwalker-info-585	667	9	In	in	IN
randomwalker-info-585	667	10	the	the	DT
randomwalker-info-585	667	11	transaction	transaction	NN
randomwalker-info-585	667	12	fees	fee	NNS
randomwalker-info-585	667	13	model	model	NN
randomwalker-info-585	667	14	,	,	,
randomwalker-info-585	667	15	when	when	WRB
randomwalker-info-585	667	16	the	the	DT
randomwalker-info-585	667	17	raw	raw	JJ
randomwalker-info-585	667	18	hash	hash	NN
randomwalker-info-585	667	19	power	power	NN
randomwalker-info-585	667	20	in	in	IN
randomwalker-info-585	667	21	the	the	DT
randomwalker-info-585	667	22	network	network	NN
randomwalker-info-585	667	23	is	be	VBZ
randomwalker-info-585	667	24	an	an	DT
randomwalker-info-585	667	25	x	x	NN
randomwalker-info-585	667	26	fraction	fraction	NN
randomwalker-info-585	667	27	of	of	IN
randomwalker-info-585	667	28	the	the	DT
randomwalker-info-585	667	29	maximum	maximum	JJ
randomwalker-info-585	667	30	possible	possible	JJ
randomwalker-info-585	667	31	,	,	,
randomwalker-info-585	667	32	the	the	DT
randomwalker-info-585	667	33	effective	effective	JJ
randomwalker-info-585	667	34	hash	hash	NN
randomwalker-info-585	667	35	power	power	NN
randomwalker-info-585	667	36	degrades	degrade	NNS
randomwalker-info-585	667	37	by	by	IN
randomwalker-info-585	667	38	a	a	DT
randomwalker-info-585	667	39	factor	factor	NN
randomwalker-info-585	667	40	of	of	IN
randomwalker-info-585	667	41	1	1	CD
randomwalker-info-585	667	42	1+x	1+x	CD
randomwalker-info-585	667	43	.	.	.
randomwalker-info-585	668	1	Recall	recall	VB
randomwalker-info-585	668	2	that	that	IN
randomwalker-info-585	668	3	in	in	IN
randomwalker-info-585	668	4	the	the	DT
randomwalker-info-585	668	5	fixed	fix	VBN
randomwalker-info-585	668	6	rewards	reward	NNS
randomwalker-info-585	668	7	model	model	NN
randomwalker-info-585	668	8	,	,	,
randomwalker-info-585	668	9	there	there	EX
randomwalker-info-585	668	10	is	be	VBZ
randomwalker-info-585	668	11	no	no	DT
randomwalker-info-585	668	12	degradation	degradation	NN
randomwalker-info-585	668	13	in	in	IN
randomwalker-info-585	668	14	effective	effective	JJ
randomwalker-info-585	668	15	hash	hash	NN
randomwalker-info-585	668	16	power	power	NN
randomwalker-info-585	668	17	when	when	WRB
randomwalker-info-585	668	18	x	x	NNP
randomwalker-info-585	668	19	≤	≤	NNP
randomwalker-info-585	668	20	1	1	CD
randomwalker-info-585	668	21	.	.	.
randomwalker-info-585	669	1	B.	B.	NNP
randomwalker-info-585	670	1	LEARNING	learn	VBG
randomwalker-info-585	670	2	MINERS	miner	NNS
randomwalker-info-585	670	3	IN	in	IN
randomwalker-info-585	670	4	SIMULATOR	SIMULATOR	NNP
randomwalker-info-585	670	5	As	as	IN
randomwalker-info-585	670	6	referenced	reference	VBN
randomwalker-info-585	670	7	in	in	IN
randomwalker-info-585	670	8	Section	section	NN
randomwalker-info-585	670	9	4.2	4.2	CD
randomwalker-info-585	670	10	,	,	,
randomwalker-info-585	670	11	we	-PRON-	PRP
randomwalker-info-585	670	12	provide	provide	VBP
randomwalker-info-585	670	13	two	two	CD
randomwalker-info-585	670	14	options	option	NNS
randomwalker-info-585	670	15	for	for	IN
randomwalker-info-585	670	16	learning	learn	VBG
randomwalker-info-585	670	17	in	in	IN
randomwalker-info-585	670	18	our	-PRON-	PRP$
randomwalker-info-585	670	19	simulator	simulator	NN
randomwalker-info-585	670	20	.	.	.
randomwalker-info-585	671	1	Let	let	VB
randomwalker-info-585	671	2	’s	-PRON-	PRP
randomwalker-info-585	671	3	introduce	introduce	VB
randomwalker-info-585	671	4	these	these	DT
randomwalker-info-585	671	5	with	with	IN
randomwalker-info-585	671	6	a	a	DT
randomwalker-info-585	671	7	clear	clear	JJ
randomwalker-info-585	671	8	set	set	NN
randomwalker-info-585	671	9	-	-	HYPH
randomwalker-info-585	671	10	up	up	NN
randomwalker-info-585	671	11	for	for	IN
randomwalker-info-585	671	12	learning	learning	NN
randomwalker-info-585	671	13	.	.	.
randomwalker-info-585	672	1	Let	let	VB
randomwalker-info-585	672	2	there	there	EX
randomwalker-info-585	672	3	be	be	VB
randomwalker-info-585	672	4	a	a	DT
randomwalker-info-585	672	5	set	set	NN
randomwalker-info-585	672	6	of	of	IN
randomwalker-info-585	672	7	strategies	strategy	NNS
randomwalker-info-585	672	8	a	a	DT
randomwalker-info-585	672	9	learner	learner	NN
randomwalker-info-585	672	10	can	can	MD
randomwalker-info-585	672	11	use	use	VB
randomwalker-info-585	672	12	,	,	,
randomwalker-info-585	672	13	indexed	index	VBN
randomwalker-info-585	672	14	by	by	IN
randomwalker-info-585	672	15	k.	k.	NN
randomwalker-info-585	672	16	At	at	IN
randomwalker-info-585	672	17	each	each	DT
randomwalker-info-585	672	18	round	round	NN
randomwalker-info-585	672	19	i	i	PRP
randomwalker-info-585	672	20	∈	∈	VBP
randomwalker-info-585	672	21	[	[	-LRB-
randomwalker-info-585	672	22	T	t	NN
randomwalker-info-585	672	23	]	]	-RRB-
randomwalker-info-585	672	24	,	,	,
randomwalker-info-585	672	25	the	the	DT
randomwalker-info-585	672	26	learner	learner	NN
randomwalker-info-585	672	27	receives	receive	VBZ
randomwalker-info-585	672	28	/	/	SYM
randomwalker-info-585	672	29	would	would	MD
randomwalker-info-585	672	30	have	have	VB
randomwalker-info-585	672	31	received	receive	VBN
randomwalker-info-585	672	32	some	some	DT
randomwalker-info-585	672	33	reward	reward	NN
randomwalker-info-585	672	34	rik	rik	CC
randomwalker-info-585	672	35	∈	∈	NNP
randomwalker-info-585	672	36	[	[	-LRB-
randomwalker-info-585	672	37	0	0	CD
randomwalker-info-585	672	38	,	,	,
randomwalker-info-585	672	39	1	1	CD
randomwalker-info-585	672	40	]	]	-RRB-
randomwalker-info-585	672	41	,	,	,
randomwalker-info-585	672	42	which	which	WDT
randomwalker-info-585	672	43	may	may	MD
randomwalker-info-585	672	44	be	be	VB
randomwalker-info-585	672	45	arbitrary	arbitrary	JJ
randomwalker-info-585	672	46	.	.	.
randomwalker-info-585	673	1	The	the	DT
randomwalker-info-585	673	2	goal	goal	NN
randomwalker-info-585	673	3	is	be	VBZ
randomwalker-info-585	673	4	to	to	TO
randomwalker-info-585	673	5	select	select	VB
randomwalker-info-585	673	6	a	a	DT
randomwalker-info-585	673	7	sequence	sequence	NN
randomwalker-info-585	673	8	of	of	IN
randomwalker-info-585	673	9	strategies	strategy	NNS
randomwalker-info-585	673	10	si	si	VBP
randomwalker-info-585	673	11	guaranteeing	guarantee	VBG
randomwalker-info-585	673	12	:	:	:
randomwalker-info-585	673	13	T∑	T∑	NNP
randomwalker-info-585	673	14	i=1	i=1	RB
randomwalker-info-585	673	15	r	r	NN
randomwalker-info-585	673	16	i	i	PRP
randomwalker-info-585	673	17	si	si	VBP
randomwalker-info-585	673	18	≥	≥	UH
randomwalker-info-585	673	19	max	max	NNP
randomwalker-info-585	673	20	k	k	NNP
randomwalker-info-585	673	21	{	{	-LRB-
randomwalker-info-585	673	22	T∑	T∑	NNP
randomwalker-info-585	673	23	i=1	i=1	NN
randomwalker-info-585	673	24	r	r	NN
randomwalker-info-585	673	25	i	i	PRP
randomwalker-info-585	673	26	k}−	k}−	XX
randomwalker-info-585	673	27	c.	c.	NN
randomwalker-info-585	673	28	In	in	IN
randomwalker-info-585	673	29	other	other	JJ
randomwalker-info-585	673	30	words	word	NNS
randomwalker-info-585	673	31	,	,	,
randomwalker-info-585	673	32	we	-PRON-	PRP
randomwalker-info-585	673	33	would	would	MD
randomwalker-info-585	673	34	like	like	VB
randomwalker-info-585	673	35	to	to	TO
randomwalker-info-585	673	36	select	select	VB
randomwalker-info-585	673	37	a	a	DT
randomwalker-info-585	673	38	sequence	sequence	NN
randomwalker-info-585	673	39	of	of	IN
randomwalker-info-585	673	40	strategies	strategy	NNS
randomwalker-info-585	673	41	that	that	WDT
randomwalker-info-585	673	42	does	do	VBZ
randomwalker-info-585	673	43	nearly	nearly	RB
randomwalker-info-585	673	44	as	as	RB
randomwalker-info-585	673	45	well	well	RB
randomwalker-info-585	673	46	as	as	IN
randomwalker-info-585	673	47	the	the	DT
randomwalker-info-585	673	48	best	good	JJS
randomwalker-info-585	673	49	strategy	strategy	NN
randomwalker-info-585	673	50	,	,	,
randomwalker-info-585	673	51	assuming	assume	VBG
randomwalker-info-585	673	52	we	-PRON-	PRP
randomwalker-info-585	673	53	knew	know	VBD
randomwalker-info-585	673	54	it	-PRON-	PRP
randomwalker-info-585	673	55	from	from	IN
randomwalker-info-585	673	56	the	the	DT
randomwalker-info-585	673	57	beginning	beginning	NN
randomwalker-info-585	673	58	.	.	.
randomwalker-info-585	674	1	It	-PRON-	PRP
randomwalker-info-585	674	2	is	be	VBZ
randomwalker-info-585	674	3	well	well	RB
randomwalker-info-585	674	4	-	-	HYPH
randomwalker-info-585	674	5	known	know	VBN
randomwalker-info-585	674	6	[	[	-LRB-
randomwalker-info-585	674	7	4	4	CD
randomwalker-info-585	674	8	]	]	-RRB-
randomwalker-info-585	674	9	that	that	DT
randomwalker-info-585	674	10	setting	set	VBG
randomwalker-info-585	674	11	wik	wik	RB
randomwalker-info-585	674	12	=	=	SYM
randomwalker-info-585	674	13	w	w	NNP
randomwalker-info-585	674	14	i−1	i−1	NNP
randomwalker-info-585	674	15	k	k	NN
randomwalker-info-585	674	16	(	(	-LRB-
randomwalker-info-585	674	17	1	1	CD
randomwalker-info-585	674	18	−	−	NNP
randomwalker-info-585	674	19	�	�	,
randomwalker-info-585	674	20	)	)	-RRB-
randomwalker-info-585	674	21	rik	rik	VBD
randomwalker-info-585	674	22	and	and	CC
randomwalker-info-585	674	23	selecting	select	VBG
randomwalker-info-585	674	24	sik	sik	JJ
randomwalker-info-585	674	25	proportional	proportional	JJ
randomwalker-info-585	674	26	to	to	IN
randomwalker-info-585	674	27	the	the	DT
randomwalker-info-585	674	28	weights	weight	NNS
randomwalker-info-585	674	29	wik	wik	JJ
randomwalker-info-585	674	30	results	result	VBZ
randomwalker-info-585	674	31	in	in	IN
randomwalker-info-585	674	32	a	a	DT
randomwalker-info-585	674	33	guarantee	guarantee	NN
randomwalker-info-585	674	34	with	with	IN
randomwalker-info-585	674	35	c	c	NN
randomwalker-info-585	674	36	=	=	SYM
randomwalker-info-585	674	37	�	�	NNP
randomwalker-info-585	674	38	T	t	NN
randomwalker-info-585	674	39	+	+	SYM
randomwalker-info-585	674	40	ln	ln	NN
randomwalker-info-585	674	41	(	(	-LRB-
randomwalker-info-585	674	42	#	#	NN
randomwalker-info-585	674	43	strategies)/	strategies)/	NNP
randomwalker-info-585	674	44	�	�	NNP
randomwalker-info-585	674	45	.	.	.
randomwalker-info-585	675	1	Similarly	similarly	RB
randomwalker-info-585	675	2	,	,	,
randomwalker-info-585	675	3	[	[	-LRB-
randomwalker-info-585	675	4	5	5	CD
randomwalker-info-585	675	5	]	]	-RRB-
randomwalker-info-585	675	6	shows	show	VBZ
randomwalker-info-585	675	7	that	that	IN
randomwalker-info-585	675	8	even	even	RB
randomwalker-info-585	675	9	if	if	IN
randomwalker-info-585	675	10	we	-PRON-	PRP
randomwalker-info-585	675	11	do	do	VBP
randomwalker-info-585	675	12	n’t	not	RB
randomwalker-info-585	675	13	learn	learn	VB
randomwalker-info-585	675	14	r	r	NN
randomwalker-info-585	675	15	i	i	NN
randomwalker-info-585	675	16	k	k	XX
randomwalker-info-585	675	17	for	for	IN
randomwalker-info-585	675	18	Figure	figure	NN
randomwalker-info-585	675	19	11	11	CD
randomwalker-info-585	675	20	:	:	:
randomwalker-info-585	675	21	Illustration	illustration	NN
randomwalker-info-585	675	22	of	of	IN
randomwalker-info-585	675	23	a	a	DT
randomwalker-info-585	675	24	mining	mining	NN
randomwalker-info-585	675	25	gap	gap	NN
randomwalker-info-585	675	26	.	.	.
randomwalker-info-585	676	1	The	the	DT
randomwalker-info-585	676	2	blue	blue	JJ
randomwalker-info-585	676	3	line	line	NN
randomwalker-info-585	676	4	shows	show	VBZ
randomwalker-info-585	676	5	the	the	DT
randomwalker-info-585	676	6	current	current	JJ
randomwalker-info-585	676	7	P.D.F.	P.D.F.	NNP
randomwalker-info-585	677	1	of	of	IN
randomwalker-info-585	677	2	the	the	DT
randomwalker-info-585	677	3	time	time	NN
randomwalker-info-585	677	4	to	to	IN
randomwalker-info-585	677	5	next	next	JJ
randomwalker-info-585	677	6	block	block	NN
randomwalker-info-585	677	7	.	.	.
randomwalker-info-585	678	1	If	if	IN
randomwalker-info-585	678	2	the	the	DT
randomwalker-info-585	678	3	block	block	NN
randomwalker-info-585	678	4	reward	reward	NN
randomwalker-info-585	678	5	by	by	IN
randomwalker-info-585	678	6	itself	-PRON-	PRP
randomwalker-info-585	678	7	is	be	VBZ
randomwalker-info-585	678	8	too	too	RB
randomwalker-info-585	678	9	small	small	JJ
randomwalker-info-585	678	10	to	to	TO
randomwalker-info-585	678	11	incentivize	incentivize	VB
randomwalker-info-585	678	12	mining	mining	NN
randomwalker-info-585	678	13	,	,	,
randomwalker-info-585	678	14	rational	rational	JJ
randomwalker-info-585	678	15	miners	miner	NNS
randomwalker-info-585	678	16	will	will	MD
randomwalker-info-585	678	17	wait	wait	VB
randomwalker-info-585	678	18	until	until	IN
randomwalker-info-585	678	19	enough	enough	JJ
randomwalker-info-585	678	20	transactions	transaction	NNS
randomwalker-info-585	678	21	have	have	VBP
randomwalker-info-585	678	22	accumulated	accumulate	VBN
randomwalker-info-585	678	23	before	before	IN
randomwalker-info-585	678	24	starting	start	VBG
randomwalker-info-585	678	25	to	to	IN
randomwalker-info-585	678	26	mine	-PRON-	PRP
randomwalker-info-585	678	27	.	.	.
randomwalker-info-585	679	1	This	this	DT
randomwalker-info-585	679	2	will	will	MD
randomwalker-info-585	679	3	lead	lead	VB
randomwalker-info-585	679	4	to	to	IN
randomwalker-info-585	679	5	a	a	DT
randomwalker-info-585	679	6	P.D.F.	P.D.F.	NNP
randomwalker-info-585	680	1	of	of	IN
randomwalker-info-585	680	2	a	a	DT
randomwalker-info-585	680	3	different	different	JJ
randomwalker-info-585	680	4	shape	shape	NN
randomwalker-info-585	680	5	(	(	-LRB-
randomwalker-info-585	680	6	red	red	JJ
randomwalker-info-585	680	7	line	line	NN
randomwalker-info-585	680	8	)	)	-RRB-
randomwalker-info-585	680	9	.	.	.
randomwalker-info-585	681	1	Note	note	VB
randomwalker-info-585	681	2	that	that	IN
randomwalker-info-585	681	3	in	in	IN
randomwalker-info-585	681	4	either	either	DT
randomwalker-info-585	681	5	scenario	scenario	NN
randomwalker-info-585	681	6	the	the	DT
randomwalker-info-585	681	7	mean	mean	JJ
randomwalker-info-585	681	8	time	time	NN
randomwalker-info-585	681	9	to	to	IN
randomwalker-info-585	681	10	the	the	DT
randomwalker-info-585	681	11	next	next	JJ
randomwalker-info-585	681	12	block	block	NN
randomwalker-info-585	681	13	is	be	VBZ
randomwalker-info-585	681	14	10	10	CD
randomwalker-info-585	681	15	minutes	minute	NNS
randomwalker-info-585	681	16	(	(	-LRB-
randomwalker-info-585	681	17	green	green	JJ
randomwalker-info-585	681	18	line	line	NN
randomwalker-info-585	681	19	)	)	-RRB-
randomwalker-info-585	681	20	strategies	strategy	NNS
randomwalker-info-585	681	21	k	k	XX
randomwalker-info-585	681	22	that	that	IN
randomwalker-info-585	681	23	we	-PRON-	PRP
randomwalker-info-585	681	24	did	do	VBD
randomwalker-info-585	681	25	n’t	not	RB
randomwalker-info-585	681	26	choose	choose	VB
randomwalker-info-585	681	27	in	in	IN
randomwalker-info-585	681	28	round	round	NN
randomwalker-info-585	681	29	i	i	PRP
randomwalker-info-585	681	30	,	,	,
randomwalker-info-585	681	31	there	there	EX
randomwalker-info-585	681	32	is	be	VBZ
randomwalker-info-585	681	33	an	an	DT
randomwalker-info-585	681	34	algorithm	algorithm	NN
randomwalker-info-585	681	35	(	(	-LRB-
randomwalker-info-585	681	36	namely	namely	RB
randomwalker-info-585	681	37	,	,	,
randomwalker-info-585	681	38	EXP3	EXP3	NNP
randomwalker-info-585	681	39	,	,	,
randomwalker-info-585	681	40	see	see	VB
randomwalker-info-585	681	41	[	[	-LRB-
randomwalker-info-585	681	42	5	5	CD
randomwalker-info-585	681	43	]	]	-RRB-
randomwalker-info-585	681	44	for	for	IN
randomwalker-info-585	681	45	description	description	NN
randomwalker-info-585	681	46	)	)	-RRB-
randomwalker-info-585	681	47	that	that	WDT
randomwalker-info-585	681	48	guarantees	guarantee	VBZ
randomwalker-info-585	681	49	c	c	NN
randomwalker-info-585	681	50	=	=	SYM
randomwalker-info-585	681	51	2	2	CD
randomwalker-info-585	681	52	�	�	NNP
randomwalker-info-585	681	53	T	t	NN
randomwalker-info-585	681	54	+	+	CC
randomwalker-info-585	681	55	#	#	NN
randomwalker-info-585	681	56	strategies	strategy	NNS
randomwalker-info-585	681	57	·	·	NFP
randomwalker-info-585	681	58	ln	ln	VBP
randomwalker-info-585	681	59	(	(	-LRB-
randomwalker-info-585	681	60	#	#	NNP
randomwalker-info-585	681	61	strategies)/	strategies)/	NNP
randomwalker-info-585	681	62	�	�	NNP
randomwalker-info-585	681	63	.	.	.
randomwalker-info-585	682	1	So	so	RB
randomwalker-info-585	682	2	option	option	VB
randomwalker-info-585	682	3	one	one	CD
randomwalker-info-585	682	4	in	in	IN
randomwalker-info-585	682	5	our	-PRON-	PRP$
randomwalker-info-585	682	6	simulator	simulator	NN
randomwalker-info-585	682	7	is	be	VBZ
randomwalker-info-585	682	8	just	just	RB
randomwalker-info-585	682	9	to	to	TO
randomwalker-info-585	682	10	run	run	VB
randomwalker-info-585	682	11	EXP3	EXP3	NNP
randomwalker-info-585	682	12	in	in	IN
randomwalker-info-585	682	13	earnest	earnest	NN
randomwalker-info-585	682	14	:	:	:
randomwalker-info-585	682	15	whenever	whenever	WRB
randomwalker-info-585	682	16	a	a	DT
randomwalker-info-585	682	17	miner	miner	NN
randomwalker-info-585	682	18	uses	use	VBZ
randomwalker-info-585	682	19	some	some	DT
randomwalker-info-585	682	20	strategy	strategy	NN
randomwalker-info-585	682	21	k	k	NN
randomwalker-info-585	682	22	during	during	IN
randomwalker-info-585	682	23	game	game	NN
randomwalker-info-585	682	24	i	i	NNP
randomwalker-info-585	682	25	,	,	,
randomwalker-info-585	682	26	they	-PRON-	PRP
randomwalker-info-585	682	27	learn	learn	VBP
randomwalker-info-585	682	28	their	-PRON-	PRP$
randomwalker-info-585	682	29	payoff	payoff	NN
randomwalker-info-585	682	30	and	and	CC
randomwalker-info-585	682	31	update	update	VB
randomwalker-info-585	682	32	their	-PRON-	PRP$
randomwalker-info-585	682	33	weights	weight	NNS
randomwalker-info-585	682	34	accordingly	accordingly	RB
randomwalker-info-585	682	35	.	.	.
randomwalker-info-585	683	1	Still	still	RB
randomwalker-info-585	683	2	,	,	,
randomwalker-info-585	683	3	MWU	mwu	NN
randomwalker-info-585	683	4	converges	converge	NNS
randomwalker-info-585	683	5	faster	fast	RBR
randomwalker-info-585	683	6	,	,	,
randomwalker-info-585	683	7	so	so	IN
randomwalker-info-585	683	8	it	-PRON-	PRP
randomwalker-info-585	683	9	would	would	MD
randomwalker-info-585	683	10	be	be	VB
randomwalker-info-585	683	11	nice	nice	JJ
randomwalker-info-585	683	12	if	if	IN
randomwalker-info-585	683	13	we	-PRON-	PRP
randomwalker-info-585	683	14	could	could	MD
randomwalker-info-585	683	15	learn	learn	VB
randomwalker-info-585	683	16	how	how	WRB
randomwalker-info-585	683	17	much	much	JJ
randomwalker-info-585	683	18	payoff	payoff	NN
randomwalker-info-585	683	19	the	the	DT
randomwalker-info-585	683	20	miner	miner	NN
randomwalker-info-585	683	21	would	would	MD
randomwalker-info-585	683	22	have	have	VB
randomwalker-info-585	683	23	received	receive	VBN
randomwalker-info-585	683	24	if	if	IN
randomwalker-info-585	683	25	they	-PRON-	PRP
randomwalker-info-585	683	26	used	use	VBD
randomwalker-info-585	683	27	strategy	strategy	NN
randomwalker-info-585	683	28	k	k	NN
randomwalker-info-585	683	29	during	during	IN
randomwalker-info-585	683	30	game	game	NN
randomwalker-info-585	683	31	i	i	PRP
randomwalker-info-585	683	32	for	for	IN
randomwalker-info-585	683	33	all	all	DT
randomwalker-info-585	683	34	k	k	NN
randomwalker-info-585	683	35	,	,	,
randomwalker-info-585	683	36	but	but	CC
randomwalker-info-585	683	37	this	this	DT
randomwalker-info-585	683	38	is	be	VBZ
randomwalker-info-585	683	39	computationally	computationally	RB
randomwalker-info-585	683	40	very	very	RB
randomwalker-info-585	683	41	expensive	expensive	JJ
randomwalker-info-585	683	42	as	as	IN
randomwalker-info-585	683	43	it	-PRON-	PRP
randomwalker-info-585	683	44	essentially	essentially	RB
randomwalker-info-585	683	45	requires	require	VBZ
randomwalker-info-585	683	46	us	-PRON-	PRP
randomwalker-info-585	683	47	to	to	TO
randomwalker-info-585	683	48	rerun	rerun	VB
randomwalker-info-585	683	49	the	the	DT
randomwalker-info-585	683	50	entire	entire	JJ
randomwalker-info-585	683	51	game	game	NN
randomwalker-info-585	683	52	for	for	IN
randomwalker-info-585	683	53	all	all	DT
randomwalker-info-585	683	54	miners	miner	NNS
randomwalker-info-585	683	55	and	and	CC
randomwalker-info-585	683	56	strategies	strategy	NNS
randomwalker-info-585	683	57	k	k	NNP
randomwalker-info-585	683	58	(	(	-LRB-
randomwalker-info-585	683	59	thereby	thereby	RB
randomwalker-info-585	683	60	becoming	become	VBG
randomwalker-info-585	683	61	more	more	RBR
randomwalker-info-585	683	62	expensive	expensive	JJ
randomwalker-info-585	683	63	than	than	IN
randomwalker-info-585	683	64	just	just	RB
randomwalker-info-585	683	65	running	run	VBG
randomwalker-info-585	683	66	the	the	DT
randomwalker-info-585	683	67	additional	additional	JJ
randomwalker-info-585	683	68	games	game	NNS
randomwalker-info-585	683	69	to	to	TO
randomwalker-info-585	683	70	let	let	VB
randomwalker-info-585	683	71	EXP3	EXP3	NNP
randomwalker-info-585	683	72	converge	converge	VB
randomwalker-info-585	683	73	)	)	-RRB-
randomwalker-info-585	683	74	.	.	.
randomwalker-info-585	684	1	Instead	instead	RB
randomwalker-info-585	684	2	,	,	,
randomwalker-info-585	684	3	we	-PRON-	PRP
randomwalker-info-585	684	4	make	make	VBP
randomwalker-info-585	684	5	the	the	DT
randomwalker-info-585	684	6	following	follow	VBG
randomwalker-info-585	684	7	observation	observation	NN
randomwalker-info-585	684	8	:	:	:
randomwalker-info-585	684	9	even	even	RB
randomwalker-info-585	684	10	if	if	IN
randomwalker-info-585	684	11	this	this	DT
randomwalker-info-585	684	12	miner	miner	NN
randomwalker-info-585	684	13	is	be	VBZ
randomwalker-info-585	684	14	not	not	RB
randomwalker-info-585	684	15	using	use	VBG
randomwalker-info-585	684	16	strategy	strategy	NN
randomwalker-info-585	684	17	k	k	NN
randomwalker-info-585	684	18	during	during	IN
randomwalker-info-585	684	19	game	game	NN
randomwalker-info-585	684	20	i	i	PRP
randomwalker-info-585	684	21	,	,	,
randomwalker-info-585	684	22	maybe	maybe	RB
randomwalker-info-585	684	23	some	some	DT
randomwalker-info-585	684	24	other	other	JJ
randomwalker-info-585	684	25	miner	miner	NN
randomwalker-info-585	684	26	is	be	VBZ
randomwalker-info-585	684	27	-	-	:
randomwalker-info-585	684	28	could	could	MD
randomwalker-info-585	684	29	we	-PRON-	PRP
randomwalker-info-585	684	30	use	use	VB
randomwalker-info-585	684	31	that	that	DT
randomwalker-info-585	684	32	miner	miner	NN
randomwalker-info-585	684	33	’s	’s	POS
randomwalker-info-585	684	34	payoff	payoff	NN
randomwalker-info-585	684	35	instead	instead	RB
randomwalker-info-585	684	36	of	of	IN
randomwalker-info-585	684	37	recomputing	recompute	VBG
randomwalker-info-585	684	38	exactly	exactly	RB
randomwalker-info-585	684	39	what	what	WP
randomwalker-info-585	684	40	payoff	payoff	NN
randomwalker-info-585	684	41	this	this	DT
randomwalker-info-585	684	42	miner	miner	NN
randomwalker-info-585	684	43	would	would	MD
randomwalker-info-585	684	44	have	have	VB
randomwalker-info-585	684	45	received	receive	VBN
randomwalker-info-585	684	46	?	?	.
randomwalker-info-585	685	1	The	the	DT
randomwalker-info-585	685	2	answer	answer	NN
randomwalker-info-585	685	3	is	be	VBZ
randomwalker-info-585	685	4	of	of	IN
randomwalker-info-585	685	5	course	course	NN
randomwalker-info-585	685	6	we	-PRON-	PRP
randomwalker-info-585	685	7	can	can	MD
randomwalker-info-585	685	8	,	,	,
randomwalker-info-585	685	9	we	-PRON-	PRP
randomwalker-info-585	685	10	just	just	RB
randomwalker-info-585	685	11	wo	will	MD
randomwalker-info-585	685	12	n’t	not	RB
randomwalker-info-585	685	13	get	get	VB
randomwalker-info-585	685	14	a	a	DT
randomwalker-info-585	685	15	theoretical	theoretical	JJ
randomwalker-info-585	685	16	guarantee	guarantee	NN
randomwalker-info-585	685	17	like	like	UH
randomwalker-info-585	685	18	if	if	IN
randomwalker-info-585	685	19	we	-PRON-	PRP
randomwalker-info-585	685	20	used	use	VBD
randomwalker-info-585	685	21	MWU	MWU	NNP
randomwalker-info-585	685	22	in	in	IN
randomwalker-info-585	685	23	earnest	earnest	NN
randomwalker-info-585	685	24	.	.	.
randomwalker-info-585	686	1	The	the	DT
randomwalker-info-585	686	2	payoff	payoff	NN
randomwalker-info-585	686	3	from	from	IN
randomwalker-info-585	686	4	different	different	JJ
randomwalker-info-585	686	5	miner	miner	NN
randomwalker-info-585	686	6	perspectives	perspective	NNS
randomwalker-info-585	686	7	are	be	VBP
randomwalker-info-585	686	8	of	of	IN
randomwalker-info-585	686	9	course	course	NN
randomwalker-info-585	686	10	different	different	JJ
randomwalker-info-585	686	11	,	,	,
randomwalker-info-585	686	12	but	but	CC
randomwalker-info-585	686	13	not	not	RB
randomwalker-info-585	686	14	wildly	wildly	RB
randomwalker-info-585	686	15	so	so	RB
randomwalker-info-585	686	16	.	.	.
randomwalker-info-585	687	1	Specifically	specifically	RB
randomwalker-info-585	687	2	,	,	,
randomwalker-info-585	687	3	the	the	DT
randomwalker-info-585	687	4	difference	difference	NN
randomwalker-info-585	687	5	is	be	VBZ
randomwalker-info-585	687	6	that	that	IN
randomwalker-info-585	687	7	miner	miner	NN
randomwalker-info-585	687	8	1	1	CD
randomwalker-info-585	687	9	is	be	VBZ
randomwalker-info-585	687	10	facing	face	VBG
randomwalker-info-585	687	11	opponents	opponent	NNS
randomwalker-info-585	687	12	2	2	CD
randomwalker-info-585	687	13	,	,	,
randomwalker-info-585	687	14	3	3	CD
randomwalker-info-585	687	15	,	,	,
randomwalker-info-585	687	16	.	.	.
randomwalker-info-585	688	1	.	.	.
randomwalker-info-585	689	1	.	.	.
randomwalker-info-585	689	2	,	,	,
randomwalker-info-585	689	3	whereas	whereas	IN
randomwalker-info-585	689	4	miner	miner	NN
randomwalker-info-585	689	5	2	2	CD
randomwalker-info-585	689	6	faces	face	VBZ
randomwalker-info-585	689	7	opponents	opponent	NNS
randomwalker-info-585	689	8	1	1	CD
randomwalker-info-585	689	9	,	,	,
randomwalker-info-585	689	10	3	3	CD
randomwalker-info-585	689	11	,	,	,
randomwalker-info-585	689	12	.	.	.
randomwalker-info-585	690	1	.	.	.
randomwalker-info-585	691	1	..	..	NFP
randomwalker-info-585	692	1	If	if	IN
randomwalker-info-585	692	2	miner	miner	NN
randomwalker-info-585	692	3	1	1	CD
randomwalker-info-585	692	4	and	and	CC
randomwalker-info-585	692	5	miner	miner	NN
randomwalker-info-585	692	6	2	2	CD
randomwalker-info-585	692	7	use	use	VB
randomwalker-info-585	692	8	different	different	JJ
randomwalker-info-585	692	9	strategies	strategy	NNS
randomwalker-info-585	692	10	in	in	IN
randomwalker-info-585	692	11	round	round	NN
randomwalker-info-585	692	12	i	i	PRP
randomwalker-info-585	692	13	,	,	,
randomwalker-info-585	692	14	then	then	RB
randomwalker-info-585	692	15	strategy	strategy	NN
randomwalker-info-585	692	16	k	k	NNP
randomwalker-info-585	692	17	would	would	MD
randomwalker-info-585	692	18	yield	yield	VB
randomwalker-info-585	692	19	slightly	slightly	RB
randomwalker-info-585	692	20	different	different	JJ
randomwalker-info-585	692	21	rewards	reward	NNS
randomwalker-info-585	692	22	when	when	WRB
randomwalker-info-585	692	23	used	use	VBN
randomwalker-info-585	692	24	by	by	IN
randomwalker-info-585	692	25	each	each	DT
randomwalker-info-585	692	26	of	of	IN
randomwalker-info-585	692	27	them	-PRON-	PRP
randomwalker-info-585	692	28	.	.	.
randomwalker-info-585	693	1	With	with	IN
randomwalker-info-585	693	2	many	many	JJ
randomwalker-info-585	693	3	small	small	JJ
randomwalker-info-585	693	4	miners	miner	NNS
randomwalker-info-585	693	5	,	,	,
randomwalker-info-585	693	6	this	this	DT
randomwalker-info-585	693	7	difference	difference	NN
randomwalker-info-585	693	8	should	should	MD
randomwalker-info-585	693	9	be	be	VB
randomwalker-info-585	693	10	small	small	JJ
randomwalker-info-585	693	11	,	,	,
randomwalker-info-585	693	12	so	so	RB
randomwalker-info-585	693	13	we	-PRON-	PRP
randomwalker-info-585	693	14	include	include	VBP
randomwalker-info-585	693	15	this	this	DT
randomwalker-info-585	693	16	learning	learning	NN
randomwalker-info-585	693	17	option	option	NN
randomwalker-info-585	693	18	as	as	IN
randomwalker-info-585	693	19	it	-PRON-	PRP
randomwalker-info-585	693	20	seems	seem	VBZ
randomwalker-info-585	693	21	to	to	TO
randomwalker-info-585	693	22	converge	converge	VB
randomwalker-info-585	693	23	faster	fast	RBR
randomwalker-info-585	693	24	than	than	IN
randomwalker-info-585	693	25	EXP3	EXP3	NNP
randomwalker-info-585	693	26	,	,	,
randomwalker-info-585	693	27	even	even	RB
randomwalker-info-585	693	28	though	though	IN
randomwalker-info-585	693	29	there	there	EX
randomwalker-info-585	693	30	is	be	VBZ
randomwalker-info-585	693	31	no	no	DT
randomwalker-info-585	693	32	theoretical	theoretical	JJ
randomwalker-info-585	693	33	guarantee	guarantee	NN
randomwalker-info-585	693	34	.	.	.
randomwalker-info-585	694	1	Specifically	specifically	RB
randomwalker-info-585	694	2	what	what	WP
randomwalker-info-585	694	3	we	-PRON-	PRP
randomwalker-info-585	694	4	mean	mean	VBP
randomwalker-info-585	694	5	is	be	VBZ
randomwalker-info-585	694	6	the	the	DT
randomwalker-info-585	694	7	following	follow	VBG
randomwalker-info-585	694	8	:	:	:
randomwalker-info-585	694	9	instead	instead	RB
randomwalker-info-585	694	10	of	of	IN
randomwalker-info-585	694	11	learning	learn	VBG
randomwalker-info-585	694	12	the	the	DT
randomwalker-info-585	694	13	payoff	payoff	NN
randomwalker-info-585	694	14	that	that	WDT
randomwalker-info-585	694	15	the	the	DT
randomwalker-info-585	694	16	miner	miner	NN
randomwalker-info-585	694	17	would	would	MD
randomwalker-info-585	694	18	have	have	VB
randomwalker-info-585	694	19	received	receive	VBN
randomwalker-info-585	694	20	had	have	VBD
randomwalker-info-585	694	21	they	-PRON-	PRP
randomwalker-info-585	694	22	used	use	VBN
randomwalker-info-585	694	23	strategy	strategy	NN
randomwalker-info-585	694	24	k	k	NN
randomwalker-info-585	694	25	during	during	IN
randomwalker-info-585	694	26	round	round	NN
randomwalker-info-585	694	27	i	i	PRP
randomwalker-info-585	694	28	,	,	,
randomwalker-info-585	694	29	they	-PRON-	PRP
randomwalker-info-585	694	30	simply	simply	RB
randomwalker-info-585	694	31	take	take	VBP
randomwalker-info-585	694	32	the	the	DT
randomwalker-info-585	694	33	average	average	JJ
randomwalker-info-585	694	34	payoffs	payoff	NNS
randomwalker-info-585	694	35	of	of	IN
randomwalker-info-585	694	36	all	all	DT
randomwalker-info-585	694	37	miners	miner	NNS
randomwalker-info-585	694	38	that	that	WDT
randomwalker-info-585	694	39	used	use	VBD
randomwalker-info-585	694	40	strategy	strategy	NN
randomwalker-info-585	694	41	k	k	NN
randomwalker-info-585	694	42	during	during	IN
randomwalker-info-585	694	43	round	round	NN
randomwalker-info-585	694	44	i	i	PRP
randomwalker-info-585	694	45	instead	instead	RB
randomwalker-info-585	694	46	.	.	.
randomwalker-info-585	695	1	It	-PRON-	PRP
randomwalker-info-585	695	2	is	be	VBZ
randomwalker-info-585	695	3	certainly	certainly	RB
randomwalker-info-585	695	4	possible	possible	JJ
randomwalker-info-585	695	5	that	that	IN
randomwalker-info-585	695	6	improvements	improvement	NNS
randomwalker-info-585	695	7	to	to	IN
randomwalker-info-585	695	8	the	the	DT
randomwalker-info-585	695	9	learning	learn	VBG
randomwalker-info-585	695	10	aspect	aspect	NN
randomwalker-info-585	695	11	of	of	IN
randomwalker-info-585	695	12	the	the	DT
randomwalker-info-585	695	13	simulation	simulation	NN
randomwalker-info-585	695	14	are	be	VBP
randomwalker-info-585	695	15	possible	possible	JJ
randomwalker-info-585	695	16	(	(	-LRB-
randomwalker-info-585	695	17	and	and	CC
randomwalker-info-585	695	18	we	-PRON-	PRP
randomwalker-info-585	695	19	encourage	encourage	VBP
randomwalker-info-585	695	20	future	future	JJ
randomwalker-info-585	695	21	work	work	NN
randomwalker-info-585	695	22	on	on	IN
randomwalker-info-585	695	23	this	this	DT
randomwalker-info-585	695	24	aspect	aspect	NN
randomwalker-info-585	695	25	once	once	IN
randomwalker-info-585	695	26	the	the	DT
randomwalker-info-585	695	27	simulator	simulator	NN
randomwalker-info-585	695	28	is	be	VBZ
randomwalker-info-585	695	29	open	open	JJ
randomwalker-info-585	695	30	-	-	HYPH
randomwalker-info-585	695	31	source	source	NN
randomwalker-info-585	695	32	)	)	-RRB-
randomwalker-info-585	695	33	,	,	,
randomwalker-info-585	695	34	but	but	CC
randomwalker-info-585	695	35	we	-PRON-	PRP
randomwalker-info-585	695	36	note	note	VBP
randomwalker-info-585	695	37	that	that	IN
randomwalker-info-585	695	38	the	the	DT
randomwalker-info-585	695	39	current	current	JJ
randomwalker-info-585	695	40	implementations	implementation	NNS
randomwalker-info-585	695	41	sufficed	suffice	VBD
randomwalker-info-585	695	42	for	for	IN
randomwalker-info-585	695	43	the	the	DT
randomwalker-info-585	695	44	settings	setting	NNS
randomwalker-info-585	695	45	we	-PRON-	PRP
randomwalker-info-585	695	46	studied	study	VBD
randomwalker-info-585	695	47	.	.	.
randomwalker-info-585	696	1	C.	C.	NNP
randomwalker-info-585	696	2	PROOF	PROOF	NNP
randomwalker-info-585	696	3	OF	of	IN
randomwalker-info-585	696	4	THEOREM	THEOREM	NNP
randomwalker-info-585	696	5	5.1	5.1	CD
randomwalker-info-585	696	6	Below	below	RB
randomwalker-info-585	696	7	is	be	VBZ
randomwalker-info-585	696	8	a	a	DT
randomwalker-info-585	696	9	complete	complete	JJ
randomwalker-info-585	696	10	proof	proof	NN
randomwalker-info-585	696	11	of	of	IN
randomwalker-info-585	696	12	Theorem	Theorem	NNP
randomwalker-info-585	696	13	5.1	5.1	CD
randomwalker-info-585	696	14	.	.	.
randomwalker-info-585	697	1	Some	some	DT
randomwalker-info-585	697	2	quick	quick	JJ
randomwalker-info-585	697	3	notation	notation	NN
randomwalker-info-585	697	4	:	:	:
randomwalker-info-585	697	5	for	for	IN
randomwalker-info-585	697	6	an	an	DT
randomwalker-info-585	697	7	increasing	increase	VBG
randomwalker-info-585	697	8	function	function	NN
randomwalker-info-585	697	9	f	f	NNP
randomwalker-info-585	697	10	(	(	-LRB-
randomwalker-info-585	697	11	·	·	NFP
randomwalker-info-585	697	12	)	)	-RRB-
randomwalker-info-585	697	13	,	,	,
randomwalker-info-585	697	14	we	-PRON-	PRP
randomwalker-info-585	697	15	’ll	will	MD
randomwalker-info-585	697	16	denote	denote	VB
randomwalker-info-585	697	17	by	by	IN
randomwalker-info-585	697	18	f−1(x	f−1(x	CD
randomwalker-info-585	697	19	)	)	-RRB-
randomwalker-info-585	697	20	=	=	NFP
randomwalker-info-585	697	21	min{y|f(y	min{y|f(y	ADD
randomwalker-info-585	697	22	)	)	-RRB-
randomwalker-info-585	697	23	≥	≥	UH
randomwalker-info-585	697	24	x	x	UH
randomwalker-info-585	697	25	}	}	-RRB-
randomwalker-info-585	697	26	.	.	.
randomwalker-info-585	698	1	If	if	IN
randomwalker-info-585	698	2	no	no	DT
randomwalker-info-585	698	3	such	such	JJ
randomwalker-info-585	698	4	y	y	NN
randomwalker-info-585	698	5	exists	exist	VBZ
randomwalker-info-585	698	6	,	,	,
randomwalker-info-585	698	7	then	then	RB
randomwalker-info-585	698	8	we	-PRON-	PRP
randomwalker-info-585	698	9	’ll	will	MD
randomwalker-info-585	698	10	denote	denote	VB
randomwalker-info-585	698	11	f−1(x	f−1(x	CD
randomwalker-info-585	698	12	)	)	-RRB-
randomwalker-info-585	698	13	=	=	NFP
randomwalker-info-585	698	14	+	+	CC
randomwalker-info-585	698	15	∞.	∞.	NN
randomwalker-info-585	699	1	First	first	RB
randomwalker-info-585	699	2	,	,	,
randomwalker-info-585	699	3	we	-PRON-	PRP
randomwalker-info-585	699	4	make	make	VBP
randomwalker-info-585	699	5	an	an	DT
randomwalker-info-585	699	6	extremely	extremely	RB
randomwalker-info-585	699	7	useful	useful	JJ
randomwalker-info-585	699	8	observation	observation	NN
randomwalker-info-585	699	9	about	about	IN
randomwalker-info-585	699	10	when	when	WRB
randomwalker-info-585	699	11	miners	miner	NNS
randomwalker-info-585	699	12	will	will	MD
randomwalker-info-585	699	13	receive	receive	VB
randomwalker-info-585	699	14	payment	payment	NN
randomwalker-info-585	699	15	for	for	IN
randomwalker-info-585	699	16	their	-PRON-	PRP$
randomwalker-info-585	699	17	blocks	block	NNS
randomwalker-info-585	699	18	.	.	.
randomwalker-info-585	700	1	Essentially	essentially	RB
randomwalker-info-585	700	2	,	,	,
randomwalker-info-585	700	3	because	because	IN
randomwalker-info-585	700	4	miners	miner	NNS
randomwalker-info-585	700	5	only	only	RB
randomwalker-info-585	700	6	consider	consider	VBP
randomwalker-info-585	700	7	mining	mine	VBG
randomwalker-info-585	700	8	on	on	IN
randomwalker-info-585	700	9	MostH	MostH	NNP
randomwalker-info-585	700	10	or	or	CC
randomwalker-info-585	700	11	MostH−1	mosth−1	CD
randomwalker-info-585	700	12	,	,	,
randomwalker-info-585	700	13	once	once	RB
randomwalker-info-585	700	14	a	a	DT
randomwalker-info-585	700	15	block	block	NN
randomwalker-info-585	700	16	is	be	VBZ
randomwalker-info-585	700	17	a	a	DT
randomwalker-info-585	700	18	predecessor	predecessor	NN
randomwalker-info-585	700	19	of	of	IN
randomwalker-info-585	700	20	both	both	DT
randomwalker-info-585	700	21	such	such	JJ
randomwalker-info-585	700	22	blocks	block	NNS
randomwalker-info-585	700	23	,	,	,
randomwalker-info-585	700	24	it	-PRON-	PRP
randomwalker-info-585	700	25	is	be	VBZ
randomwalker-info-585	700	26	guaranteed	guarantee	VBN
randomwalker-info-585	700	27	to	to	TO
randomwalker-info-585	700	28	be	be	VB
randomwalker-info-585	700	29	in	in	IN
randomwalker-info-585	700	30	the	the	DT
randomwalker-info-585	700	31	eventual	eventual	JJ
randomwalker-info-585	700	32	longest	long	JJS
randomwalker-info-585	700	33	chain	chain	NN
randomwalker-info-585	700	34	.	.	.
randomwalker-info-585	701	1	Observation	observation	NN
randomwalker-info-585	701	2	1	1	CD
randomwalker-info-585	701	3	.	.	.
randomwalker-info-585	702	1	As	as	RB
randomwalker-info-585	702	2	long	long	RB
randomwalker-info-585	702	3	as	as	IN
randomwalker-info-585	702	4	miners	miner	NNS
randomwalker-info-585	702	5	only	only	RB
randomwalker-info-585	702	6	consider	consider	VBP
randomwalker-info-585	702	7	mining	mine	VBG
randomwalker-info-585	702	8	on	on	IN
randomwalker-info-585	702	9	top	top	NN
randomwalker-info-585	702	10	of	of	IN
randomwalker-info-585	702	11	blocks	block	NNS
randomwalker-info-585	702	12	MostH	MostH	NNP
randomwalker-info-585	702	13	or	or	CC
randomwalker-info-585	702	14	MostH−1	MostH−1	NNP
randomwalker-info-585	702	15	,	,	,
randomwalker-info-585	702	16	a	a	DT
randomwalker-info-585	702	17	miner	miner	NN
randomwalker-info-585	702	18	receives	receive	VBZ
randomwalker-info-585	702	19	eventual	eventual	JJ
randomwalker-info-585	702	20	payment	payment	NN
randomwalker-info-585	702	21	for	for	IN
randomwalker-info-585	702	22	mining	mine	VBG
randomwalker-info-585	702	23	a	a	DT
randomwalker-info-585	702	24	block	block	NN
randomwalker-info-585	702	25	if	if	IN
randomwalker-info-585	702	26	and	and	CC
randomwalker-info-585	702	27	only	only	RB
randomwalker-info-585	702	28	if	if	IN
randomwalker-info-585	702	29	the	the	DT
randomwalker-info-585	702	30	next	next	JJ
randomwalker-info-585	702	31	block	block	NN
randomwalker-info-585	702	32	found	find	VBD
randomwalker-info-585	702	33	chooses	choose	NNS
randomwalker-info-585	702	34	to	to	TO
randomwalker-info-585	702	35	continue	continue	VB
randomwalker-info-585	702	36	her	-PRON-	PRP$
randomwalker-info-585	702	37	chain	chain	NN
randomwalker-info-585	702	38	instead	instead	RB
randomwalker-info-585	702	39	of	of	IN
randomwalker-info-585	702	40	undercutting	undercut	VBG
randomwalker-info-585	702	41	.	.	.
randomwalker-info-585	703	1	Proof	proof	NN
randomwalker-info-585	703	2	.	.	.
randomwalker-info-585	704	1	Because	because	IN
randomwalker-info-585	704	2	miners	miner	NNS
randomwalker-info-585	704	3	only	only	RB
randomwalker-info-585	704	4	consider	consider	VBP
randomwalker-info-585	704	5	chains	chain	NNS
randomwalker-info-585	704	6	MostH−1	mosth−1	CD
randomwalker-info-585	704	7	or	or	CC
randomwalker-info-585	704	8	MostH	MostH	NNP
randomwalker-info-585	704	9	,	,	,
randomwalker-info-585	704	10	immediately	immediately	RB
randomwalker-info-585	704	11	after	after	IN
randomwalker-info-585	704	12	producing	produce	VBG
randomwalker-info-585	704	13	a	a	DT
randomwalker-info-585	704	14	new	new	JJ
randomwalker-info-585	704	15	block	block	NN
randomwalker-info-585	704	16	B	b	NN
randomwalker-info-585	704	17	,	,	,
randomwalker-info-585	704	18	B	B	NNP
randomwalker-info-585	704	19	is	be	VBZ
randomwalker-info-585	704	20	in	in	IN
randomwalker-info-585	704	21	the	the	DT
randomwalker-info-585	704	22	longest	long	JJS
randomwalker-info-585	704	23	chain	chain	NN
randomwalker-info-585	704	24	.	.	.
randomwalker-info-585	705	1	Either	either	CC
randomwalker-info-585	705	2	B	B	NNP
randomwalker-info-585	705	3	goes	go	VBZ
randomwalker-info-585	705	4	on	on	IN
randomwalker-info-585	705	5	top	top	NN
randomwalker-info-585	705	6	of	of	IN
randomwalker-info-585	705	7	MostH−1	mosth−1	CD
randomwalker-info-585	705	8	,	,	,
randomwalker-info-585	705	9	in	in	IN
randomwalker-info-585	705	10	which	which	WDT
randomwalker-info-585	705	11	case	case	NN
randomwalker-info-585	705	12	it	-PRON-	PRP
randomwalker-info-585	705	13	is	be	VBZ
randomwalker-info-585	705	14	in	in	IN
randomwalker-info-585	705	15	a	a	DT
randomwalker-info-585	705	16	chain	chain	NN
randomwalker-info-585	705	17	of	of	IN
randomwalker-info-585	705	18	length	length	NN
randomwalker-info-585	705	19	H	h	NN
randomwalker-info-585	705	20	,	,	,
randomwalker-info-585	705	21	which	which	WDT
randomwalker-info-585	705	22	is	be	VBZ
randomwalker-info-585	705	23	the	the	DT
randomwalker-info-585	705	24	longest	long	JJS
randomwalker-info-585	705	25	.	.	.
randomwalker-info-585	706	1	Or	or	CC
randomwalker-info-585	706	2	it	-PRON-	PRP
randomwalker-info-585	706	3	goes	go	VBZ
randomwalker-info-585	706	4	on	on	IN
randomwalker-info-585	706	5	top	top	NN
randomwalker-info-585	706	6	of	of	IN
randomwalker-info-585	706	7	MostH	MostH	NNP
randomwalker-info-585	706	8	,	,	,
randomwalker-info-585	706	9	which	which	WDT
randomwalker-info-585	706	10	creates	create	VBZ
randomwalker-info-585	706	11	a	a	DT
randomwalker-info-585	706	12	new	new	JJ
randomwalker-info-585	706	13	longest	long	JJS
randomwalker-info-585	706	14	chain	chain	NN
randomwalker-info-585	706	15	of	of	IN
randomwalker-info-585	706	16	length	length	NN
randomwalker-info-585	706	17	H	h	NN
randomwalker-info-585	706	18	+	+	CC
randomwalker-info-585	706	19	1	1	CD
randomwalker-info-585	706	20	.	.	.
randomwalker-info-585	707	1	Let	let	VB
randomwalker-info-585	707	2	Hnew	Hnew	NNP
randomwalker-info-585	707	3	denote	denote	VB
randomwalker-info-585	707	4	the	the	DT
randomwalker-info-585	707	5	new	new	JJ
randomwalker-info-585	707	6	length	length	NN
randomwalker-info-585	707	7	of	of	IN
randomwalker-info-585	707	8	the	the	DT
randomwalker-info-585	707	9	longest	long	JJS
randomwalker-info-585	707	10	chain	chain	NN
randomwalker-info-585	707	11	(	(	-LRB-
randomwalker-info-585	707	12	H	h	NN
randomwalker-info-585	707	13	if	if	IN
randomwalker-info-585	707	14	the	the	DT
randomwalker-info-585	707	15	miner	miner	NN
randomwalker-info-585	707	16	undercut	undercut	NN
randomwalker-info-585	707	17	,	,	,
randomwalker-info-585	707	18	and	and	CC
randomwalker-info-585	707	19	H	h	NN
randomwalker-info-585	707	20	+	+	CC
randomwalker-info-585	707	21	1	1	CD
randomwalker-info-585	707	22	if	if	IN
randomwalker-info-585	707	23	she	-PRON-	PRP
randomwalker-info-585	707	24	continued	continue	VBD
randomwalker-info-585	707	25	)	)	-RRB-
randomwalker-info-585	707	26	.	.	.
randomwalker-info-585	708	1	Either	either	CC
randomwalker-info-585	708	2	the	the	DT
randomwalker-info-585	708	3	newly	newly	RB
randomwalker-info-585	708	4	minted	mint	VBN
randomwalker-info-585	708	5	B	b	NN
randomwalker-info-585	708	6	is	be	VBZ
randomwalker-info-585	708	7	equal	equal	JJ
randomwalker-info-585	708	8	to	to	IN
randomwalker-info-585	708	9	MostHnew	MostHnew	NNP
randomwalker-info-585	708	10	,	,	,
randomwalker-info-585	708	11	or	or	CC
randomwalker-info-585	708	12	it	-PRON-	PRP
randomwalker-info-585	708	13	is	be	VBZ
randomwalker-info-585	708	14	n’t	not	RB
randomwalker-info-585	708	15	.	.	.
randomwalker-info-585	709	1	If	if	IN
randomwalker-info-585	709	2	it	-PRON-	PRP
randomwalker-info-585	709	3	is	be	VBZ
randomwalker-info-585	709	4	n’t	not	RB
randomwalker-info-585	709	5	,	,	,
randomwalker-info-585	709	6	then	then	RB
randomwalker-info-585	709	7	neither	neither	CC
randomwalker-info-585	709	8	the	the	DT
randomwalker-info-585	709	9	next	next	JJ
randomwalker-info-585	709	10	miner	miner	NN
randomwalker-info-585	709	11	,	,	,
randomwalker-info-585	709	12	nor	nor	CC
randomwalker-info-585	709	13	any	any	DT
randomwalker-info-585	709	14	other	other	JJ
randomwalker-info-585	709	15	miner	miner	NN
randomwalker-info-585	709	16	in	in	IN
randomwalker-info-585	709	17	the	the	DT
randomwalker-info-585	709	18	future	future	NN
randomwalker-info-585	709	19	will	will	MD
randomwalker-info-585	709	20	ever	ever	RB
randomwalker-info-585	709	21	mine	mine	VB
randomwalker-info-585	709	22	on	on	IN
randomwalker-info-585	709	23	top	top	NN
randomwalker-info-585	709	24	of	of	IN
randomwalker-info-585	709	25	it	-PRON-	PRP
randomwalker-info-585	709	26	,	,	,
randomwalker-info-585	709	27	because	because	IN
randomwalker-info-585	709	28	there	there	EX
randomwalker-info-585	709	29	is	be	VBZ
randomwalker-info-585	709	30	a	a	DT
randomwalker-info-585	709	31	“	"	``
randomwalker-info-585	709	32	better	well	JJR
randomwalker-info-585	709	33	”	"	''
randomwalker-info-585	709	34	chain	chain	NN
randomwalker-info-585	709	35	of	of	IN
randomwalker-info-585	709	36	length	length	NN
randomwalker-info-585	709	37	Hnew	Hnew	NNP
randomwalker-info-585	709	38	to	to	TO
randomwalker-info-585	709	39	mine	-PRON-	PRP
randomwalker-info-585	709	40	on	on	IN
randomwalker-info-585	709	41	top	top	NN
randomwalker-info-585	709	42	of	of	IN
randomwalker-info-585	709	43	instead	instead	RB
randomwalker-info-585	709	44	.	.	.
randomwalker-info-585	710	1	If	if	IN
randomwalker-info-585	710	2	it	-PRON-	PRP
randomwalker-info-585	710	3	is	be	VBZ
randomwalker-info-585	710	4	,	,	,
randomwalker-info-585	710	5	then	then	RB
randomwalker-info-585	710	6	the	the	DT
randomwalker-info-585	710	7	next	next	JJ
randomwalker-info-585	710	8	miner	miner	NN
randomwalker-info-585	710	9	will	will	MD
randomwalker-info-585	710	10	either	either	CC
randomwalker-info-585	710	11	undercut	undercut	VB
randomwalker-info-585	710	12	or	or	CC
randomwalker-info-585	710	13	continue	continue	VB
randomwalker-info-585	710	14	.	.	.
randomwalker-info-585	711	1	If	if	IN
randomwalker-info-585	711	2	the	the	DT
randomwalker-info-585	711	3	next	next	JJ
randomwalker-info-585	711	4	miner	miner	NN
randomwalker-info-585	711	5	continues	continue	VBZ
randomwalker-info-585	711	6	,	,	,
randomwalker-info-585	711	7	then	then	RB
randomwalker-info-585	711	8	B	b	NN
randomwalker-info-585	711	9	is	be	VBZ
randomwalker-info-585	711	10	now	now	RB
randomwalker-info-585	711	11	equal	equal	JJ
randomwalker-info-585	711	12	to	to	IN
randomwalker-info-585	711	13	MostHnew	MostHnew	NNP
randomwalker-info-585	711	14	and	and	CC
randomwalker-info-585	711	15	the	the	DT
randomwalker-info-585	711	16	predecessor	predecessor	NN
randomwalker-info-585	711	17	of	of	IN
randomwalker-info-585	711	18	MostHnew+1	MostHnew+1	NNP
randomwalker-info-585	711	19	.	.	.
randomwalker-info-585	712	1	This	this	DT
randomwalker-info-585	712	2	means	mean	VBZ
randomwalker-info-585	712	3	that	that	IN
randomwalker-info-585	712	4	all	all	DT
randomwalker-info-585	712	5	future	future	JJ
randomwalker-info-585	712	6	miners	miner	NNS
randomwalker-info-585	712	7	will	will	MD
randomwalker-info-585	712	8	continue	continue	VB
randomwalker-info-585	712	9	a	a	DT
randomwalker-info-585	712	10	chain	chain	NN
randomwalker-info-585	712	11	containing	contain	VBG
randomwalker-info-585	712	12	B	b	NN
randomwalker-info-585	712	13	,	,	,
randomwalker-info-585	712	14	and	and	CC
randomwalker-info-585	712	15	therefore	therefore	RB
randomwalker-info-585	712	16	it	-PRON-	PRP
randomwalker-info-585	712	17	will	will	MD
randomwalker-info-585	712	18	certainly	certainly	RB
randomwalker-info-585	712	19	be	be	VB
randomwalker-info-585	712	20	in	in	IN
randomwalker-info-585	712	21	the	the	DT
randomwalker-info-585	712	22	eventual	eventual	JJ
randomwalker-info-585	712	23	longest	long	JJS
randomwalker-info-585	712	24	chain	chain	NN
randomwalker-info-585	712	25	.	.	.
randomwalker-info-585	713	1	If	if	IN
randomwalker-info-585	713	2	instead	instead	RB
randomwalker-info-585	713	3	the	the	DT
randomwalker-info-585	713	4	next	next	JJ
randomwalker-info-585	713	5	miner	miner	NN
randomwalker-info-585	713	6	undercuts	undercut	NNS
randomwalker-info-585	713	7	,	,	,
randomwalker-info-585	713	8	then	then	RB
randomwalker-info-585	713	9	there	there	EX
randomwalker-info-585	713	10	will	will	MD
randomwalker-info-585	713	11	be	be	VB
randomwalker-info-585	713	12	a	a	DT
randomwalker-info-585	713	13	new	new	JJ
randomwalker-info-585	713	14	chain	chain	NN
randomwalker-info-585	713	15	of	of	IN
randomwalker-info-585	713	16	length	length	NN
randomwalker-info-585	713	17	Hnew	Hnew	NNP
randomwalker-info-585	713	18	that	that	WDT
randomwalker-info-585	713	19	leaves	leave	VBZ
randomwalker-info-585	713	20	more	more	RBR
randomwalker-info-585	713	21	available	available	JJ
randomwalker-info-585	713	22	BTC	BTC	NNP
randomwalker-info-585	713	23	,	,	,
randomwalker-info-585	713	24	meaning	mean	VBG
randomwalker-info-585	713	25	that	that	IN
randomwalker-info-585	713	26	MostHnew	MostHnew	NNP
randomwalker-info-585	713	27	does	do	VBZ
randomwalker-info-585	713	28	not	not	RB
randomwalker-info-585	713	29	contain	contain	VB
randomwalker-info-585	713	30	B	b	NN
randomwalker-info-585	713	31	as	as	IN
randomwalker-info-585	713	32	a	a	DT
randomwalker-info-585	713	33	predecessor	predecessor	NN
randomwalker-info-585	713	34	.	.	.
randomwalker-info-585	714	1	MostHnew−1	MostHnew−1	VBZ
randomwalker-info-585	714	2	clearly	clearly	RB
randomwalker-info-585	714	3	does	do	VBZ
randomwalker-info-585	714	4	not	not	RB
randomwalker-info-585	714	5	contain	contain	VB
randomwalker-info-585	714	6	B	b	NN
randomwalker-info-585	714	7	either	either	RB
randomwalker-info-585	714	8	,	,	,
randomwalker-info-585	714	9	as	as	IN
randomwalker-info-585	714	10	B	b	NN
randomwalker-info-585	714	11	was	be	VBD
randomwalker-info-585	714	12	mined	mine	VBN
randomwalker-info-585	714	13	on	on	IN
randomwalker-info-585	714	14	top	top	JJ
randomwalker-info-585	714	15	Figure	figure	NN
randomwalker-info-585	714	16	12	12	CD
randomwalker-info-585	714	17	:	:	:
randomwalker-info-585	714	18	One	one	CD
randomwalker-info-585	714	19	example	example	NN
randomwalker-info-585	714	20	of	of	IN
randomwalker-info-585	714	21	the	the	DT
randomwalker-info-585	714	22	function	function	NN
randomwalker-info-585	714	23	that	that	IN
randomwalker-info-585	714	24	function	function	NN
randomwalker-info-585	714	25	forking	fork	VBG
randomwalker-info-585	714	26	miners	miner	NNS
randomwalker-info-585	714	27	might	may	MD
randomwalker-info-585	714	28	use	use	VB
randomwalker-info-585	714	29	that	that	DT
randomwalker-info-585	714	30	leads	lead	VBZ
randomwalker-info-585	714	31	to	to	IN
randomwalker-info-585	714	32	an	an	DT
randomwalker-info-585	714	33	equilibrium	equilibrium	NN
randomwalker-info-585	714	34	.	.	.
randomwalker-info-585	715	1	Recall	recall	NN
randomwalker-info-585	715	2	,	,	,
randomwalker-info-585	715	3	the	the	DT
randomwalker-info-585	715	4	function	function	NN
randomwalker-info-585	715	5	is	be	VBZ
randomwalker-info-585	715	6	f(x	f(x	ADD
randomwalker-info-585	715	7	)	)	-RRB-
randomwalker-info-585	715	8	=	=	NFP
randomwalker-info-585	715	9	x	x	NNS
randomwalker-info-585	715	10	on	on	IN
randomwalker-info-585	715	11	the	the	DT
randomwalker-info-585	715	12	range	range	NN
randomwalker-info-585	715	13	[	[	-LRB-
randomwalker-info-585	715	14	0,y	0,y	NNP
randomwalker-info-585	715	15	]	]	-RRB-
randomwalker-info-585	715	16	,	,	,
randomwalker-info-585	715	17	the	the	DT
randomwalker-info-585	715	18	−W0(−yex−2y	−W0(−yex−2y	NNP
randomwalker-info-585	715	19	)	)	-RRB-
randomwalker-info-585	715	20	on	on	IN
randomwalker-info-585	715	21	[	[	-LRB-
randomwalker-info-585	715	22	y	y	NNP
randomwalker-info-585	715	23	,	,	,
randomwalker-info-585	715	24	2y−ln(y)−1	2y−ln(y)−1	CD
randomwalker-info-585	715	25	,	,	,
randomwalker-info-585	715	26	and	and	CC
randomwalker-info-585	715	27	1	1	CD
randomwalker-info-585	715	28	on	on	IN
randomwalker-info-585	715	29	[	[	-LRB-
randomwalker-info-585	715	30	2y−ln(y)−1,∞	2y−ln(y)−1,∞	CD
randomwalker-info-585	715	31	)	)	-RRB-
randomwalker-info-585	715	32	.	.	.
randomwalker-info-585	716	1	of	of	IN
randomwalker-info-585	716	2	this	this	DT
randomwalker-info-585	716	3	chain	chain	NN
randomwalker-info-585	716	4	.	.	.
randomwalker-info-585	717	1	So	so	RB
randomwalker-info-585	717	2	B	B	NNP
randomwalker-info-585	717	3	is	be	VBZ
randomwalker-info-585	717	4	contained	contain	VBN
randomwalker-info-585	717	5	in	in	IN
randomwalker-info-585	717	6	neither	neither	CC
randomwalker-info-585	717	7	MostHnew	MostHnew	NNP
randomwalker-info-585	717	8	nor	nor	CC
randomwalker-info-585	717	9	MostHnew−1	mosthnew−1	JJ
randomwalker-info-585	717	10	,	,	,
randomwalker-info-585	717	11	and	and	CC
randomwalker-info-585	717	12	therefore	therefore	RB
randomwalker-info-585	717	13	no	no	DT
randomwalker-info-585	717	14	future	future	JJ
randomwalker-info-585	717	15	miners	miner	NNS
randomwalker-info-585	717	16	will	will	MD
randomwalker-info-585	717	17	ever	ever	RB
randomwalker-info-585	717	18	consider	consider	VB
randomwalker-info-585	717	19	a	a	DT
randomwalker-info-585	717	20	chain	chain	NN
randomwalker-info-585	717	21	containing	contain	VBG
randomwalker-info-585	717	22	B.	B.	NNP
randomwalker-info-585	718	1	In	in	IN
randomwalker-info-585	718	2	conclusion	conclusion	NN
randomwalker-info-585	718	3	,	,	,
randomwalker-info-585	718	4	whether	whether	IN
randomwalker-info-585	718	5	or	or	CC
randomwalker-info-585	718	6	not	not	RB
randomwalker-info-585	718	7	a	a	DT
randomwalker-info-585	718	8	miner	miner	NN
randomwalker-info-585	718	9	receives	receive	VBZ
randomwalker-info-585	718	10	payment	payment	NN
randomwalker-info-585	718	11	for	for	IN
randomwalker-info-585	718	12	block	block	NNP
randomwalker-info-585	718	13	B	B	NNP
randomwalker-info-585	718	14	depends	depend	VBZ
randomwalker-info-585	718	15	entirely	entirely	RB
randomwalker-info-585	718	16	on	on	IN
randomwalker-info-585	718	17	whether	whether	IN
randomwalker-info-585	718	18	or	or	CC
randomwalker-info-585	718	19	not	not	RB
randomwalker-info-585	718	20	the	the	DT
randomwalker-info-585	718	21	subsequent	subsequent	JJ
randomwalker-info-585	718	22	miner	miner	NN
randomwalker-info-585	718	23	decides	decide	VBZ
randomwalker-info-585	718	24	to	to	IN
randomwalker-info-585	718	25	mine	-PRON-	PRP
randomwalker-info-585	718	26	on	on	IN
randomwalker-info-585	718	27	top	top	NN
randomwalker-info-585	718	28	of	of	IN
randomwalker-info-585	718	29	B	b	NN
randomwalker-info-585	718	30	or	or	CC
randomwalker-info-585	718	31	not	not	RB
randomwalker-info-585	718	32	.	.	.
randomwalker-info-585	719	1	We	-PRON-	PRP
randomwalker-info-585	719	2	now	now	RB
randomwalker-info-585	719	3	want	want	VBP
randomwalker-info-585	719	4	to	to	TO
randomwalker-info-585	719	5	figure	figure	VB
randomwalker-info-585	719	6	out	out	RP
randomwalker-info-585	719	7	a	a	DT
randomwalker-info-585	719	8	best	good	JJS
randomwalker-info-585	719	9	response	response	NN
randomwalker-info-585	719	10	for	for	IN
randomwalker-info-585	719	11	an	an	DT
randomwalker-info-585	719	12	individual	individual	JJ
randomwalker-info-585	719	13	non	non	JJ
randomwalker-info-585	719	14	-	-	JJ
randomwalker-info-585	719	15	atomic	atomic	JJ
randomwalker-info-585	719	16	miner	miner	NN
randomwalker-info-585	719	17	,	,	,
randomwalker-info-585	719	18	conditioned	condition	VBN
randomwalker-info-585	719	19	on	on	IN
randomwalker-info-585	719	20	all	all	DT
randomwalker-info-585	719	21	other	other	JJ
randomwalker-info-585	719	22	miners	miner	NNS
randomwalker-info-585	719	23	using	use	VBG
randomwalker-info-585	719	24	FunctionFork(f	FunctionFork(f	NNS
randomwalker-info-585	719	25	)	)	-RRB-
randomwalker-info-585	719	26	.	.	.
randomwalker-info-585	720	1	So	so	RB
randomwalker-info-585	720	2	we	-PRON-	PRP
randomwalker-info-585	720	3	need	need	VBP
randomwalker-info-585	720	4	to	to	TO
randomwalker-info-585	720	5	figure	figure	VB
randomwalker-info-585	720	6	out	out	RP
randomwalker-info-585	720	7	the	the	DT
randomwalker-info-585	720	8	probability	probability	NN
randomwalker-info-585	720	9	that	that	IN
randomwalker-info-585	720	10	a	a	DT
randomwalker-info-585	720	11	miner	miner	NN
randomwalker-info-585	720	12	will	will	MD
randomwalker-info-585	720	13	get	get	VB
randomwalker-info-585	720	14	undercut	undercut	JJ
randomwalker-info-585	720	15	when	when	WRB
randomwalker-info-585	720	16	authorizing	authorize	VBG
randomwalker-info-585	720	17	B	B	NNP
randomwalker-info-585	720	18	BTC	BTC	NNP
randomwalker-info-585	720	19	in	in	IN
randomwalker-info-585	720	20	transactions	transaction	NNS
randomwalker-info-585	720	21	,	,	,
randomwalker-info-585	720	22	assuming	assume	VBG
randomwalker-info-585	720	23	that	that	IN
randomwalker-info-585	720	24	all	all	DT
randomwalker-info-585	720	25	other	other	JJ
randomwalker-info-585	720	26	miners	miner	NNS
randomwalker-info-585	720	27	are	be	VBP
randomwalker-info-585	720	28	using	use	VBG
randomwalker-info-585	720	29	FunctionFork(f	FunctionFork(f	NNS
randomwalker-info-585	720	30	)	)	-RRB-
randomwalker-info-585	720	31	.	.	.
randomwalker-info-585	721	1	Note	note	VB
randomwalker-info-585	721	2	that	that	IN
randomwalker-info-585	721	3	as	as	IN
randomwalker-info-585	721	4	more	more	JJR
randomwalker-info-585	721	5	and	and	CC
randomwalker-info-585	721	6	more	more	JJR
randomwalker-info-585	721	7	new	new	JJ
randomwalker-info-585	721	8	BTC	btc	NN
randomwalker-info-585	721	9	of	of	IN
randomwalker-info-585	721	10	transactions	transaction	NNS
randomwalker-info-585	721	11	arrive	arrive	VBP
randomwalker-info-585	721	12	,	,	,
randomwalker-info-585	721	13	other	other	JJ
randomwalker-info-585	721	14	miners	miner	NNS
randomwalker-info-585	721	15	become	become	VBP
randomwalker-info-585	721	16	less	less	RBR
randomwalker-info-585	721	17	inclined	inclined	JJ
randomwalker-info-585	721	18	to	to	TO
randomwalker-info-585	721	19	undercut	undercut	VB
randomwalker-info-585	721	20	.	.	.
randomwalker-info-585	722	1	What	what	WP
randomwalker-info-585	722	2	we	-PRON-	PRP
randomwalker-info-585	722	3	need	need	VBP
randomwalker-info-585	722	4	to	to	TO
randomwalker-info-585	722	5	figure	figure	VB
randomwalker-info-585	722	6	out	out	RP
randomwalker-info-585	722	7	is	be	VBZ
randomwalker-info-585	722	8	exactly	exactly	RB
randomwalker-info-585	722	9	how	how	WRB
randomwalker-info-585	722	10	many	many	JJ
randomwalker-info-585	722	11	new	new	JJ
randomwalker-info-585	722	12	BTC	btc	NN
randomwalker-info-585	722	13	of	of	IN
randomwalker-info-585	722	14	transactions	transaction	NNS
randomwalker-info-585	722	15	need	need	VBP
randomwalker-info-585	722	16	to	to	TO
randomwalker-info-585	722	17	arrive	arrive	VB
randomwalker-info-585	722	18	before	before	IN
randomwalker-info-585	722	19	the	the	DT
randomwalker-info-585	722	20	next	next	JJ
randomwalker-info-585	722	21	miner	miner	NN
randomwalker-info-585	722	22	switches	switch	NNS
randomwalker-info-585	722	23	from	from	IN
randomwalker-info-585	722	24	preferring	prefer	VBG
randomwalker-info-585	722	25	to	to	TO
randomwalker-info-585	722	26	undercut	undercut	VB
randomwalker-info-585	722	27	to	to	IN
randomwalker-info-585	722	28	preferring	prefer	VBG
randomwalker-info-585	722	29	to	to	TO
randomwalker-info-585	722	30	continue	continue	VB
randomwalker-info-585	722	31	the	the	DT
randomwalker-info-585	722	32	longest	long	JJS
randomwalker-info-585	722	33	chain	chain	NN
randomwalker-info-585	722	34	.	.	.
randomwalker-info-585	723	1	Lemma	Lemma	NNP
randomwalker-info-585	723	2	C.1	C.1	NNP
randomwalker-info-585	723	3	.	.	.
randomwalker-info-585	724	1	If	if	IN
randomwalker-info-585	724	2	a	a	DT
randomwalker-info-585	724	3	miner	miner	NN
randomwalker-info-585	724	4	authorizes	authorize	VBZ
randomwalker-info-585	724	5	B	B	NNP
randomwalker-info-585	724	6	BTC	BTC	NNP
randomwalker-info-585	724	7	of	of	IN
randomwalker-info-585	724	8	transactions	transaction	NNS
randomwalker-info-585	724	9	on	on	IN
randomwalker-info-585	724	10	Mosti	Mosti	NNP
randomwalker-info-585	724	11	(	(	-LRB-
randomwalker-info-585	724	12	of	of	RB
randomwalker-info-585	724	13	course	course	NN
randomwalker-info-585	724	14	,	,	,
randomwalker-info-585	724	15	i	i	PRP
randomwalker-info-585	724	16	will	will	MD
randomwalker-info-585	724	17	be	be	VB
randomwalker-info-585	724	18	in	in	IN
randomwalker-info-585	724	19	{	{	-LRB-
randomwalker-info-585	724	20	H	h	NN
randomwalker-info-585	724	21	−	−	NNP
randomwalker-info-585	724	22	1,H	1,h	CD
randomwalker-info-585	724	23	}	}	-RRB-
randomwalker-info-585	724	24	)	)	-RRB-
randomwalker-info-585	724	25	,	,	,
randomwalker-info-585	724	26	then	then	RB
randomwalker-info-585	724	27	other	other	JJ
randomwalker-info-585	724	28	FunctionFork(f	FunctionFork(f	NNS
randomwalker-info-585	724	29	)	)	-RRB-
randomwalker-info-585	724	30	miners	miner	NNS
randomwalker-info-585	724	31	will	will	MD
randomwalker-info-585	724	32	try	try	VB
randomwalker-info-585	724	33	to	to	TO
randomwalker-info-585	724	34	undercut	undercut	VB
randomwalker-info-585	724	35	her	-PRON-	PRP
randomwalker-info-585	724	36	until	until	IN
randomwalker-info-585	724	37	max{0,f−1(B	max{0,f−1(B	NNP
randomwalker-info-585	724	38	)	)	-RRB-
randomwalker-info-585	724	39	+	+	SYM
randomwalker-info-585	724	40	B−Rem(Mosti	b−rem(mosti	NN
randomwalker-info-585	724	41	)	)	-RRB-
randomwalker-info-585	724	42	}	}	-RRB-
randomwalker-info-585	724	43	new	new	JJ
randomwalker-info-585	724	44	BTC	btc	NN
randomwalker-info-585	724	45	of	of	IN
randomwalker-info-585	724	46	transactions	transaction	NNS
randomwalker-info-585	724	47	arrive	arrive	VBP
randomwalker-info-585	724	48	(	(	-LRB-
randomwalker-info-585	724	49	Rem(Mosti	Rem(Mosti	NNP
randomwalker-info-585	724	50	)	)	-RRB-
randomwalker-info-585	724	51	taken	take	VBN
randomwalker-info-585	724	52	at	at	IN
randomwalker-info-585	724	53	the	the	DT
randomwalker-info-585	724	54	instant	instant	NN
randomwalker-info-585	724	55	that	that	IN
randomwalker-info-585	724	56	the	the	DT
randomwalker-info-585	724	57	miner	miner	NN
randomwalker-info-585	724	58	authorizes	authorize	VBZ
randomwalker-info-585	724	59	her	-PRON-	PRP$
randomwalker-info-585	724	60	block	block	NN
randomwalker-info-585	724	61	)	)	-RRB-
randomwalker-info-585	724	62	.	.	.
randomwalker-info-585	725	1	Therefore	therefore	RB
randomwalker-info-585	725	2	,	,	,
randomwalker-info-585	725	3	the	the	DT
randomwalker-info-585	725	4	expected	expect	VBN
randomwalker-info-585	725	5	BTC	BTC	NNP
randomwalker-info-585	725	6	obtained	obtain	VBN
randomwalker-info-585	725	7	by	by	IN
randomwalker-info-585	725	8	authorizing	authorize	VBG
randomwalker-info-585	725	9	B	B	NNP
randomwalker-info-585	725	10	BTC	BTC	NNP
randomwalker-info-585	725	11	of	of	IN
randomwalker-info-585	725	12	transactions	transaction	NNS
randomwalker-info-585	725	13	is	be	VBZ
randomwalker-info-585	725	14	Be−max{0,f	Be−max{0,f	NNPS
randomwalker-info-585	725	15	−1(B)+B−Rem(Mosti	−1(b)+b−rem(mosti	XX
randomwalker-info-585	725	16	)	)	-RRB-
randomwalker-info-585	725	17	}	}	-RRB-
randomwalker-info-585	725	18	.	.	.
randomwalker-info-585	726	1	Proof	proof	NN
randomwalker-info-585	726	2	.	.	.
randomwalker-info-585	727	1	First	first	RB
randomwalker-info-585	727	2	,	,	,
randomwalker-info-585	727	3	observe	observe	VB
randomwalker-info-585	727	4	that	that	IN
randomwalker-info-585	727	5	because	because	IN
randomwalker-info-585	727	6	the	the	DT
randomwalker-info-585	727	7	miner	miner	NN
randomwalker-info-585	727	8	chooses	choose	VBZ
randomwalker-info-585	727	9	to	to	TO
randomwalker-info-585	727	10	build	build	VB
randomwalker-info-585	727	11	upon	upon	IN
randomwalker-info-585	727	12	MostH−1	MostH−1	NNP
randomwalker-info-585	727	13	or	or	CC
randomwalker-info-585	727	14	MostH	MostH	NNP
randomwalker-info-585	727	15	,	,	,
randomwalker-info-585	727	16	then	then	RB
randomwalker-info-585	727	17	the	the	DT
randomwalker-info-585	727	18	chain	chain	NN
randomwalker-info-585	727	19	containing	contain	VBG
randomwalker-info-585	727	20	their	-PRON-	PRP$
randomwalker-info-585	727	21	block	block	NN
randomwalker-info-585	727	22	is	be	VBZ
randomwalker-info-585	727	23	the	the	DT
randomwalker-info-585	727	24	new	new	JJ
randomwalker-info-585	727	25	MostH	MostH	NNP
randomwalker-info-585	727	26	,	,	,
randomwalker-info-585	727	27	and	and	CC
randomwalker-info-585	727	28	that	that	DT
randomwalker-info-585	727	29	same	same	JJ
randomwalker-info-585	727	30	chain	chain	NN
randomwalker-info-585	727	31	minus	minu	VBD
randomwalker-info-585	727	32	their	-PRON-	PRP$
randomwalker-info-585	727	33	block	block	NN
randomwalker-info-585	727	34	is	be	VBZ
randomwalker-info-585	727	35	the	the	DT
randomwalker-info-585	727	36	new	new	JJ
randomwalker-info-585	727	37	MostH−1	mosth−1	CD
randomwalker-info-585	727	38	.	.	.
randomwalker-info-585	728	1	So	so	RB
randomwalker-info-585	728	2	the	the	DT
randomwalker-info-585	728	3	gap	gap	NN
randomwalker-info-585	728	4	between	between	IN
randomwalker-info-585	728	5	the	the	DT
randomwalker-info-585	728	6	number	number	NN
randomwalker-info-585	728	7	of	of	IN
randomwalker-info-585	728	8	available	available	JJ
randomwalker-info-585	728	9	BTC	BTC	NNP
randomwalker-info-585	728	10	in	in	IN
randomwalker-info-585	728	11	MostH	MostH	NNP
randomwalker-info-585	728	12	versus	versus	IN
randomwalker-info-585	728	13	MostH−1	MostH−1	NNP
randomwalker-info-585	728	14	(	(	-LRB-
randomwalker-info-585	728	15	GapH	GapH	NNP
randomwalker-info-585	728	16	=	=	SYM
randomwalker-info-585	728	17	Rem(MostH−1	rem(mosth−1	NN
randomwalker-info-585	728	18	)	)	-RRB-
randomwalker-info-585	728	19	−Rem(MostH	−rem(mosth	NN
randomwalker-info-585	728	20	)	)	-RRB-
randomwalker-info-585	728	21	)	)	-RRB-
randomwalker-info-585	728	22	for	for	IN
randomwalker-info-585	728	23	the	the	DT
randomwalker-info-585	728	24	next	next	JJ
randomwalker-info-585	728	25	miner	miner	NN
randomwalker-info-585	728	26	is	be	VBZ
randomwalker-info-585	728	27	exactly	exactly	RB
randomwalker-info-585	728	28	B.	B.	NNP
randomwalker-info-585	729	1	Now	now	RB
randomwalker-info-585	729	2	,	,	,
randomwalker-info-585	729	3	immediately	immediately	RB
randomwalker-info-585	729	4	when	when	WRB
randomwalker-info-585	729	5	the	the	DT
randomwalker-info-585	729	6	miner	miner	NN
randomwalker-info-585	729	7	publishes	publish	VBZ
randomwalker-info-585	729	8	her	-PRON-	PRP$
randomwalker-info-585	729	9	block	block	NN
randomwalker-info-585	729	10	,	,	,
randomwalker-info-585	729	11	there	there	EX
randomwalker-info-585	729	12	are	be	VBP
randomwalker-info-585	729	13	Rem(Mosti	rem(mosti	NN
randomwalker-info-585	729	14	)	)	-RRB-
randomwalker-info-585	729	15	BTC	BTC	NNP
randomwalker-info-585	729	16	of	of	IN
randomwalker-info-585	729	17	transactions	transaction	NNS
randomwalker-info-585	729	18	available	available	JJ
randomwalker-info-585	729	19	on	on	IN
randomwalker-info-585	729	20	MostH−1	mosth−1	CD
randomwalker-info-585	729	21	,	,	,
randomwalker-info-585	729	22	and	and	CC
randomwalker-info-585	729	23	Rem(Mosti	Rem(Mosti	NNP
randomwalker-info-585	729	24	)	)	-RRB-
randomwalker-info-585	729	25	−B	−B	NNP
randomwalker-info-585	729	26	BTC	BTC	NNP
randomwalker-info-585	729	27	of	of	IN
randomwalker-info-585	729	28	transactions	transaction	NNS
randomwalker-info-585	729	29	available	available	JJ
randomwalker-info-585	729	30	on	on	IN
randomwalker-info-585	729	31	MostH.	MostH.	NNS
randomwalker-info-585	730	1	So	so	CC
randomwalker-info-585	730	2	at	at	IN
randomwalker-info-585	730	3	this	this	DT
randomwalker-info-585	730	4	point	point	NN
randomwalker-info-585	730	5	,	,	,
randomwalker-info-585	730	6	other	other	JJ
randomwalker-info-585	730	7	miners	miner	NNS
randomwalker-info-585	730	8	would	would	MD
randomwalker-info-585	730	9	choose	choose	VB
randomwalker-info-585	730	10	to	to	TO
randomwalker-info-585	730	11	undercut	undercut	VB
randomwalker-info-585	730	12	iff	iff	NNP
randomwalker-info-585	730	13	f(Rem(Mosti)−B	f(Rem(Mosti)−B	NNP
randomwalker-info-585	730	14	)	)	-RRB-
randomwalker-info-585	730	15	<	<	XX
randomwalker-info-585	730	16	B.	B.	NNP
randomwalker-info-585	731	1	As	as	IN
randomwalker-info-585	731	2	more	more	JJR
randomwalker-info-585	731	3	new	new	JJ
randomwalker-info-585	731	4	BTC	btc	NN
randomwalker-info-585	731	5	of	of	IN
randomwalker-info-585	731	6	transactions	transaction	NNS
randomwalker-info-585	731	7	arrive	arrive	VBP
randomwalker-info-585	731	8	(	(	-LRB-
randomwalker-info-585	731	9	call	call	VB
randomwalker-info-585	731	10	it	-PRON-	PRP
randomwalker-info-585	731	11	x	x	LS
randomwalker-info-585	731	12	)	)	-RRB-
randomwalker-info-585	731	13	,	,	,
randomwalker-info-585	731	14	the	the	DT
randomwalker-info-585	731	15	other	other	JJ
randomwalker-info-585	731	16	miners	miner	NNS
randomwalker-info-585	731	17	would	would	MD
randomwalker-info-585	731	18	choose	choose	VB
randomwalker-info-585	731	19	to	to	TO
randomwalker-info-585	731	20	undercut	undercut	VB
randomwalker-info-585	731	21	iff	iff	NNP
randomwalker-info-585	731	22	f(Rem(Mosti	f(Rem(Mosti	NNP
randomwalker-info-585	731	23	)	)	-RRB-
randomwalker-info-585	731	24	−B	−B	NNP
randomwalker-info-585	731	25	+	+	NNS
randomwalker-info-585	731	26	x	x	NN
randomwalker-info-585	731	27	)	)	-RRB-
randomwalker-info-585	731	28	<	<	XX
randomwalker-info-585	731	29	B.	B.	NNP
randomwalker-info-585	732	1	As	as	IN
randomwalker-info-585	732	2	f	f	NNP
randomwalker-info-585	732	3	(	(	-LRB-
randomwalker-info-585	732	4	·	·	NFP
randomwalker-info-585	732	5	)	)	-RRB-
randomwalker-info-585	732	6	is	be	VBZ
randomwalker-info-585	732	7	increasing	increase	VBG
randomwalker-info-585	732	8	,	,	,
randomwalker-info-585	732	9	we	-PRON-	PRP
randomwalker-info-585	732	10	can	can	MD
randomwalker-info-585	732	11	look	look	VB
randomwalker-info-585	732	12	for	for	IN
randomwalker-info-585	732	13	the	the	DT
randomwalker-info-585	732	14	minimum	minimum	JJ
randomwalker-info-585	732	15	x	x	NNS
randomwalker-info-585	732	16	where	where	WRB
randomwalker-info-585	732	17	this	this	DT
randomwalker-info-585	732	18	ceases	cease	VBZ
randomwalker-info-585	732	19	hold	hold	VBP
randomwalker-info-585	732	20	,	,	,
randomwalker-info-585	732	21	which	which	WDT
randomwalker-info-585	732	22	is	be	VBZ
randomwalker-info-585	732	23	exactly	exactly	RB
randomwalker-info-585	732	24	when	when	WRB
randomwalker-info-585	732	25	Rem(Mosti	Rem(Mosti	NNP
randomwalker-info-585	732	26	)	)	-RRB-
randomwalker-info-585	732	27	−B	−B	NNP
randomwalker-info-585	732	28	+	+	NNS
randomwalker-info-585	732	29	x	x	SYM
randomwalker-info-585	732	30	=	=	SYM
randomwalker-info-585	732	31	f−1(B	f−1(B	NNP
randomwalker-info-585	732	32	)	)	-RRB-
randomwalker-info-585	732	33	,	,	,
randomwalker-info-585	732	34	or	or	CC
randomwalker-info-585	732	35	x	x	SYM
randomwalker-info-585	732	36	=	=	SYM
randomwalker-info-585	732	37	f−1(B	f−1(B	NNP
randomwalker-info-585	732	38	)	)	-RRB-
randomwalker-info-585	732	39	+	+	NFP
randomwalker-info-585	732	40	B	B	NNP
randomwalker-info-585	732	41	−Rem(Mosti	−Rem(Mosti	NNP
randomwalker-info-585	732	42	)	)	-RRB-
randomwalker-info-585	732	43	.	.	.
randomwalker-info-585	733	1	We	-PRON-	PRP
randomwalker-info-585	733	2	now	now	RB
randomwalker-info-585	733	3	prove	prove	VBP
randomwalker-info-585	733	4	three	three	CD
randomwalker-info-585	733	5	corollaries	corollary	NNS
randomwalker-info-585	733	6	of	of	IN
randomwalker-info-585	733	7	Lemma	Lemma	NNP
randomwalker-info-585	733	8	C.1	C.1	NNP
randomwalker-info-585	733	9	regarding	regard	VBG
randomwalker-info-585	733	10	what	what	WP
randomwalker-info-585	733	11	choices	choice	NNS
randomwalker-info-585	733	12	of	of	IN
randomwalker-info-585	733	13	B	B	NNP
randomwalker-info-585	733	14	might	may	MD
randomwalker-info-585	733	15	possibly	possibly	RB
randomwalker-info-585	733	16	be	be	VB
randomwalker-info-585	733	17	optimal	optimal	JJ
randomwalker-info-585	733	18	.	.	.
randomwalker-info-585	734	1	Corollary	corollary	JJ
randomwalker-info-585	734	2	C.2	C.2	NNP
randomwalker-info-585	734	3	.	.	.
randomwalker-info-585	735	1	If	if	IN
randomwalker-info-585	735	2	every	every	DT
randomwalker-info-585	735	3	other	other	JJ
randomwalker-info-585	735	4	miner	miner	NN
randomwalker-info-585	735	5	is	be	VBZ
randomwalker-info-585	735	6	playing	play	VBG
randomwalker-info-585	735	7	FunctionFork(f	FunctionFork(f	NNS
randomwalker-info-585	735	8	)	)	-RRB-
randomwalker-info-585	735	9	,	,	,
randomwalker-info-585	735	10	then	then	RB
randomwalker-info-585	735	11	the	the	DT
randomwalker-info-585	735	12	optimal	optimal	JJ
randomwalker-info-585	735	13	choice	choice	NN
randomwalker-info-585	735	14	B∗	B∗	NNS
randomwalker-info-585	735	15	of	of	IN
randomwalker-info-585	735	16	BTC	BTC	NNP
randomwalker-info-585	735	17	to	to	TO
randomwalker-info-585	735	18	authorize	authorize	VB
randomwalker-info-585	735	19	when	when	WRB
randomwalker-info-585	735	20	building	build	VBG
randomwalker-info-585	735	21	upon	upon	IN
randomwalker-info-585	735	22	chain	chain	NN
randomwalker-info-585	735	23	Mosti	Mosti	NNP
randomwalker-info-585	735	24	satisfies	satisfie	NNS
randomwalker-info-585	735	25	•	•	VBP
randomwalker-info-585	735	26	B∗	B∗	NNS
randomwalker-info-585	735	27	∈	∈	NNP
randomwalker-info-585	735	28	argmaxB∈[0,GapH]{Be	argmaxB∈[0,GapH]{Be	NNP
randomwalker-info-585	735	29	−max{0,f−1(B)+B−Rem(MostH−1	−max{0,f−1(B)+B−Rem(MostH−1	NNP
randomwalker-info-585	735	30	)	)	-RRB-
randomwalker-info-585	735	31	}	}	-RRB-
randomwalker-info-585	735	32	}	}	-RRB-
randomwalker-info-585	735	33	,	,	,
randomwalker-info-585	735	34	if	if	IN
randomwalker-info-585	735	35	i	i	PRP
randomwalker-info-585	735	36	=	=	SYM
randomwalker-info-585	735	37	H−	H−	NNP
randomwalker-info-585	735	38	1	1	CD
randomwalker-info-585	735	39	.	.	.
randomwalker-info-585	736	1	•	•	VB
randomwalker-info-585	736	2	B∗	B∗	NNS
randomwalker-info-585	736	3	∈	∈	IN
randomwalker-info-585	736	4	argmaxB∈[0,Rem(MostH)]{Be	argmaxb∈[0,rem(mosth)]{be	NN
randomwalker-info-585	736	5	−max{0,f−1(B)+B−Rem(MostH−1	−max{0,f−1(b)+b−rem(mosth−1	NN
randomwalker-info-585	736	6	)	)	-RRB-
randomwalker-info-585	736	7	}	}	-RRB-
randomwalker-info-585	736	8	}	}	-RRB-
randomwalker-info-585	736	9	,	,	,
randomwalker-info-585	736	10	if	if	IN
randomwalker-info-585	736	11	i	i	PRP
randomwalker-info-585	736	12	=	=	SYM
randomwalker-info-585	736	13	H.	H.	NNP
randomwalker-info-585	736	14	Proof	Proof	NNP
randomwalker-info-585	736	15	.	.	.
randomwalker-info-585	737	1	This	this	DT
randomwalker-info-585	737	2	is	be	VBZ
randomwalker-info-585	737	3	an	an	DT
randomwalker-info-585	737	4	immediate	immediate	JJ
randomwalker-info-585	737	5	corollary	corollary	NN
randomwalker-info-585	737	6	of	of	IN
randomwalker-info-585	737	7	Lemma	Lemma	NNP
randomwalker-info-585	737	8	C.1	C.1	NNP
randomwalker-info-585	737	9	,	,	,
randomwalker-info-585	737	10	combined	combine	VBN
randomwalker-info-585	737	11	with	with	IN
randomwalker-info-585	737	12	the	the	DT
randomwalker-info-585	737	13	fact	fact	NN
randomwalker-info-585	737	14	that	that	IN
randomwalker-info-585	737	15	a	a	DT
randomwalker-info-585	737	16	miner	miner	NN
randomwalker-info-585	737	17	who	who	WP
randomwalker-info-585	737	18	chooses	choose	VBZ
randomwalker-info-585	737	19	to	to	TO
randomwalker-info-585	737	20	undercut	undercut	VB
randomwalker-info-585	737	21	can	can	MD
randomwalker-info-585	737	22	authorize	authorize	VB
randomwalker-info-585	737	23	at	at	IN
randomwalker-info-585	737	24	most	most	JJS
randomwalker-info-585	737	25	GapH	GapH	NNP
randomwalker-info-585	737	26	BTC	BTC	NNP
randomwalker-info-585	737	27	,	,	,
randomwalker-info-585	737	28	while	while	IN
randomwalker-info-585	737	29	a	a	DT
randomwalker-info-585	737	30	miner	miner	NN
randomwalker-info-585	737	31	who	who	WP
randomwalker-info-585	737	32	chooses	choose	VBZ
randomwalker-info-585	737	33	to	to	TO
randomwalker-info-585	737	34	continue	continue	VB
randomwalker-info-585	737	35	can	can	MD
randomwalker-info-585	737	36	authorize	authorize	VB
randomwalker-info-585	737	37	at	at	IN
randomwalker-info-585	737	38	most	most	JJS
randomwalker-info-585	737	39	Rem(MostH	Rem(MostH	NNS
randomwalker-info-585	737	40	)	)	-RRB-
randomwalker-info-585	737	41	.	.	.
randomwalker-info-585	738	1	Corollary	Corollary	NNP
randomwalker-info-585	738	2	C.3	C.3	NNP
randomwalker-info-585	738	3	.	.	.
randomwalker-info-585	739	1	If	if	IN
randomwalker-info-585	739	2	B1	b1	NN
randomwalker-info-585	739	3	≥	≥	NN
randomwalker-info-585	739	4	B2	b2	NN
randomwalker-info-585	739	5	,	,	,
randomwalker-info-585	739	6	and	and	CC
randomwalker-info-585	739	7	B1e−B1−f	B1e−B1−f	NNP
randomwalker-info-585	739	8	−1(B1	−1(B1	NNP
randomwalker-info-585	739	9	)	)	-RRB-
randomwalker-info-585	739	10	≥	≥	UH
randomwalker-info-585	739	11	B2e−B1−f	B2e−B1−f	NNP
randomwalker-info-585	739	12	−1(B1	−1(B1	NNP
randomwalker-info-585	739	13	)	)	-RRB-
randomwalker-info-585	739	14	,	,	,
randomwalker-info-585	739	15	then	then	RB
randomwalker-info-585	739	16	for	for	IN
randomwalker-info-585	739	17	all	all	DT
randomwalker-info-585	739	18	X	x	NN
randomwalker-info-585	739	19	,	,	,
randomwalker-info-585	739	20	the	the	DT
randomwalker-info-585	739	21	expected	expected	JJ
randomwalker-info-585	739	22	reward	reward	NN
randomwalker-info-585	739	23	from	from	IN
randomwalker-info-585	739	24	authorizing	authorize	VBG
randomwalker-info-585	739	25	B1	B1	NNP
randomwalker-info-585	739	26	BTC	BTC	NNP
randomwalker-info-585	739	27	in	in	IN
randomwalker-info-585	739	28	transactions	transaction	NNS
randomwalker-info-585	739	29	is	be	VBZ
randomwalker-info-585	739	30	at	at	IN
randomwalker-info-585	739	31	least	least	JJS
randomwalker-info-585	739	32	as	as	RB
randomwalker-info-585	739	33	large	large	JJ
randomwalker-info-585	739	34	as	as	IN
randomwalker-info-585	739	35	the	the	DT
randomwalker-info-585	739	36	expected	expect	VBN
randomwalker-info-585	739	37	reward	reward	NN
randomwalker-info-585	739	38	from	from	IN
randomwalker-info-585	739	39	authorizing	authorize	VBG
randomwalker-info-585	739	40	B2	B2	NNP
randomwalker-info-585	739	41	BTC	BTC	NNP
randomwalker-info-585	739	42	when	when	WRB
randomwalker-info-585	739	43	Rem(MostH	Rem(MostH	NNP
randomwalker-info-585	739	44	)	)	-RRB-
randomwalker-info-585	739	45	=	=	NFP
randomwalker-info-585	739	46	X.	X.	NNP
randomwalker-info-585	740	1	Proof	proof	NN
randomwalker-info-585	740	2	.	.	.
randomwalker-info-585	741	1	There	there	EX
randomwalker-info-585	741	2	are	be	VBP
randomwalker-info-585	741	3	two	two	CD
randomwalker-info-585	741	4	cases	case	NNS
randomwalker-info-585	741	5	to	to	TO
randomwalker-info-585	741	6	consider	consider	VB
randomwalker-info-585	741	7	.	.	.
randomwalker-info-585	742	1	First	first	RB
randomwalker-info-585	742	2	,	,	,
randomwalker-info-585	742	3	maybe	maybe	RB
randomwalker-info-585	742	4	X	x	NN
randomwalker-info-585	742	5	>	>	XX
randomwalker-info-585	742	6	B1	b1	NN
randomwalker-info-585	742	7	+	+	CC
randomwalker-info-585	742	8	f	f	NN
randomwalker-info-585	742	9	−1(B1	−1(B1	NNP
randomwalker-info-585	742	10	)	)	-RRB-
randomwalker-info-585	742	11	(	(	-LRB-
randomwalker-info-585	742	12	the	the	DT
randomwalker-info-585	742	13	miner	miner	NN
randomwalker-info-585	742	14	guarantees	guarantee	VBZ
randomwalker-info-585	742	15	that	that	IN
randomwalker-info-585	742	16	she	-PRON-	PRP
randomwalker-info-585	742	17	is	be	VBZ
randomwalker-info-585	742	18	not	not	RB
randomwalker-info-585	742	19	undercut	undercut	JJ
randomwalker-info-585	742	20	by	by	IN
randomwalker-info-585	742	21	authorizing	authorize	VBG
randomwalker-info-585	742	22	B1	B1	NNP
randomwalker-info-585	742	23	BTC	BTC	NNP
randomwalker-info-585	742	24	in	in	IN
randomwalker-info-585	742	25	transactions	transaction	NNS
randomwalker-info-585	742	26	)	)	-RRB-
randomwalker-info-585	742	27	.	.	.
randomwalker-info-585	743	1	In	in	IN
randomwalker-info-585	743	2	this	this	DT
randomwalker-info-585	743	3	case	case	NN
randomwalker-info-585	743	4	,	,	,
randomwalker-info-585	743	5	because	because	IN
randomwalker-info-585	743	6	B1	b1	NN
randomwalker-info-585	743	7	≥	≥	NN
randomwalker-info-585	743	8	B2	b2	NN
randomwalker-info-585	743	9	and	and	CC
randomwalker-info-585	743	10	f−1	f−1	NNP
randomwalker-info-585	743	11	(	(	-LRB-
randomwalker-info-585	743	12	·	·	NFP
randomwalker-info-585	743	13	)	)	-RRB-
randomwalker-info-585	743	14	is	be	VBZ
randomwalker-info-585	743	15	increasing	increase	VBG
randomwalker-info-585	743	16	,	,	,
randomwalker-info-585	743	17	we	-PRON-	PRP
randomwalker-info-585	743	18	clearly	clearly	RB
randomwalker-info-585	743	19	have	have	VBP
randomwalker-info-585	743	20	X	x	NN
randomwalker-info-585	743	21	>	>	NN
randomwalker-info-585	743	22	B2+f−1(B2	b2+f−1(b2	NN
randomwalker-info-585	743	23	)	)	-RRB-
randomwalker-info-585	743	24	as	as	IN
randomwalker-info-585	743	25	well	well	RB
randomwalker-info-585	743	26	,	,	,
randomwalker-info-585	743	27	meaning	mean	VBG
randomwalker-info-585	743	28	that	that	IN
randomwalker-info-585	743	29	the	the	DT
randomwalker-info-585	743	30	expected	expect	VBN
randomwalker-info-585	743	31	reward	reward	NN
randomwalker-info-585	743	32	by	by	IN
randomwalker-info-585	743	33	authorizing	authorize	VBG
randomwalker-info-585	743	34	B1	B1	NNP
randomwalker-info-585	743	35	BTC	BTC	NNP
randomwalker-info-585	743	36	is	be	VBZ
randomwalker-info-585	743	37	exactly	exactly	RB
randomwalker-info-585	743	38	B1	b1	NN
randomwalker-info-585	743	39	,	,	,
randomwalker-info-585	743	40	and	and	CC
randomwalker-info-585	743	41	that	that	IN
randomwalker-info-585	743	42	the	the	DT
randomwalker-info-585	743	43	expected	expect	VBN
randomwalker-info-585	743	44	reward	reward	NN
randomwalker-info-585	743	45	by	by	IN
randomwalker-info-585	743	46	authorizing	authorize	VBG
randomwalker-info-585	743	47	B2	B2	NNP
randomwalker-info-585	743	48	BTC	BTC	NNP
randomwalker-info-585	743	49	is	be	VBZ
randomwalker-info-585	743	50	exactly	exactly	RB
randomwalker-info-585	743	51	B2	b2	NN
randomwalker-info-585	743	52	,	,	,
randomwalker-info-585	743	53	by	by	IN
randomwalker-info-585	743	54	Lemma	Lemma	NNP
randomwalker-info-585	743	55	C.1	C.1	NNP
randomwalker-info-585	743	56	.	.	.
randomwalker-info-585	744	1	As	as	IN
randomwalker-info-585	744	2	B1	b1	NN
randomwalker-info-585	744	3	≥	≥	NNP
randomwalker-info-585	744	4	B2	b2	NN
randomwalker-info-585	744	5	,	,	,
randomwalker-info-585	744	6	the	the	DT
randomwalker-info-585	744	7	reward	reward	NN
randomwalker-info-585	744	8	from	from	IN
randomwalker-info-585	744	9	B1	b1	NN
randomwalker-info-585	744	10	is	be	VBZ
randomwalker-info-585	744	11	at	at	IN
randomwalker-info-585	744	12	least	least	JJS
randomwalker-info-585	744	13	as	as	IN
randomwalker-info-585	744	14	large	large	JJ
randomwalker-info-585	744	15	.	.	.
randomwalker-info-585	745	1	In	in	IN
randomwalker-info-585	745	2	the	the	DT
randomwalker-info-585	745	3	second	second	JJ
randomwalker-info-585	745	4	case	case	NN
randomwalker-info-585	745	5	,	,	,
randomwalker-info-585	745	6	maybe	maybe	RB
randomwalker-info-585	745	7	X	x	NN
randomwalker-info-585	745	8	≤	≤	NN
randomwalker-info-585	745	9	B1	b1	NN
randomwalker-info-585	745	10	+	+	SYM
randomwalker-info-585	745	11	f−1(B1	f−1(b1	NN
randomwalker-info-585	745	12	)	)	-RRB-
randomwalker-info-585	745	13	(	(	-LRB-
randomwalker-info-585	745	14	the	the	DT
randomwalker-info-585	745	15	miner	miner	NN
randomwalker-info-585	745	16	is	be	VBZ
randomwalker-info-585	745	17	undercut	undercut	JJ
randomwalker-info-585	745	18	with	with	IN
randomwalker-info-585	745	19	positive	positive	JJ
randomwalker-info-585	745	20	probability	probability	NN
randomwalker-info-585	745	21	by	by	IN
randomwalker-info-585	745	22	authorizing	authorize	VBG
randomwalker-info-585	745	23	B1	B1	NNP
randomwalker-info-585	745	24	BTC	BTC	NNP
randomwalker-info-585	745	25	in	in	IN
randomwalker-info-585	745	26	transactions	transaction	NNS
randomwalker-info-585	745	27	)	)	-RRB-
randomwalker-info-585	745	28	.	.	.
randomwalker-info-585	746	1	In	in	IN
randomwalker-info-585	746	2	this	this	DT
randomwalker-info-585	746	3	case	case	NN
randomwalker-info-585	746	4	,	,	,
randomwalker-info-585	746	5	the	the	DT
randomwalker-info-585	746	6	reward	reward	NN
randomwalker-info-585	746	7	from	from	IN
randomwalker-info-585	746	8	authorizing	authorize	VBG
randomwalker-info-585	746	9	B1	B1	NNP
randomwalker-info-585	746	10	BTC	BTC	NNP
randomwalker-info-585	746	11	is	be	VBZ
randomwalker-info-585	746	12	B1e	B1e	NNP
randomwalker-info-585	746	13	−B1−f−1(B1)+X	−B1−f−1(B1)+X	NNP
randomwalker-info-585	746	14	,	,	,
randomwalker-info-585	746	15	by	by	IN
randomwalker-info-585	746	16	Lemma	Lemma	NNP
randomwalker-info-585	746	17	C.1	C.1	NNP
randomwalker-info-585	746	18	.	.	.
randomwalker-info-585	747	1	Also	also	RB
randomwalker-info-585	747	2	by	by	IN
randomwalker-info-585	747	3	Lemma	Lemma	NNP
randomwalker-info-585	747	4	C.1	C.1	NNP
randomwalker-info-585	747	5	,	,	,
randomwalker-info-585	747	6	the	the	DT
randomwalker-info-585	747	7	reward	reward	NN
randomwalker-info-585	747	8	from	from	IN
randomwalker-info-585	747	9	authorizing	authorize	VBG
randomwalker-info-585	747	10	B2	B2	NNP
randomwalker-info-585	747	11	BTC	BTC	NNP
randomwalker-info-585	747	12	is	be	VBZ
randomwalker-info-585	747	13	B2e	B2e	NNP
randomwalker-info-585	747	14	−max{0,B2+f−1(B2)−X	−max{0,B2+f−1(B2)−X	NNP
randomwalker-info-585	747	15	}	}	-RRB-
randomwalker-info-585	747	16	≤	≤	JJ
randomwalker-info-585	747	17	B2eX−B2−f	B2eX−B2−f	NNP
randomwalker-info-585	747	18	−1(B2	−1(B2	NNP
randomwalker-info-585	747	19	)	)	-RRB-
randomwalker-info-585	747	20	=	=	NFP
randomwalker-info-585	747	21	eX	eX	NNP
randomwalker-info-585	747	22	·	·	NFP
randomwalker-info-585	747	23	B2e−B2−f	B2e−B2−f	NNP
randomwalker-info-585	747	24	−1(B2	−1(B2	NNP
randomwalker-info-585	747	25	)	)	-RRB-
randomwalker-info-585	747	26	.	.	.
randomwalker-info-585	748	1	By	by	IN
randomwalker-info-585	748	2	hypothe-	hypothe-	JJ
randomwalker-info-585	748	3	sis	sis	NN
randomwalker-info-585	748	4	,	,	,
randomwalker-info-585	748	5	this	this	DT
randomwalker-info-585	748	6	is	be	VBZ
randomwalker-info-585	748	7	upper	upper	JJ
randomwalker-info-585	748	8	bounded	bound	VBN
randomwalker-info-585	748	9	by	by	IN
randomwalker-info-585	748	10	eXB1e	eXB1e	NNP
randomwalker-info-585	748	11	−B1−f−1(B1	−B1−f−1(B1	NNP
randomwalker-info-585	748	12	)	)	-RRB-
randomwalker-info-585	748	13	,	,	,
randomwalker-info-585	748	14	which	which	WDT
randomwalker-info-585	748	15	is	be	VBZ
randomwalker-info-585	748	16	exactly	exactly	RB
randomwalker-info-585	748	17	the	the	DT
randomwalker-info-585	748	18	reward	reward	NN
randomwalker-info-585	748	19	obtained	obtain	VBN
randomwalker-info-585	748	20	by	by	IN
randomwalker-info-585	748	21	authorizing	authorize	VBG
randomwalker-info-585	748	22	B1	B1	NNP
randomwalker-info-585	748	23	BTC	BTC	NNP
randomwalker-info-585	748	24	.	.	.
randomwalker-info-585	749	1	So	so	RB
randomwalker-info-585	749	2	authorizing	authorize	VBG
randomwalker-info-585	749	3	B1	B1	NNP
randomwalker-info-585	749	4	BTC	BTC	NNP
randomwalker-info-585	749	5	provides	provide	VBZ
randomwalker-info-585	749	6	at	at	IN
randomwalker-info-585	749	7	least	least	JJS
randomwalker-info-585	749	8	as	as	IN
randomwalker-info-585	749	9	much	much	JJ
randomwalker-info-585	749	10	reward	reward	NN
randomwalker-info-585	749	11	.	.	.
randomwalker-info-585	750	1	In	in	IN
randomwalker-info-585	750	2	both	both	DT
randomwalker-info-585	750	3	cases	case	NNS
randomwalker-info-585	750	4	,	,	,
randomwalker-info-585	750	5	we	-PRON-	PRP
randomwalker-info-585	750	6	see	see	VBP
randomwalker-info-585	750	7	that	that	IN
randomwalker-info-585	750	8	authorizing	authorize	VBG
randomwalker-info-585	750	9	B1	B1	NNP
randomwalker-info-585	750	10	BTC	BTC	NNP
randomwalker-info-585	750	11	is	be	VBZ
randomwalker-info-585	750	12	at	at	IN
randomwalker-info-585	750	13	least	least	JJS
randomwalker-info-585	750	14	as	as	RB
randomwalker-info-585	750	15	good	good	JJ
randomwalker-info-585	750	16	as	as	IN
randomwalker-info-585	750	17	B2	b2	NN
randomwalker-info-585	750	18	.	.	.
randomwalker-info-585	751	1	Corollary	Corollary	NNP
randomwalker-info-585	751	2	C.4	C.4	NNP
randomwalker-info-585	751	3	.	.	.
randomwalker-info-585	752	1	If	if	IN
randomwalker-info-585	752	2	B1	b1	NN
randomwalker-info-585	752	3	≥	≥	NN
randomwalker-info-585	752	4	B2	b2	NN
randomwalker-info-585	752	5	,	,	,
randomwalker-info-585	752	6	and	and	CC
randomwalker-info-585	752	7	B1e−B1−f	B1e−B1−f	NNP
randomwalker-info-585	752	8	−1(B1	−1(B1	NNP
randomwalker-info-585	752	9	)	)	-RRB-
randomwalker-info-585	752	10	≤	≤	NNP
randomwalker-info-585	752	11	B2e−B2−f	B2e−B2−f	NNP
randomwalker-info-585	752	12	−1(B2	−1(B2	NNP
randomwalker-info-585	752	13	)	)	-RRB-
randomwalker-info-585	752	14	,	,	,
randomwalker-info-585	752	15	then	then	RB
randomwalker-info-585	752	16	for	for	IN
randomwalker-info-585	752	17	all	all	DT
randomwalker-info-585	752	18	X	x	NN
randomwalker-info-585	752	19	≤	≤	NN
randomwalker-info-585	752	20	B2	b2	NN
randomwalker-info-585	752	21	+	+	CC
randomwalker-info-585	752	22	f−1(B2	f−1(b2	NN
randomwalker-info-585	752	23	)	)	-RRB-
randomwalker-info-585	752	24	,	,	,
randomwalker-info-585	752	25	the	the	DT
randomwalker-info-585	752	26	expected	expect	VBN
randomwalker-info-585	752	27	re-	re-	RB
randomwalker-info-585	752	28	ward	ward	RB
randomwalker-info-585	752	29	from	from	IN
randomwalker-info-585	752	30	authorizing	authorize	VBG
randomwalker-info-585	752	31	B2	B2	NNP
randomwalker-info-585	752	32	BTC	BTC	NNP
randomwalker-info-585	752	33	in	in	IN
randomwalker-info-585	752	34	transactions	transaction	NNS
randomwalker-info-585	752	35	is	be	VBZ
randomwalker-info-585	752	36	at	at	IN
randomwalker-info-585	752	37	least	least	JJS
randomwalker-info-585	752	38	as	as	RB
randomwalker-info-585	752	39	large	large	JJ
randomwalker-info-585	752	40	as	as	IN
randomwalker-info-585	752	41	the	the	DT
randomwalker-info-585	752	42	expected	expect	VBN
randomwalker-info-585	752	43	reward	reward	NN
randomwalker-info-585	752	44	from	from	IN
randomwalker-info-585	752	45	authorizing	authorize	VBG
randomwalker-info-585	752	46	B1	B1	NNP
randomwalker-info-585	752	47	BTC	BTC	NNP
randomwalker-info-585	752	48	when	when	WRB
randomwalker-info-585	752	49	Rem(MostH	Rem(MostH	NNP
randomwalker-info-585	752	50	)	)	-RRB-
randomwalker-info-585	752	51	=	=	NFP
randomwalker-info-585	752	52	X.	X.	NNP
randomwalker-info-585	753	1	Proof	proof	NN
randomwalker-info-585	753	2	.	.	.
randomwalker-info-585	754	1	By	by	IN
randomwalker-info-585	754	2	hypothesis	hypothesis	NN
randomwalker-info-585	754	3	,	,	,
randomwalker-info-585	754	4	X	X	NNP
randomwalker-info-585	754	5	≤	≤	NN
randomwalker-info-585	754	6	B2	b2	NN
randomwalker-info-585	754	7	+	+	CC
randomwalker-info-585	754	8	f−1(B2	f−1(b2	NN
randomwalker-info-585	754	9	)	)	-RRB-
randomwalker-info-585	754	10	(	(	-LRB-
randomwalker-info-585	754	11	the	the	DT
randomwalker-info-585	754	12	miner	miner	NN
randomwalker-info-585	754	13	is	be	VBZ
randomwalker-info-585	754	14	undercut	undercut	JJ
randomwalker-info-585	754	15	with	with	IN
randomwalker-info-585	754	16	positive	positive	JJ
randomwalker-info-585	754	17	probability	probability	NN
randomwalker-info-585	754	18	by	by	IN
randomwalker-info-585	754	19	authorizing	authorize	VBG
randomwalker-info-585	754	20	B2	B2	NNP
randomwalker-info-585	754	21	BTC	BTC	NNP
randomwalker-info-585	754	22	in	in	IN
randomwalker-info-585	754	23	transactions	transaction	NNS
randomwalker-info-585	754	24	)	)	-RRB-
randomwalker-info-585	754	25	.	.	.
randomwalker-info-585	755	1	Therefore	therefore	RB
randomwalker-info-585	755	2	,	,	,
randomwalker-info-585	755	3	the	the	DT
randomwalker-info-585	755	4	expected	expected	JJ
randomwalker-info-585	755	5	reward	reward	NN
randomwalker-info-585	755	6	from	from	IN
randomwalker-info-585	755	7	authorizing	authorize	VBG
randomwalker-info-585	755	8	B2	B2	NNP
randomwalker-info-585	755	9	BTC	BTC	NNP
randomwalker-info-585	755	10	is	be	VBZ
randomwalker-info-585	755	11	B2e	B2e	NNP
randomwalker-info-585	755	12	−B2−f−1(B2)+X.	−b2−f−1(b2)+x.	ADD
randomwalker-info-585	756	1	As	as	IN
randomwalker-info-585	756	2	B1	b1	NN
randomwalker-info-585	756	3	>	>	FW
randomwalker-info-585	756	4	B2	b2	NN
randomwalker-info-585	756	5	and	and	CC
randomwalker-info-585	756	6	f	f	NNP
randomwalker-info-585	756	7	−1	−1	NNP
randomwalker-info-585	756	8	(	(	-LRB-
randomwalker-info-585	756	9	·	·	NFP
randomwalker-info-585	756	10	)	)	-RRB-
randomwalker-info-585	756	11	is	be	VBZ
randomwalker-info-585	756	12	increasing	increase	VBG
randomwalker-info-585	756	13	,	,	,
randomwalker-info-585	756	14	we	-PRON-	PRP
randomwalker-info-585	756	15	have	have	VBP
randomwalker-info-585	756	16	X	X	NNP
randomwalker-info-585	756	17	≤	≤	NN
randomwalker-info-585	756	18	B1	b1	NN
randomwalker-info-585	756	19	+	+	SYM
randomwalker-info-585	756	20	f−1(B1	f−1(b1	NN
randomwalker-info-585	756	21	)	)	-RRB-
randomwalker-info-585	756	22	as	as	RB
randomwalker-info-585	756	23	well	well	RB
randomwalker-info-585	756	24	.	.	.
randomwalker-info-585	757	1	This	this	DT
randomwalker-info-585	757	2	means	mean	VBZ
randomwalker-info-585	757	3	that	that	IN
randomwalker-info-585	757	4	the	the	DT
randomwalker-info-585	757	5	expected	expected	JJ
randomwalker-info-585	757	6	reward	reward	NN
randomwalker-info-585	757	7	from	from	IN
randomwalker-info-585	757	8	authorizing	authorize	VBG
randomwalker-info-585	757	9	B1	B1	NNP
randomwalker-info-585	757	10	BTC	BTC	NNP
randomwalker-info-585	757	11	is	be	VBZ
randomwalker-info-585	757	12	B1e	b1e	XX
randomwalker-info-585	757	13	−B1−f−1(B1)+X.	−b1−f−1(b1)+x.	ADD
randomwalker-info-585	758	1	By	by	IN
randomwalker-info-585	758	2	hypothesis	hypothesis	NN
randomwalker-info-585	758	3	,	,	,
randomwalker-info-585	758	4	this	this	DT
randomwalker-info-585	758	5	is	be	VBZ
randomwalker-info-585	758	6	less	less	JJR
randomwalker-info-585	758	7	than	than	IN
randomwalker-info-585	758	8	the	the	DT
randomwalker-info-585	758	9	reward	reward	NN
randomwalker-info-585	758	10	of	of	IN
randomwalker-info-585	758	11	authorizing	authorize	VBG
randomwalker-info-585	758	12	B2	b2	NN
randomwalker-info-585	758	13	.	.	.
randomwalker-info-585	759	1	We	-PRON-	PRP
randomwalker-info-585	759	2	now	now	RB
randomwalker-info-585	759	3	recall	recall	VBP
randomwalker-info-585	759	4	quickly	quickly	RB
randomwalker-info-585	759	5	properties	property	NNS
randomwalker-info-585	759	6	of	of	IN
randomwalker-info-585	759	7	W0	w0	NN
randomwalker-info-585	759	8	(	(	-LRB-
randomwalker-info-585	759	9	·	·	NFP
randomwalker-info-585	759	10	)	)	-RRB-
randomwalker-info-585	759	11	:	:	:
randomwalker-info-585	759	12	•	•	VB
randomwalker-info-585	759	13	The	the	DT
randomwalker-info-585	759	14	domain	domain	NN
randomwalker-info-585	759	15	of	of	IN
randomwalker-info-585	759	16	W0	w0	NN
randomwalker-info-585	759	17	(	(	-LRB-
randomwalker-info-585	759	18	·	·	NFP
randomwalker-info-585	759	19	)	)	-RRB-
randomwalker-info-585	759	20	is	be	VBZ
randomwalker-info-585	759	21	[	[	-LRB-
randomwalker-info-585	759	22	−1	−1	NNP
randomwalker-info-585	759	23	/	/	SYM
randomwalker-info-585	759	24	e,∞	e,∞	NN
randomwalker-info-585	759	25	)	)	-RRB-
randomwalker-info-585	759	26	and	and	CC
randomwalker-info-585	759	27	the	the	DT
randomwalker-info-585	759	28	range	range	NN
randomwalker-info-585	759	29	is	be	VBZ
randomwalker-info-585	759	30	[	[	-LRB-
randomwalker-info-585	759	31	−1,∞	−1,∞	UH
randomwalker-info-585	759	32	)	)	-RRB-
randomwalker-info-585	759	33	.	.	.
randomwalker-info-585	760	1	•	•	NNP
randomwalker-info-585	760	2	W0	w0	NN
randomwalker-info-585	760	3	(	(	-LRB-
randomwalker-info-585	760	4	·	·	NFP
randomwalker-info-585	760	5	)	)	-RRB-
randomwalker-info-585	760	6	is	be	VBZ
randomwalker-info-585	760	7	increasing	increase	VBG
randomwalker-info-585	760	8	.	.	.
randomwalker-info-585	761	1	•	•	NNP
randomwalker-info-585	761	2	W0(xex	w0(xex	NN
randomwalker-info-585	761	3	)	)	-RRB-
randomwalker-info-585	761	4	=	=	NFP
randomwalker-info-585	761	5	x	x	NN
randomwalker-info-585	761	6	for	for	IN
randomwalker-info-585	761	7	all	all	DT
randomwalker-info-585	761	8	x	x	NN
randomwalker-info-585	761	9	∈	∈	JJ
randomwalker-info-585	761	10	[	[	-LRB-
randomwalker-info-585	761	11	−1,∞	−1,∞	UH
randomwalker-info-585	761	12	)	)	-RRB-
randomwalker-info-585	761	13	.	.	.
randomwalker-info-585	762	1	We	-PRON-	PRP
randomwalker-info-585	762	2	will	will	MD
randomwalker-info-585	762	3	need	need	VB
randomwalker-info-585	762	4	to	to	TO
randomwalker-info-585	762	5	make	make	VB
randomwalker-info-585	762	6	use	use	NN
randomwalker-info-585	762	7	of	of	IN
randomwalker-info-585	762	8	some	some	DT
randomwalker-info-585	762	9	technical	technical	JJ
randomwalker-info-585	762	10	facts	fact	NNS
randomwalker-info-585	762	11	about	about	IN
randomwalker-info-585	762	12	f	f	NNP
randomwalker-info-585	762	13	(	(	-LRB-
randomwalker-info-585	762	14	·	·	NFP
randomwalker-info-585	762	15	)	)	-RRB-
randomwalker-info-585	762	16	(	(	-LRB-
randomwalker-info-585	762	17	our	-PRON-	PRP$
randomwalker-info-585	762	18	specific	specific	JJ
randomwalker-info-585	762	19	choice	choice	NN
randomwalker-info-585	762	20	from	from	IN
randomwalker-info-585	762	21	the	the	DT
randomwalker-info-585	762	22	statement	statement	NN
randomwalker-info-585	762	23	of	of	IN
randomwalker-info-585	762	24	Theorem	Theorem	NNP
randomwalker-info-585	762	25	5.1	5.1	CD
randomwalker-info-585	762	26	)	)	-RRB-
randomwalker-info-585	762	27	that	that	IN
randomwalker-info-585	762	28	we	-PRON-	PRP
randomwalker-info-585	762	29	first	first	RB
randomwalker-info-585	762	30	prove	prove	VBP
randomwalker-info-585	762	31	below	below	RB
randomwalker-info-585	762	32	.	.	.
randomwalker-info-585	763	1	Fact	fact	NN
randomwalker-info-585	763	2	1	1	CD
randomwalker-info-585	763	3	.	.	.
randomwalker-info-585	763	4	f(x	f(x	CD
randomwalker-info-585	763	5	)	)	-RRB-
randomwalker-info-585	763	6	≤	≤	VBD
randomwalker-info-585	763	7	x	x	RB
randomwalker-info-585	763	8	everywhere	everywhere	RB
randomwalker-info-585	763	9	.	.	.
randomwalker-info-585	764	1	Proof	proof	NN
randomwalker-info-585	764	2	.	.	.
randomwalker-info-585	765	1	Clearly	clearly	RB
randomwalker-info-585	765	2	,	,	,
randomwalker-info-585	765	3	f(x	f(x	NNP
randomwalker-info-585	765	4	)	)	-RRB-
randomwalker-info-585	765	5	≤	≤	VBD
randomwalker-info-585	765	6	x	x	NNS
randomwalker-info-585	765	7	on	on	IN
randomwalker-info-585	765	8	[	[	-LRB-
randomwalker-info-585	765	9	0,y	0,y	NN
randomwalker-info-585	765	10	]	]	-RRB-
randomwalker-info-585	765	11	.	.	.
randomwalker-info-585	766	1	Also	also	RB
randomwalker-info-585	766	2	clearly	clearly	RB
randomwalker-info-585	766	3	,	,	,
randomwalker-info-585	766	4	f(x	f(x	ADD
randomwalker-info-585	766	5	)	)	-RRB-
randomwalker-info-585	766	6	≤	≤	VBD
randomwalker-info-585	766	7	x	x	NNS
randomwalker-info-585	766	8	on	on	IN
randomwalker-info-585	766	9	[	[	-LRB-
randomwalker-info-585	766	10	2y	2y	CD
randomwalker-info-585	766	11	−	−	NNP
randomwalker-info-585	766	12	ln(y	ln(y	CD
randomwalker-info-585	766	13	)	)	-RRB-
randomwalker-info-585	766	14	−	−	NNP
randomwalker-info-585	766	15	1,∞	1,∞	CD
randomwalker-info-585	766	16	)	)	-RRB-
randomwalker-info-585	766	17	iff	iff	VBD
randomwalker-info-585	766	18	f(2y	f(2y	NNP
randomwalker-info-585	766	19	−	−	NNP
randomwalker-info-585	766	20	ln(y	ln(y	CD
randomwalker-info-585	766	21	)	)	-RRB-
randomwalker-info-585	766	22	−	−	NNP
randomwalker-info-585	766	23	1	1	CD
randomwalker-info-585	766	24	)	)	-RRB-
randomwalker-info-585	766	25	≤	≤	NNP
randomwalker-info-585	766	26	2y	2y	CD
randomwalker-info-585	766	27	−	−	NNP
randomwalker-info-585	766	28	ln(y	ln(y	NNP
randomwalker-info-585	766	29	)	)	-RRB-
randomwalker-info-585	766	30	−	−	NNP
randomwalker-info-585	766	31	1	1	CD
randomwalker-info-585	766	32	.	.	.
randomwalker-info-585	767	1	So	so	RB
randomwalker-info-585	767	2	we	-PRON-	PRP
randomwalker-info-585	767	3	just	just	RB
randomwalker-info-585	767	4	need	need	VBP
randomwalker-info-585	767	5	to	to	TO
randomwalker-info-585	767	6	check	check	VB
randomwalker-info-585	767	7	the	the	DT
randomwalker-info-585	767	8	range	range	NN
randomwalker-info-585	767	9	[	[	-LRB-
randomwalker-info-585	767	10	y	y	NNP
randomwalker-info-585	767	11	,	,	,
randomwalker-info-585	767	12	2y−	2y−	CD
randomwalker-info-585	767	13	ln(y)−1	ln(y)−1	NNP
randomwalker-info-585	767	14	]	]	-RRB-
randomwalker-info-585	767	15	.	.	.
randomwalker-info-585	768	1	The	the	DT
randomwalker-info-585	768	2	derivative	derivative	NN
randomwalker-info-585	768	3	of	of	IN
randomwalker-info-585	768	4	W0(x	w0(x	NN
randomwalker-info-585	768	5	)	)	-RRB-
randomwalker-info-585	768	6	=	=	NFP
randomwalker-info-585	768	7	W0(x)x(W0(x)+1	W0(x)x(W0(x)+1	NNP
randomwalker-info-585	768	8	)	)	-RRB-
randomwalker-info-585	768	9	.	.	.
randomwalker-info-585	769	1	So	so	RB
randomwalker-info-585	769	2	the	the	DT
randomwalker-info-585	769	3	derivative	derivative	NN
randomwalker-info-585	769	4	of	of	IN
randomwalker-info-585	769	5	f	f	NNP
randomwalker-info-585	769	6	on	on	IN
randomwalker-info-585	769	7	this	this	DT
randomwalker-info-585	769	8	range	range	NN
randomwalker-info-585	769	9	is	be	VBZ
randomwalker-info-585	769	10	(	(	-LRB-
randomwalker-info-585	769	11	by	by	IN
randomwalker-info-585	769	12	the	the	DT
randomwalker-info-585	769	13	chain	chain	NN
randomwalker-info-585	769	14	rule	rule	NN
randomwalker-info-585	769	15	)	)	-RRB-
randomwalker-info-585	769	16	:	:	:
randomwalker-info-585	769	17	−	−	NNP
randomwalker-info-585	769	18	W0(−yex−2y	w0(−yex−2y	NN
randomwalker-info-585	769	19	)	)	-RRB-
randomwalker-info-585	769	20	−yex−2y(W0(−yex−2y	−yex−2y(W0(−yex−2y	NNP
randomwalker-info-585	769	21	)	)	-RRB-
randomwalker-info-585	769	22	+	+	CC
randomwalker-info-585	769	23	1	1	LS
randomwalker-info-585	769	24	)	)	-RRB-
randomwalker-info-585	769	25	·	·	NFP
randomwalker-info-585	769	26	−yex−2y	−yex−2y	NNP
randomwalker-info-585	769	27	=	=	SYM
randomwalker-info-585	769	28	−W0(−yex−2y	−W0(−yex−2y	NNP
randomwalker-info-585	769	29	)	)	-RRB-
randomwalker-info-585	769	30	1	1	CD
randomwalker-info-585	769	31	+	+	CC
randomwalker-info-585	769	32	W0(−yex−2y	w0(−yex−2y	NN
randomwalker-info-585	769	33	)	)	-RRB-
randomwalker-info-585	769	34	=	=	NFP
randomwalker-info-585	769	35	f(x	f(x	CD
randomwalker-info-585	769	36	)	)	-RRB-
randomwalker-info-585	769	37	1	1	CD
randomwalker-info-585	769	38	−f(x	−f(x	ADD
randomwalker-info-585	769	39	)	)	-RRB-
randomwalker-info-585	769	40	As	as	IN
randomwalker-info-585	769	41	f	f	NNP
randomwalker-info-585	769	42	(	(	-LRB-
randomwalker-info-585	769	43	·	·	NFP
randomwalker-info-585	769	44	)	)	-RRB-
randomwalker-info-585	769	45	is	be	VBZ
randomwalker-info-585	769	46	increasing	increase	VBG
randomwalker-info-585	769	47	and	and	CC
randomwalker-info-585	769	48	positive	positive	JJ
randomwalker-info-585	769	49	on	on	IN
randomwalker-info-585	769	50	[	[	-LRB-
randomwalker-info-585	769	51	y	y	NNP
randomwalker-info-585	769	52	,	,	,
randomwalker-info-585	769	53	2y−ln(y)−1	2y−ln(y)−1	CD
randomwalker-info-585	769	54	]	]	-RRB-
randomwalker-info-585	769	55	(	(	-LRB-
randomwalker-info-585	769	56	because	because	IN
randomwalker-info-585	769	57	of	of	IN
randomwalker-info-585	769	58	the	the	DT
randomwalker-info-585	769	59	form	form	NN
randomwalker-info-585	769	60	for	for	IN
randomwalker-info-585	769	61	f′(x	f′(x	NNP
randomwalker-info-585	769	62	)	)	-RRB-
randomwalker-info-585	769	63	we	-PRON-	PRP
randomwalker-info-585	769	64	just	just	RB
randomwalker-info-585	769	65	derived	derive	VBD
randomwalker-info-585	769	66	above	above	RB
randomwalker-info-585	769	67	-	-	:
randomwalker-info-585	769	68	not	not	RB
randomwalker-info-585	769	69	all	all	DT
randomwalker-info-585	769	70	positive	positive	JJ
randomwalker-info-585	769	71	,	,	,
randomwalker-info-585	769	72	increasing	increase	VBG
randomwalker-info-585	769	73	f	f	NN
randomwalker-info-585	769	74	(	(	-LRB-
randomwalker-info-585	769	75	·	·	NFP
randomwalker-info-585	769	76	)	)	-RRB-
randomwalker-info-585	769	77	have	have	VBP
randomwalker-info-585	769	78	increasing	increase	VBG
randomwalker-info-585	769	79	derivatives	derivative	NNS
randomwalker-info-585	769	80	)	)	-RRB-
randomwalker-info-585	769	81	,	,	,
randomwalker-info-585	769	82	this	this	DT
randomwalker-info-585	769	83	means	mean	VBZ
randomwalker-info-585	769	84	that	that	IN
randomwalker-info-585	769	85	f′	f′	NN
randomwalker-info-585	769	86	(	(	-LRB-
randomwalker-info-585	769	87	·	·	NFP
randomwalker-info-585	769	88	)	)	-RRB-
randomwalker-info-585	769	89	is	be	VBZ
randomwalker-info-585	769	90	also	also	RB
randomwalker-info-585	769	91	increasing	increase	VBG
randomwalker-info-585	769	92	and	and	CC
randomwalker-info-585	769	93	positive	positive	JJ
randomwalker-info-585	769	94	on	on	IN
randomwalker-info-585	769	95	[	[	-LRB-
randomwalker-info-585	769	96	y	y	NNP
randomwalker-info-585	769	97	,	,	,
randomwalker-info-585	769	98	2y−	2y−	CD
randomwalker-info-585	769	99	ln(y	ln(y	NNP
randomwalker-info-585	769	100	)	)	-RRB-
randomwalker-info-585	769	101	−	−	NNP
randomwalker-info-585	769	102	1	1	CD
randomwalker-info-585	769	103	]	]	-RRB-
randomwalker-info-585	769	104	.	.	.
randomwalker-info-585	770	1	As	as	IN
randomwalker-info-585	770	2	the	the	DT
randomwalker-info-585	770	3	derivative	derivative	NN
randomwalker-info-585	770	4	of	of	IN
randomwalker-info-585	770	5	x	x	SYM
randomwalker-info-585	770	6	is	be	VBZ
randomwalker-info-585	770	7	constant	constant	JJ
randomwalker-info-585	770	8	(	(	-LRB-
randomwalker-info-585	770	9	1	1	CD
randomwalker-info-585	770	10	)	)	-RRB-
randomwalker-info-585	770	11	,	,	,
randomwalker-info-585	770	12	this	this	DT
randomwalker-info-585	770	13	means	mean	VBZ
randomwalker-info-585	770	14	that	that	IN
randomwalker-info-585	770	15	if	if	IN
randomwalker-info-585	770	16	f(x	f(x	NNP
randomwalker-info-585	770	17	)	)	-RRB-
randomwalker-info-585	770	18	>	>	XX
randomwalker-info-585	770	19	x	x	LS
randomwalker-info-585	770	20	anywhere	anywhere	RB
randomwalker-info-585	770	21	on	on	IN
randomwalker-info-585	770	22	this	this	DT
randomwalker-info-585	770	23	interval	interval	NN
randomwalker-info-585	770	24	,	,	,
randomwalker-info-585	770	25	f(2y	f(2y	NNP
randomwalker-info-585	770	26	−	−	NNP
randomwalker-info-585	770	27	ln(y	ln(y	CD
randomwalker-info-585	770	28	)	)	-RRB-
randomwalker-info-585	770	29	−	−	NNP
randomwalker-info-585	770	30	1	1	CD
randomwalker-info-585	770	31	)	)	-RRB-
randomwalker-info-585	770	32	>	>	XX
randomwalker-info-585	770	33	2y	2y	CD
randomwalker-info-585	770	34	−	−	NNP
randomwalker-info-585	770	35	ln(y	ln(y	NNP
randomwalker-info-585	770	36	)	)	-RRB-
randomwalker-info-585	770	37	−	−	NNP
randomwalker-info-585	770	38	1	1	CD
randomwalker-info-585	770	39	or	or	CC
randomwalker-info-585	770	40	f(y	f(y	NNP
randomwalker-info-585	770	41	)	)	-RRB-
randomwalker-info-585	770	42	>	>	XX
randomwalker-info-585	770	43	y.	y.	NNP
randomwalker-info-585	771	1	We	-PRON-	PRP
randomwalker-info-585	771	2	can	can	MD
randomwalker-info-585	771	3	clearly	clearly	RB
randomwalker-info-585	771	4	see	see	VB
randomwalker-info-585	771	5	that	that	IN
randomwalker-info-585	771	6	f(y	f(y	NNP
randomwalker-info-585	771	7	)	)	-RRB-
randomwalker-info-585	771	8	=	=	SYM
randomwalker-info-585	771	9	−W0(−ye−y	−w0(−ye−y	NN
randomwalker-info-585	771	10	)	)	-RRB-
randomwalker-info-585	771	11	=	=	NFP
randomwalker-info-585	771	12	y	y	NNP
randomwalker-info-585	771	13	,	,	,
randomwalker-info-585	771	14	and	and	CC
randomwalker-info-585	771	15	f(2y−	f(2y−	NNP
randomwalker-info-585	771	16	ln(y)−1	ln(y)−1	NNP
randomwalker-info-585	771	17	)	)	-RRB-
randomwalker-info-585	771	18	=	=	NFP
randomwalker-info-585	771	19	−W0(−ye2y−ln(y)−1	−W0(−ye2y−ln(y)−1	NNP
randomwalker-info-585	771	20	)	)	-RRB-
randomwalker-info-585	771	21	=	=	NFP
randomwalker-info-585	771	22	−W0(−1	−W0(−1	NNP
randomwalker-info-585	771	23	/	/	SYM
randomwalker-info-585	771	24	e	e	NNP
randomwalker-info-585	771	25	)	)	-RRB-
randomwalker-info-585	771	26	=	=	SYM
randomwalker-info-585	771	27	1	1	CD
randomwalker-info-585	771	28	.	.	.
randomwalker-info-585	772	1	So	so	RB
randomwalker-info-585	772	2	we	-PRON-	PRP
randomwalker-info-585	772	3	ca	can	MD
randomwalker-info-585	772	4	n’t	not	RB
randomwalker-info-585	772	5	have	have	VB
randomwalker-info-585	772	6	f(y	f(y	NNP
randomwalker-info-585	772	7	)	)	-RRB-
randomwalker-info-585	772	8	>	>	XX
randomwalker-info-585	772	9	y	y	NNP
randomwalker-info-585	772	10	,	,	,
randomwalker-info-585	772	11	and	and	CC
randomwalker-info-585	772	12	we	-PRON-	PRP
randomwalker-info-585	772	13	have	have	VBP
randomwalker-info-585	772	14	f(2y−ln(y)−1	f(2y−ln(y)−1	NNS
randomwalker-info-585	772	15	)	)	-RRB-
randomwalker-info-585	772	16	>	>	XX
randomwalker-info-585	772	17	2y−ln(y)−1	2y−ln(y)−1	CD
randomwalker-info-585	772	18	if	if	IN
randomwalker-info-585	772	19	and	and	CC
randomwalker-info-585	772	20	only	only	RB
randomwalker-info-585	772	21	if	if	IN
randomwalker-info-585	772	22	2y−ln(y)−1	2y−ln(y)−1	CD
randomwalker-info-585	772	23	<	<	XX
randomwalker-info-585	772	24	1	1	CD
randomwalker-info-585	772	25	,	,	,
randomwalker-info-585	772	26	which	which	WDT
randomwalker-info-585	772	27	is	be	VBZ
randomwalker-info-585	772	28	the	the	DT
randomwalker-info-585	772	29	same	same	JJ
randomwalker-info-585	772	30	as	as	IN
randomwalker-info-585	772	31	2y−	2y−	CD
randomwalker-info-585	772	32	ln(y	ln(y	NNP
randomwalker-info-585	772	33	)	)	-RRB-
randomwalker-info-585	772	34	<	<	XX
randomwalker-info-585	772	35	2	2	CD
randomwalker-info-585	772	36	.	.	.
randomwalker-info-585	773	1	As	as	IN
randomwalker-info-585	773	2	this	this	DT
randomwalker-info-585	773	3	is	be	VBZ
randomwalker-info-585	773	4	exactly	exactly	RB
randomwalker-info-585	773	5	the	the	DT
randomwalker-info-585	773	6	range	range	NN
randomwalker-info-585	773	7	of	of	IN
randomwalker-info-585	773	8	y	y	NNP
randomwalker-info-585	773	9	we	-PRON-	PRP
randomwalker-info-585	773	10	disallow	disallow	VBP
randomwalker-info-585	773	11	,	,	,
randomwalker-info-585	773	12	we	-PRON-	PRP
randomwalker-info-585	773	13	see	see	VBP
randomwalker-info-585	773	14	that	that	IN
randomwalker-info-585	773	15	we	-PRON-	PRP
randomwalker-info-585	773	16	also	also	RB
randomwalker-info-585	773	17	ca	can	MD
randomwalker-info-585	773	18	n’t	not	RB
randomwalker-info-585	773	19	have	have	VB
randomwalker-info-585	773	20	f(2y−	f(2y−	NNP
randomwalker-info-585	773	21	ln(y)−1	ln(y)−1	NNP
randomwalker-info-585	773	22	)	)	-RRB-
randomwalker-info-585	773	23	>	>	XX
randomwalker-info-585	773	24	2y−	2y−	CD
randomwalker-info-585	773	25	ln(y)−1	ln(y)−1	NNP
randomwalker-info-585	773	26	for	for	IN
randomwalker-info-585	773	27	any	any	DT
randomwalker-info-585	773	28	y	y	NN
randomwalker-info-585	773	29	we	-PRON-	PRP
randomwalker-info-585	773	30	allow	allow	VBP
randomwalker-info-585	773	31	.	.	.
randomwalker-info-585	774	1	Therefore	therefore	RB
randomwalker-info-585	774	2	,	,	,
randomwalker-info-585	774	3	f(x	f(x	NNP
randomwalker-info-585	774	4	)	)	-RRB-
randomwalker-info-585	774	5	≤	≤	VBD
randomwalker-info-585	774	6	x	x	RB
randomwalker-info-585	774	7	everywhere	everywhere	RB
randomwalker-info-585	774	8	.	.	.
randomwalker-info-585	775	1	Fact	fact	NN
randomwalker-info-585	775	2	2	2	CD
randomwalker-info-585	775	3	.	.	.
randomwalker-info-585	776	1	Be−B−f	Be−B−f	NNP
randomwalker-info-585	776	2	−1(B	−1(B	NNP
randomwalker-info-585	776	3	)	)	-RRB-
randomwalker-info-585	776	4	=	=	NFP
randomwalker-info-585	776	5	•	•	UH
randomwalker-info-585	776	6	Be−2B	be−2b	NN
randomwalker-info-585	776	7	,	,	,
randomwalker-info-585	776	8	B	b	NN
randomwalker-info-585	776	9	∈	∈	IN
randomwalker-info-585	776	10	[	[	-LRB-
randomwalker-info-585	776	11	0,y	0,y	NN
randomwalker-info-585	776	12	]	]	-RRB-
randomwalker-info-585	776	13	.	.	.
randomwalker-info-585	777	1	•	•	NNP
randomwalker-info-585	777	2	ce−2c	ce−2c	NN
randomwalker-info-585	777	3	,	,	,
randomwalker-info-585	777	4	B	b	NN
randomwalker-info-585	777	5	∈	∈	NNP
randomwalker-info-585	777	6	[	[	-LRB-
randomwalker-info-585	777	7	y	y	NNP
randomwalker-info-585	777	8	,	,	,
randomwalker-info-585	777	9	1	1	CD
randomwalker-info-585	777	10	]	]	-RRB-
randomwalker-info-585	777	11	.	.	.
randomwalker-info-585	778	1	•	•	NN
randomwalker-info-585	778	2	0,B	0,b	CD
randomwalker-info-585	778	3	>	>	NN
randomwalker-info-585	778	4	1	1	CD
randomwalker-info-585	778	5	.	.	.
randomwalker-info-585	779	1	Proof	proof	NN
randomwalker-info-585	779	2	.	.	.
randomwalker-info-585	780	1	We	-PRON-	PRP
randomwalker-info-585	780	2	first	first	RB
randomwalker-info-585	780	3	observe	observe	VBP
randomwalker-info-585	780	4	that	that	IN
randomwalker-info-585	780	5	f−1(B	f−1(B	NNP
randomwalker-info-585	780	6	)	)	-RRB-
randomwalker-info-585	780	7	=	=	NFP
randomwalker-info-585	780	8	B	b	NN
randomwalker-info-585	780	9	for	for	IN
randomwalker-info-585	780	10	all	all	DT
randomwalker-info-585	780	11	B	b	NN
randomwalker-info-585	780	12	∈	∈	RB
randomwalker-info-585	780	13	[	[	-LRB-
randomwalker-info-585	780	14	0,y	0,y	NN
randomwalker-info-585	780	15	]	]	-RRB-
randomwalker-info-585	780	16	,	,	,
randomwalker-info-585	780	17	which	which	WDT
randomwalker-info-585	780	18	immediately	immediately	RB
randomwalker-info-585	780	19	proves	prove	VBZ
randomwalker-info-585	780	20	the	the	DT
randomwalker-info-585	780	21	first	first	JJ
randomwalker-info-585	780	22	bullet	bullet	NN
randomwalker-info-585	780	23	.	.	.
randomwalker-info-585	781	1	We	-PRON-	PRP
randomwalker-info-585	781	2	next	next	RB
randomwalker-info-585	781	3	observe	observe	VBP
randomwalker-info-585	781	4	that	that	IN
randomwalker-info-585	781	5	f−1(B	f−1(B	NNP
randomwalker-info-585	781	6	)	)	-RRB-
randomwalker-info-585	781	7	=	=	NFP
randomwalker-info-585	781	8	+	+	CC
randomwalker-info-585	781	9	∞	∞	NN
randomwalker-info-585	781	10	for	for	IN
randomwalker-info-585	781	11	all	all	DT
randomwalker-info-585	781	12	B	b	NN
randomwalker-info-585	781	13	>	>	NN
randomwalker-info-585	781	14	1	1	CD
randomwalker-info-585	781	15	,	,	,
randomwalker-info-585	781	16	which	which	WDT
randomwalker-info-585	781	17	immediately	immediately	RB
randomwalker-info-585	781	18	proves	prove	VBZ
randomwalker-info-585	781	19	the	the	DT
randomwalker-info-585	781	20	last	last	JJ
randomwalker-info-585	781	21	bullet	bullet	NN
randomwalker-info-585	781	22	.	.	.
randomwalker-info-585	782	1	For	for	IN
randomwalker-info-585	782	2	the	the	DT
randomwalker-info-585	782	3	middle	middle	JJ
randomwalker-info-585	782	4	bullet	bullet	NN
randomwalker-info-585	782	5	,	,	,
randomwalker-info-585	782	6	observe	observe	VBP
randomwalker-info-585	782	7	that	that	DT
randomwalker-info-585	782	8	:	:	:
randomwalker-info-585	782	9	−W0(−ye(2y+ln(z	−W0(−ye(2y+ln(z	NNP
randomwalker-info-585	782	10	/	/	SYM
randomwalker-info-585	782	11	y)−y)−2y	y)−y)−2y	NNP
randomwalker-info-585	782	12	)	)	-RRB-
randomwalker-info-585	782	13	=	=	NFP
randomwalker-info-585	782	14	−W0(−yeln(z	−W0(−yeln(z	NNP
randomwalker-info-585	782	15	/	/	SYM
randomwalker-info-585	782	16	y)−z	y)−z	NNP
randomwalker-info-585	782	17	)	)	-RRB-
randomwalker-info-585	782	18	=	=	NFP
randomwalker-info-585	782	19	−W0(−ze−z	−W0(−ze−z	.
randomwalker-info-585	782	20	)	)	-RRB-
randomwalker-info-585	782	21	=	=	NFP
randomwalker-info-585	782	22	z.	z.	NNP
randomwalker-info-585	783	1	Note	note	VB
randomwalker-info-585	783	2	that	that	IN
randomwalker-info-585	783	3	the	the	DT
randomwalker-info-585	783	4	last	last	JJ
randomwalker-info-585	783	5	equality	equality	NN
randomwalker-info-585	783	6	is	be	VBZ
randomwalker-info-585	783	7	due	due	JJ
randomwalker-info-585	783	8	to	to	IN
randomwalker-info-585	783	9	the	the	DT
randomwalker-info-585	783	10	fact	fact	NN
randomwalker-info-585	783	11	that	that	IN
randomwalker-info-585	783	12	W0	w0	NN
randomwalker-info-585	783	13	(	(	-LRB-
randomwalker-info-585	783	14	·	·	NFP
randomwalker-info-585	783	15	)	)	-RRB-
randomwalker-info-585	783	16	is	be	VBZ
randomwalker-info-585	783	17	the	the	DT
randomwalker-info-585	783	18	inverse	inverse	NN
randomwalker-info-585	783	19	of	of	IN
randomwalker-info-585	783	20	xex	xex	NN
randomwalker-info-585	783	21	.	.	.
randomwalker-info-585	784	1	This	this	DT
randomwalker-info-585	784	2	proves	prove	VBZ
randomwalker-info-585	784	3	that	that	IN
randomwalker-info-585	784	4	f−1(B	f−1(B	NNP
randomwalker-info-585	784	5	)	)	-RRB-
randomwalker-info-585	784	6	=	=	NFP
randomwalker-info-585	784	7	2y	2y	NN
randomwalker-info-585	784	8	+	+	CC
randomwalker-info-585	784	9	ln(B	ln(b	NN
randomwalker-info-585	784	10	/	/	SYM
randomwalker-info-585	784	11	y)−B	y)−B	NNP
randomwalker-info-585	784	12	when	when	WRB
randomwalker-info-585	784	13	B	b	NN
randomwalker-info-585	784	14	∈	∈	NNP
randomwalker-info-585	784	15	[	[	-LRB-
randomwalker-info-585	784	16	y	y	NNP
randomwalker-info-585	784	17	,	,	,
randomwalker-info-585	784	18	1	1	CD
randomwalker-info-585	784	19	]	]	-RRB-
randomwalker-info-585	784	20	and	and	CC
randomwalker-info-585	784	21	completes	complete	VBZ
randomwalker-info-585	784	22	the	the	DT
randomwalker-info-585	784	23	middle	middle	JJ
randomwalker-info-585	784	24	bullet	bullet	NN
randomwalker-info-585	784	25	.	.	.
randomwalker-info-585	785	1	Corollary	Corollary	NNP
randomwalker-info-585	785	2	C.5	C.5	NNP
randomwalker-info-585	785	3	.	.	.
randomwalker-info-585	786	1	If	if	IN
randomwalker-info-585	786	2	y	y	NNP
randomwalker-info-585	786	3	∈	∈	NNP
randomwalker-info-585	786	4	(	(	-LRB-
randomwalker-info-585	786	5	0	0	CD
randomwalker-info-585	786	6	,	,	,
randomwalker-info-585	786	7	1/2	1/2	CD
randomwalker-info-585	786	8	]	]	-RRB-
randomwalker-info-585	786	9	,	,	,
randomwalker-info-585	786	10	then	then	RB
randomwalker-info-585	786	11	Be−B−f	Be−B−f	NNP
randomwalker-info-585	786	12	−1(B	−1(B	NNP
randomwalker-info-585	786	13	)	)	-RRB-
randomwalker-info-585	786	14	is	be	VBZ
randomwalker-info-585	786	15	strictly	strictly	RB
randomwalker-info-585	786	16	increasing	increase	VBG
randomwalker-info-585	786	17	on	on	IN
randomwalker-info-585	786	18	[	[	-LRB-
randomwalker-info-585	786	19	0,y	0,y	NN
randomwalker-info-585	786	20	]	]	-RRB-
randomwalker-info-585	786	21	and	and	CC
randomwalker-info-585	786	22	constant	constant	JJ
randomwalker-info-585	786	23	on	on	IN
randomwalker-info-585	786	24	[	[	-LRB-
randomwalker-info-585	786	25	y	y	NNP
randomwalker-info-585	786	26	,	,	,
randomwalker-info-585	786	27	1	1	CD
randomwalker-info-585	786	28	]	]	-RRB-
randomwalker-info-585	786	29	.	.	.
randomwalker-info-585	787	1	Proof	proof	NN
randomwalker-info-585	787	2	.	.	.
randomwalker-info-585	788	1	Be−B−f	Be−B−f	NNP
randomwalker-info-585	788	2	−1(B	−1(B	NNP
randomwalker-info-585	788	3	)	)	-RRB-
randomwalker-info-585	788	4	is	be	VBZ
randomwalker-info-585	788	5	clearly	clearly	RB
randomwalker-info-585	788	6	constant	constant	JJ
randomwalker-info-585	788	7	on	on	IN
randomwalker-info-585	788	8	[	[	-LRB-
randomwalker-info-585	788	9	y	y	NNP
randomwalker-info-585	788	10	,	,	,
randomwalker-info-585	788	11	1	1	CD
randomwalker-info-585	788	12	]	]	-RRB-
randomwalker-info-585	788	13	,	,	,
randomwalker-info-585	788	14	so	so	CC
randomwalker-info-585	788	15	we	-PRON-	PRP
randomwalker-info-585	788	16	just	just	RB
randomwalker-info-585	788	17	need	need	VBP
randomwalker-info-585	788	18	to	to	TO
randomwalker-info-585	788	19	confirm	confirm	VB
randomwalker-info-585	788	20	that	that	IN
randomwalker-info-585	788	21	it	-PRON-	PRP
randomwalker-info-585	788	22	’s	’	VBZ
randomwalker-info-585	788	23	strictly	strictly	RB
randomwalker-info-585	788	24	increasing	increase	VBG
randomwalker-info-585	788	25	on	on	IN
randomwalker-info-585	788	26	[	[	-LRB-
randomwalker-info-585	788	27	0,y	0,y	NN
randomwalker-info-585	788	28	]	]	-RRB-
randomwalker-info-585	788	29	.	.	.
randomwalker-info-585	789	1	The	the	DT
randomwalker-info-585	789	2	derivative	derivative	NN
randomwalker-info-585	789	3	of	of	IN
randomwalker-info-585	789	4	Be−2B	Be−2B	NNP
randomwalker-info-585	789	5	is	be	VBZ
randomwalker-info-585	789	6	(	(	-LRB-
randomwalker-info-585	789	7	1−2B)e−2B	1−2b)e−2b	CD
randomwalker-info-585	789	8	,	,	,
randomwalker-info-585	789	9	which	which	WDT
randomwalker-info-585	789	10	is	be	VBZ
randomwalker-info-585	789	11	strictly	strictly	RB
randomwalker-info-585	789	12	positive	positive	JJ
randomwalker-info-585	789	13	on	on	IN
randomwalker-info-585	789	14	[	[	-LRB-
randomwalker-info-585	789	15	0	0	CD
randomwalker-info-585	789	16	,	,	,
randomwalker-info-585	789	17	1/2	1/2	CD
randomwalker-info-585	789	18	]	]	-RRB-
randomwalker-info-585	789	19	(	(	-LRB-
randomwalker-info-585	789	20	and	and	CC
randomwalker-info-585	789	21	therefore	therefore	RB
randomwalker-info-585	789	22	on	on	IN
randomwalker-info-585	789	23	[	[	-LRB-
randomwalker-info-585	789	24	0,y	0,y	NN
randomwalker-info-585	789	25	]	]	-RRB-
randomwalker-info-585	789	26	for	for	IN
randomwalker-info-585	789	27	all	all	DT
randomwalker-info-585	789	28	y	y	NN
randomwalker-info-585	789	29	≤	≤	NN
randomwalker-info-585	789	30	1/2	1/2	CD
randomwalker-info-585	789	31	)	)	-RRB-
randomwalker-info-585	789	32	,	,	,
randomwalker-info-585	789	33	as	as	IN
randomwalker-info-585	789	34	desired	desire	VBN
randomwalker-info-585	789	35	.	.	.
randomwalker-info-585	790	1	Proof	Proof	NNP
randomwalker-info-585	790	2	of	of	IN
randomwalker-info-585	790	3	Theorem	Theorem	NNP
randomwalker-info-585	790	4	5.1	5.1	CD
randomwalker-info-585	790	5	:	:	:
randomwalker-info-585	790	6	We	-PRON-	PRP
randomwalker-info-585	790	7	want	want	VBP
randomwalker-info-585	790	8	to	to	TO
randomwalker-info-585	790	9	invoke	invoke	VB
randomwalker-info-585	790	10	Corollary	Corollary	NNP
randomwalker-info-585	790	11	C.3	C.3	NNP
randomwalker-info-585	790	12	combined	combine	VBN
randomwalker-info-585	790	13	with	with	IN
randomwalker-info-585	790	14	Corollary	Corollary	NNP
randomwalker-info-585	790	15	C.5	C.5	NNP
randomwalker-info-585	790	16	.	.	.
randomwalker-info-585	791	1	Together	together	RB
randomwalker-info-585	791	2	,	,	,
randomwalker-info-585	791	3	these	these	DT
randomwalker-info-585	791	4	immediately	immediately	RB
randomwalker-info-585	791	5	say	say	VBP
randomwalker-info-585	791	6	that	that	IN
randomwalker-info-585	791	7	for	for	IN
randomwalker-info-585	791	8	any	any	DT
randomwalker-info-585	791	9	1	1	CD
randomwalker-info-585	791	10	≥	≥	UH
randomwalker-info-585	791	11	B1	b1	NN
randomwalker-info-585	791	12	>	>	FW
randomwalker-info-585	791	13	B2	b2	NN
randomwalker-info-585	791	14	≥	≥	CD
randomwalker-info-585	791	15	0	0	NFP
randomwalker-info-585	791	16	,	,	,
randomwalker-info-585	791	17	it	-PRON-	PRP
randomwalker-info-585	791	18	is	be	VBZ
randomwalker-info-585	791	19	at	at	IN
randomwalker-info-585	791	20	least	least	JJS
randomwalker-info-585	791	21	as	as	IN
randomwalker-info-585	791	22	good	good	JJ
randomwalker-info-585	791	23	to	to	TO
randomwalker-info-585	791	24	authorize	authorize	VB
randomwalker-info-585	791	25	B1	B1	NNP
randomwalker-info-585	791	26	BTC	BTC	NNP
randomwalker-info-585	791	27	as	as	IN
randomwalker-info-585	791	28	B2	b2	NN
randomwalker-info-585	791	29	.	.	.
randomwalker-info-585	792	1	As	as	IN
randomwalker-info-585	792	2	authorizing	authorize	VBG
randomwalker-info-585	792	3	B	b	NN
randomwalker-info-585	792	4	>	>	NN
randomwalker-info-585	792	5	1	1	CD
randomwalker-info-585	792	6	BTC	BTC	NNP
randomwalker-info-585	792	7	always	always	RB
randomwalker-info-585	792	8	results	result	VBZ
randomwalker-info-585	792	9	in	in	IN
randomwalker-info-585	792	10	expected	expected	JJ
randomwalker-info-585	792	11	reward	reward	NN
randomwalker-info-585	792	12	of	of	IN
randomwalker-info-585	792	13	0	0	CD
randomwalker-info-585	792	14	,	,	,
randomwalker-info-585	792	15	this	this	DT
randomwalker-info-585	792	16	immediately	immediately	RB
randomwalker-info-585	792	17	implies	imply	VBZ
randomwalker-info-585	792	18	by	by	IN
randomwalker-info-585	792	19	Corollary	Corollary	NNP
randomwalker-info-585	792	20	C.2	C.2	NNP
randomwalker-info-585	792	21	that	that	DT
randomwalker-info-585	792	22	for	for	IN
randomwalker-info-585	792	23	any	any	DT
randomwalker-info-585	792	24	b	b	NN
randomwalker-info-585	792	25	,	,	,
randomwalker-info-585	792	26	min{1,b}∈	min{1,b}∈	.
randomwalker-info-585	792	27	argmaxB∈[0,b]{Be	argmaxB∈[0,b]{Be	NNS
randomwalker-info-585	792	28	−max{0,B+f−1(B)−Rem(Mosti	−max{0,B+f−1(B)−Rem(Mosti	NNP
randomwalker-info-585	792	29	)	)	-RRB-
randomwalker-info-585	792	30	}	}	-RRB-
randomwalker-info-585	792	31	}	}	-RRB-
randomwalker-info-585	792	32	.	.	.
randomwalker-info-585	793	1	Now	now	RB
randomwalker-info-585	793	2	,	,	,
randomwalker-info-585	793	3	we	-PRON-	PRP
randomwalker-info-585	793	4	also	also	RB
randomwalker-info-585	793	5	want	want	VBP
randomwalker-info-585	793	6	to	to	TO
randomwalker-info-585	793	7	invoke	invoke	VB
randomwalker-info-585	793	8	Corollary	Corollary	NNP
randomwalker-info-585	793	9	C.4	C.4	NNP
randomwalker-info-585	793	10	to	to	TO
randomwalker-info-585	793	11	show	show	VB
randomwalker-info-585	793	12	that	that	IN
randomwalker-info-585	793	13	there	there	EX
randomwalker-info-585	793	14	may	may	MD
randomwalker-info-585	793	15	exist	exist	VB
randomwalker-info-585	793	16	other	other	JJ
randomwalker-info-585	793	17	maximizers	maximizer	NNS
randomwalker-info-585	793	18	as	as	RB
randomwalker-info-585	793	19	well	well	RB
randomwalker-info-585	793	20	if	if	IN
randomwalker-info-585	793	21	Rem(Mosti	Rem(Mosti	NNP
randomwalker-info-585	793	22	)	)	-RRB-
randomwalker-info-585	793	23	∈	∈	NNP
randomwalker-info-585	793	24	[	[	-LRB-
randomwalker-info-585	793	25	y	y	NNP
randomwalker-info-585	793	26	,	,	,
randomwalker-info-585	793	27	2y	2y	CD
randomwalker-info-585	793	28	−	−	NNP
randomwalker-info-585	793	29	ln(y	ln(y	NNP
randomwalker-info-585	793	30	)	)	-RRB-
randomwalker-info-585	793	31	−	−	NNP
randomwalker-info-585	793	32	1	1	CD
randomwalker-info-585	793	33	]	]	-RRB-
randomwalker-info-585	793	34	.	.	.
randomwalker-info-585	794	1	Note	note	VB
randomwalker-info-585	794	2	that	that	IN
randomwalker-info-585	794	3	f	f	NNP
randomwalker-info-585	794	4	(	(	-LRB-
randomwalker-info-585	794	5	·	·	NFP
randomwalker-info-585	794	6	)	)	-RRB-
randomwalker-info-585	794	7	is	be	VBZ
randomwalker-info-585	794	8	strictly	strictly	RB
randomwalker-info-585	794	9	increasing	increase	VBG
randomwalker-info-585	794	10	in	in	IN
randomwalker-info-585	794	11	this	this	DT
randomwalker-info-585	794	12	range	range	NN
randomwalker-info-585	794	13	,	,	,
randomwalker-info-585	794	14	meaning	mean	VBG
randomwalker-info-585	794	15	that	that	IN
randomwalker-info-585	794	16	f−1(f(Rem(Mosti	f−1(f(Rem(Mosti	NNP
randomwalker-info-585	794	17	)	)	-RRB-
randomwalker-info-585	794	18	)	)	-RRB-
randomwalker-info-585	794	19	)	)	-RRB-
randomwalker-info-585	794	20	=	=	NFP
randomwalker-info-585	794	21	Rem(Mosti	rem(mosti	XX
randomwalker-info-585	794	22	)	)	-RRB-
randomwalker-info-585	794	23	.	.	.
randomwalker-info-585	795	1	Therefore	therefore	RB
randomwalker-info-585	795	2	,	,	,
randomwalker-info-585	795	3	we	-PRON-	PRP
randomwalker-info-585	795	4	see	see	VBP
randomwalker-info-585	795	5	that	that	IN
randomwalker-info-585	795	6	Rem(Mosti	rem(mosti	NN
randomwalker-info-585	795	7	)	)	-RRB-
randomwalker-info-585	795	8	≤	≤	NNP
randomwalker-info-585	795	9	f(Rem(Mosti	f(Rem(Mosti	NNP
randomwalker-info-585	795	10	)	)	-RRB-
randomwalker-info-585	795	11	)	)	-RRB-
randomwalker-info-585	795	12	+	+	NFP
randomwalker-info-585	795	13	f−1(f(Rem(Mosti	f−1(f(Rem(Mosti	NNP
randomwalker-info-585	795	14	)	)	-RRB-
randomwalker-info-585	795	15	)	)	-RRB-
randomwalker-info-585	795	16	)	)	-RRB-
randomwalker-info-585	795	17	(	(	-LRB-
randomwalker-info-585	795	18	the	the	DT
randomwalker-info-585	795	19	miner	miner	NN
randomwalker-info-585	795	20	will	will	MD
randomwalker-info-585	795	21	be	be	VB
randomwalker-info-585	795	22	undercut	undercut	JJ
randomwalker-info-585	795	23	with	with	IN
randomwalker-info-585	795	24	positive	positive	JJ
randomwalker-info-585	795	25	probability	probability	NN
randomwalker-info-585	795	26	when	when	WRB
randomwalker-info-585	795	27	authorizing	authorize	VBG
randomwalker-info-585	795	28	f(Rem(Mosti	f(Rem(Mosti	NNP
randomwalker-info-585	795	29	)	)	-RRB-
randomwalker-info-585	795	30	)	)	-RRB-
randomwalker-info-585	795	31	BTC	BTC	NNP
randomwalker-info-585	795	32	)	)	-RRB-
randomwalker-info-585	795	33	on	on	IN
randomwalker-info-585	795	34	this	this	DT
randomwalker-info-585	795	35	entire	entire	JJ
randomwalker-info-585	795	36	range	range	NN
randomwalker-info-585	795	37	.	.	.
randomwalker-info-585	796	1	Together	together	RB
randomwalker-info-585	796	2	with	with	IN
randomwalker-info-585	796	3	Corollary	Corollary	NNP
randomwalker-info-585	796	4	C.5	C.5	NNP
randomwalker-info-585	796	5	,	,	,
randomwalker-info-585	796	6	this	this	DT
randomwalker-info-585	796	7	means	mean	VBZ
randomwalker-info-585	796	8	that	that	IN
randomwalker-info-585	796	9	the	the	DT
randomwalker-info-585	796	10	hypotheses	hypothesis	NNS
randomwalker-info-585	796	11	of	of	IN
randomwalker-info-585	796	12	Corollary	Corollary	NNP
randomwalker-info-585	796	13	C.4	C.4	NNP
randomwalker-info-585	796	14	are	be	VBP
randomwalker-info-585	796	15	satisfied	satisfied	JJ
randomwalker-info-585	796	16	taking	take	VBG
randomwalker-info-585	796	17	B2	b2	NN
randomwalker-info-585	796	18	=	=	SYM
randomwalker-info-585	796	19	f(Rem(Mosti	f(Rem(Mosti	NNP
randomwalker-info-585	796	20	)	)	-RRB-
randomwalker-info-585	796	21	)	)	-RRB-
randomwalker-info-585	796	22	and	and	CC
randomwalker-info-585	796	23	any	any	DT
randomwalker-info-585	796	24	B1	B1	NNP
randomwalker-info-585	796	25	≥	≥	NN
randomwalker-info-585	796	26	B2	b2	NN
randomwalker-info-585	796	27	.	.	.
randomwalker-info-585	797	1	Combined	combine	VBN
randomwalker-info-585	797	2	with	with	IN
randomwalker-info-585	797	3	the	the	DT
randomwalker-info-585	797	4	reasoning	reasoning	NN
randomwalker-info-585	797	5	above	above	RB
randomwalker-info-585	797	6	,	,	,
randomwalker-info-585	797	7	this	this	DT
randomwalker-info-585	797	8	means	mean	VBZ
randomwalker-info-585	797	9	that	that	IN
randomwalker-info-585	797	10	when	when	WRB
randomwalker-info-585	797	11	Rem(Mosti	Rem(Mosti	NNP
randomwalker-info-585	797	12	)	)	-RRB-
randomwalker-info-585	797	13	∈	∈	NNP
randomwalker-info-585	797	14	[	[	-LRB-
randomwalker-info-585	797	15	y	y	NNP
randomwalker-info-585	797	16	,	,	,
randomwalker-info-585	797	17	2y	2y	CD
randomwalker-info-585	797	18	−	−	NNP
randomwalker-info-585	797	19	ln(y	ln(y	NNP
randomwalker-info-585	797	20	)	)	-RRB-
randomwalker-info-585	797	21	−	−	NNP
randomwalker-info-585	797	22	1	1	CD
randomwalker-info-585	797	23	]	]	-RRB-
randomwalker-info-585	797	24	and	and	CC
randomwalker-info-585	797	25	b	b	NN
randomwalker-info-585	797	26	≥	≥	NN
randomwalker-info-585	797	27	f(Rem(Mosti	f(Rem(Mosti	NNP
randomwalker-info-585	797	28	)	)	-RRB-
randomwalker-info-585	797	29	)	)	-RRB-
randomwalker-info-585	797	30	,	,	,
randomwalker-info-585	797	31	we	-PRON-	PRP
randomwalker-info-585	797	32	also	also	RB
randomwalker-info-585	797	33	have	have	VBP
randomwalker-info-585	797	34	f(Rem(Mosti	f(Rem(Mosti	NNP
randomwalker-info-585	797	35	)	)	-RRB-
randomwalker-info-585	797	36	)	)	-RRB-
randomwalker-info-585	797	37	∈	∈	VBZ
randomwalker-info-585	797	38	argmaxB∈[0,b]{Be	argmaxB∈[0,b]{Be	NNS
randomwalker-info-585	797	39	−max{0,B+f−1(B)−Rem(Mosti	−max{0,B+f−1(B)−Rem(Mosti	NNP
randomwalker-info-585	797	40	)	)	-RRB-
randomwalker-info-585	797	41	}	}	-RRB-
randomwalker-info-585	797	42	}	}	-RRB-
randomwalker-info-585	797	43	.	.	.
randomwalker-info-585	798	1	Therefore	therefore	RB
randomwalker-info-585	798	2	,	,	,
randomwalker-info-585	798	3	when	when	WRB
randomwalker-info-585	798	4	b	b	NN
randomwalker-info-585	798	5	=	=	SYM
randomwalker-info-585	798	6	Rem(MostH	Rem(MostH	NNP
randomwalker-info-585	798	7	)	)	-RRB-
randomwalker-info-585	798	8	,	,	,
randomwalker-info-585	798	9	we	-PRON-	PRP
randomwalker-info-585	798	10	recover	recover	VBP
randomwalker-info-585	798	11	that	that	DT
randomwalker-info-585	798	12	f(Rem(MostH	f(rem(mosth	NN
randomwalker-info-585	798	13	)	)	-RRB-
randomwalker-info-585	798	14	)	)	-RRB-
randomwalker-info-585	798	15	is	be	VBZ
randomwalker-info-585	798	16	an	an	DT
randomwalker-info-585	798	17	optimal	optimal	JJ
randomwalker-info-585	798	18	choice	choice	NN
randomwalker-info-585	798	19	of	of	IN
randomwalker-info-585	798	20	BTC	BTC	NNP
randomwalker-info-585	798	21	to	to	TO
randomwalker-info-585	798	22	authorize	authorize	VB
randomwalker-info-585	798	23	when	when	WRB
randomwalker-info-585	798	24	continuing	continue	VBG
randomwalker-info-585	798	25	.	.	.
randomwalker-info-585	799	1	When	when	WRB
randomwalker-info-585	799	2	b	b	NNP
randomwalker-info-585	799	3	=	=	SYM
randomwalker-info-585	799	4	GapH	GapH	NNP
randomwalker-info-585	799	5	,	,	,
randomwalker-info-585	799	6	we	-PRON-	PRP
randomwalker-info-585	799	7	recover	recover	VBP
randomwalker-info-585	799	8	that	that	IN
randomwalker-info-585	799	9	min{1,GapH	min{1,gaph	RB
randomwalker-info-585	799	10	,	,	,
randomwalker-info-585	799	11	f(Rem(MostH−1	f(rem(mosth−1	LS
randomwalker-info-585	799	12	)	)	-RRB-
randomwalker-info-585	799	13	)	)	-RRB-
randomwalker-info-585	799	14	}	}	-RRB-
randomwalker-info-585	799	15	=	=	NFP
randomwalker-info-585	799	16	min{GapH	min{GapH	''
randomwalker-info-585	799	17	,	,	,
randomwalker-info-585	799	18	f(Rem(MostH−1	f(rem(mosth−1	LS
randomwalker-info-585	799	19	)	)	-RRB-
randomwalker-info-585	799	20	)	)	-RRB-
randomwalker-info-585	799	21	}	}	-RRB-
randomwalker-info-585	799	22	is	be	VBZ
randomwalker-info-585	799	23	an	an	DT
randomwalker-info-585	799	24	optimal	optimal	JJ
randomwalker-info-585	799	25	choice	choice	NN
randomwalker-info-585	799	26	of	of	IN
randomwalker-info-585	799	27	BTC	BTC	NNP
randomwalker-info-585	799	28	to	to	TO
randomwalker-info-585	799	29	authorize	authorize	VB
randomwalker-info-585	799	30	when	when	WRB
randomwalker-info-585	799	31	undercutting	undercut	VBG
randomwalker-info-585	799	32	.	.	.
randomwalker-info-585	800	1	So	so	CC
randomwalker-info-585	800	2	FunctionFork(f	FunctionFork(f	NNS
randomwalker-info-585	800	3	)	)	-RRB-
randomwalker-info-585	800	4	correctly	correctly	RB
randomwalker-info-585	800	5	chooses	choose	VBZ
randomwalker-info-585	800	6	how	how	WRB
randomwalker-info-585	800	7	many	many	JJ
randomwalker-info-585	800	8	BTC	BTC	NNP
randomwalker-info-585	800	9	to	to	TO
randomwalker-info-585	800	10	authorize	authorize	VB
randomwalker-info-585	800	11	when	when	WRB
randomwalker-info-585	800	12	continuing	continue	VBG
randomwalker-info-585	800	13	and	and	CC
randomwalker-info-585	800	14	when	when	WRB
randomwalker-info-585	800	15	undercutting	undercut	VBG
randomwalker-info-585	800	16	,	,	,
randomwalker-info-585	800	17	we	-PRON-	PRP
randomwalker-info-585	800	18	just	just	RB
randomwalker-info-585	800	19	need	need	VBP
randomwalker-info-585	800	20	to	to	TO
randomwalker-info-585	800	21	check	check	VB
randomwalker-info-585	800	22	that	that	IN
randomwalker-info-585	800	23	it	-PRON-	PRP
randomwalker-info-585	800	24	also	also	RB
randomwalker-info-585	800	25	chooses	choose	VBZ
randomwalker-info-585	800	26	when	when	WRB
randomwalker-info-585	800	27	to	to	TO
randomwalker-info-585	800	28	undercut	undercut	VB
randomwalker-info-585	800	29	and	and	CC
randomwalker-info-585	800	30	when	when	WRB
randomwalker-info-585	800	31	to	to	TO
randomwalker-info-585	800	32	continue	continue	VB
randomwalker-info-585	800	33	.	.	.
randomwalker-info-585	801	1	If	if	IN
randomwalker-info-585	801	2	GapH	GapH	NNP
randomwalker-info-585	801	3	>	>	XX
randomwalker-info-585	801	4	f(Rem(MostH	f(rem(mosth	NN
randomwalker-info-585	801	5	)	)	-RRB-
randomwalker-info-585	801	6	)	)	-RRB-
randomwalker-info-585	801	7	,	,	,
randomwalker-info-585	801	8	then	then	RB
randomwalker-info-585	801	9	min{GapH	min{GapH	``
randomwalker-info-585	801	10	,	,	,
randomwalker-info-585	801	11	f(Rem(MostH−1))}≥	f(rem(mosth−1))}≥	ADD
randomwalker-info-585	801	12	f(Rem(MostH	f(rem(mosth	NN
randomwalker-info-585	801	13	)	)	-RRB-
randomwalker-info-585	801	14	)	)	-RRB-
randomwalker-info-585	801	15	as	as	RB
randomwalker-info-585	801	16	well	well	RB
randomwalker-info-585	801	17	,	,	,
randomwalker-info-585	801	18	and	and	CC
randomwalker-info-585	801	19	we	-PRON-	PRP
randomwalker-info-585	801	20	can	can	MD
randomwalker-info-585	801	21	invoke	invoke	VB
randomwalker-info-585	801	22	Corollary	Corollary	NNP
randomwalker-info-585	801	23	C.3	C.3	NNP
randomwalker-info-585	801	24	with	with	IN
randomwalker-info-585	801	25	B1	b1	NN
randomwalker-info-585	801	26	=	=	SYM
randomwalker-info-585	801	27	min{GapH	min{GapH	''
randomwalker-info-585	801	28	,	,	,
randomwalker-info-585	801	29	f(Rem(MostH−1	f(rem(mosth−1	LS
randomwalker-info-585	801	30	)	)	-RRB-
randomwalker-info-585	801	31	)	)	-RRB-
randomwalker-info-585	801	32	}	}	-RRB-
randomwalker-info-585	801	33	and	and	CC
randomwalker-info-585	801	34	B2	b2	NN
randomwalker-info-585	801	35	=	=	SYM
randomwalker-info-585	801	36	f(Rem(MostH	f(rem(mosth	NN
randomwalker-info-585	801	37	)	)	-RRB-
randomwalker-info-585	801	38	)	)	-RRB-
randomwalker-info-585	801	39	.	.	.
randomwalker-info-585	802	1	By	by	IN
randomwalker-info-585	802	2	the	the	DT
randomwalker-info-585	802	3	argument	argument	NN
randomwalker-info-585	802	4	above	above	RB
randomwalker-info-585	802	5	,	,	,
randomwalker-info-585	802	6	because	because	IN
randomwalker-info-585	802	7	1	1	CD
randomwalker-info-585	802	8	≥	≥	UH
randomwalker-info-585	802	9	B1	B1	NNP
randomwalker-info-585	802	10	≥	≥	NNP
randomwalker-info-585	802	11	B2	b2	NN
randomwalker-info-585	802	12	,	,	,
randomwalker-info-585	802	13	the	the	DT
randomwalker-info-585	802	14	hypotheses	hypothesis	NNS
randomwalker-info-585	802	15	of	of	IN
randomwalker-info-585	802	16	Corollary	Corollary	NNP
randomwalker-info-585	802	17	C.3	C.3	NNP
randomwalker-info-585	802	18	are	be	VBP
randomwalker-info-585	802	19	satisfied	satisfied	JJ
randomwalker-info-585	802	20	,	,	,
randomwalker-info-585	802	21	and	and	CC
randomwalker-info-585	802	22	the	the	DT
randomwalker-info-585	802	23	expected	expect	VBN
randomwalker-info-585	802	24	re-	re-	NN
randomwalker-info-585	802	25	ward	ward	NN
randomwalker-info-585	802	26	is	be	VBZ
randomwalker-info-585	802	27	at	at	IN
randomwalker-info-585	802	28	least	least	JJS
randomwalker-info-585	802	29	as	as	RB
randomwalker-info-585	802	30	high	high	JJ
randomwalker-info-585	802	31	when	when	WRB
randomwalker-info-585	802	32	authorizing	authorize	VBG
randomwalker-info-585	802	33	B1	b1	NN
randomwalker-info-585	802	34	as	as	IN
randomwalker-info-585	802	35	B2	b2	NN
randomwalker-info-585	802	36	,	,	,
randomwalker-info-585	802	37	so	so	RB
randomwalker-info-585	802	38	undercutting	undercutting	NN
randomwalker-info-585	802	39	is	be	VBZ
randomwalker-info-585	802	40	at	at	IN
randomwalker-info-585	802	41	least	least	JJS
randomwalker-info-585	802	42	as	as	RB
randomwalker-info-585	802	43	good	good	JJ
randomwalker-info-585	802	44	as	as	IN
randomwalker-info-585	802	45	continuing	continue	VBG
randomwalker-info-585	802	46	.	.	.
randomwalker-info-585	803	1	Similarly	similarly	RB
randomwalker-info-585	803	2	,	,	,
randomwalker-info-585	803	3	if	if	IN
randomwalker-info-585	803	4	f(Rem(MostH	f(rem(mosth	NN
randomwalker-info-585	803	5	)	)	-RRB-
randomwalker-info-585	803	6	)	)	-RRB-
randomwalker-info-585	803	7	≥	≥	UH
randomwalker-info-585	803	8	GapH	GapH	NNP
randomwalker-info-585	803	9	,	,	,
randomwalker-info-585	803	10	then	then	RB
randomwalker-info-585	803	11	f(Rem(MostH	f(Rem(MostH	NNP
randomwalker-info-585	803	12	)	)	-RRB-
randomwalker-info-585	803	13	)	)	-RRB-
randomwalker-info-585	803	14	≥	≥	UH
randomwalker-info-585	803	15	min{GapH	min{GapH	:
randomwalker-info-585	803	16	,	,	,
randomwalker-info-585	803	17	f(Rem(MostH−1	f(rem(mosth−1	LS
randomwalker-info-585	803	18	)	)	-RRB-
randomwalker-info-585	803	19	)	)	-RRB-
randomwalker-info-585	803	20	}	}	-RRB-
randomwalker-info-585	803	21	.	.	.
randomwalker-info-585	804	1	So	so	RB
randomwalker-info-585	804	2	we	-PRON-	PRP
randomwalker-info-585	804	3	may	may	MD
randomwalker-info-585	804	4	again	again	RB
randomwalker-info-585	804	5	invoke	invoke	VB
randomwalker-info-585	804	6	Corollary	Corollary	NNP
randomwalker-info-585	804	7	C.3	C.3	NNP
randomwalker-info-585	804	8	,	,	,
randomwalker-info-585	804	9	this	this	DT
randomwalker-info-585	804	10	time	time	NN
randomwalker-info-585	804	11	with	with	IN
randomwalker-info-585	804	12	B1	b1	NN
randomwalker-info-585	804	13	=	=	SYM
randomwalker-info-585	804	14	f(Rem(MostH	f(rem(mosth	NN
randomwalker-info-585	804	15	)	)	-RRB-
randomwalker-info-585	804	16	)	)	-RRB-
randomwalker-info-585	804	17	and	and	CC
randomwalker-info-585	804	18	B2	b2	NN
randomwalker-info-585	804	19	=	=	SYM
randomwalker-info-585	804	20	min{GapH	min{GapH	''
randomwalker-info-585	804	21	,	,	,
randomwalker-info-585	804	22	f(Rem(MostH−1	f(rem(mosth−1	LS
randomwalker-info-585	804	23	)	)	-RRB-
randomwalker-info-585	804	24	)	)	-RRB-
randomwalker-info-585	804	25	}	}	-RRB-
randomwalker-info-585	804	26	.	.	.
randomwalker-info-585	805	1	So	so	RB
randomwalker-info-585	805	2	now	now	RB
randomwalker-info-585	805	3	we	-PRON-	PRP
randomwalker-info-585	805	4	have	have	VBP
randomwalker-info-585	805	5	shown	show	VBN
randomwalker-info-585	805	6	that	that	IN
randomwalker-info-585	805	7	the	the	DT
randomwalker-info-585	805	8	FunctionFork(f	FunctionFork(f	NNS
randomwalker-info-585	805	9	)	)	-RRB-
randomwalker-info-585	805	10	correctly	correctly	RB
randomwalker-info-585	805	11	chooses	choose	VBZ
randomwalker-info-585	805	12	how	how	WRB
randomwalker-info-585	805	13	many	many	JJ
randomwalker-info-585	805	14	BTC	BTC	NNP
randomwalker-info-585	805	15	to	to	TO
randomwalker-info-585	805	16	authorize	authorize	VB
randomwalker-info-585	805	17	when	when	WRB
randomwalker-info-585	805	18	continuing	continue	VBG
randomwalker-info-585	805	19	and	and	CC
randomwalker-info-585	805	20	when	when	WRB
randomwalker-info-585	805	21	undercutting	undercut	VBG
randomwalker-info-585	805	22	,	,	,
randomwalker-info-585	805	23	and	and	CC
randomwalker-info-585	805	24	also	also	RB
randomwalker-info-585	805	25	chooses	choose	VBZ
randomwalker-info-585	805	26	correctly	correctly	RB
randomwalker-info-585	805	27	whether	whether	IN
randomwalker-info-585	805	28	to	to	TO
randomwalker-info-585	805	29	continue	continue	VB
randomwalker-info-585	805	30	or	or	CC
randomwalker-info-585	805	31	undercut	undercut	JJ
randomwalker-info-585	805	32	.	.	.
randomwalker-info-585	806	1	So	so	CC
randomwalker-info-585	806	2	it	-PRON-	PRP
randomwalker-info-585	806	3	is	be	VBZ
randomwalker-info-585	806	4	an	an	DT
randomwalker-info-585	806	5	equilibrium	equilibrium	NN
randomwalker-info-585	806	6	.	.	.
randomwalker-info-585	807	1	The	the	DT
randomwalker-info-585	807	2	last	last	JJ
randomwalker-info-585	807	3	part	part	NN
randomwalker-info-585	807	4	we	-PRON-	PRP
randomwalker-info-585	807	5	need	need	VBP
randomwalker-info-585	807	6	to	to	TO
randomwalker-info-585	807	7	reason	reason	VB
randomwalker-info-585	807	8	about	about	IN
randomwalker-info-585	807	9	is	be	VBZ
randomwalker-info-585	807	10	the	the	DT
randomwalker-info-585	807	11	connection	connection	NN
randomwalker-info-585	807	12	to	to	IN
randomwalker-info-585	807	13	random	random	JJ
randomwalker-info-585	807	14	walks	walk	NNS
randomwalker-info-585	807	15	.	.	.
randomwalker-info-585	808	1	Observe	observe	VB
randomwalker-info-585	808	2	that	that	IN
randomwalker-info-585	808	3	the	the	DT
randomwalker-info-585	808	4	number	number	NN
randomwalker-info-585	808	5	of	of	IN
randomwalker-info-585	808	6	transaction	transaction	NN
randomwalker-info-585	808	7	fees	fee	NNS
randomwalker-info-585	808	8	grows	grow	VBZ
randomwalker-info-585	808	9	continuously	continuously	RB
randomwalker-info-585	808	10	at	at	IN
randomwalker-info-585	808	11	a	a	DT
randomwalker-info-585	808	12	rate	rate	NN
randomwalker-info-585	808	13	of	of	IN
randomwalker-info-585	808	14	1	1	CD
randomwalker-info-585	808	15	per	per	IN
randomwalker-info-585	808	16	unit	unit	NN
randomwalker-info-585	808	17	.	.	.
randomwalker-info-585	809	1	Every	every	DT
randomwalker-info-585	809	2	time	time	NN
randomwalker-info-585	809	3	a	a	DT
randomwalker-info-585	809	4	block	block	NN
randomwalker-info-585	809	5	is	be	VBZ
randomwalker-info-585	809	6	found	find	VBN
randomwalker-info-585	809	7	,	,	,
randomwalker-info-585	809	8	it	-PRON-	PRP
randomwalker-info-585	809	9	drops	drop	VBZ
randomwalker-info-585	809	10	by	by	IN
randomwalker-info-585	809	11	at	at	IN
randomwalker-info-585	809	12	most	most	JJS
randomwalker-info-585	809	13	1	1	CD
randomwalker-info-585	809	14	.	.	.
randomwalker-info-585	810	1	So	so	RB
randomwalker-info-585	810	2	definitely	definitely	RB
randomwalker-info-585	810	3	the	the	DT
randomwalker-info-585	810	4	backlogged	backlogge	VBN
randomwalker-info-585	810	5	transactions	transaction	NNS
randomwalker-info-585	810	6	will	will	MD
randomwalker-info-585	810	7	be	be	VB
randomwalker-info-585	810	8	at	at	IN
randomwalker-info-585	810	9	least	least	JJS
randomwalker-info-585	810	10	as	as	RB
randomwalker-info-585	810	11	bad	bad	JJ
randomwalker-info-585	810	12	as	as	IN
randomwalker-info-585	810	13	a	a	DT
randomwalker-info-585	810	14	random	random	JJ
randomwalker-info-585	810	15	walk	walk	NN
randomwalker-info-585	810	16	that	that	WDT
randomwalker-info-585	810	17	drops	drop	VBZ
randomwalker-info-585	810	18	by	by	IN
randomwalker-info-585	810	19	exactly	exactly	RB
randomwalker-info-585	810	20	1	1	CD
randomwalker-info-585	810	21	(	(	-LRB-
randomwalker-info-585	810	22	because	because	IN
randomwalker-info-585	810	23	it	-PRON-	PRP
randomwalker-info-585	810	24	will	will	MD
randomwalker-info-585	810	25	only	only	RB
randomwalker-info-585	810	26	drop	drop	VB
randomwalker-info-585	810	27	further	further	RB
randomwalker-info-585	810	28	)	)	-RRB-
randomwalker-info-585	810	29	.	.	.
randomwalker-info-585	811	1	Lemma	Lemma	NNP
randomwalker-info-585	811	2	C.7	C.7	NNP
randomwalker-info-585	811	3	below	below	IN
randomwalker-info-585	811	4	proves	prove	VBZ
randomwalker-info-585	811	5	that	that	IN
randomwalker-info-585	811	6	with	with	IN
randomwalker-info-585	811	7	constant	constant	JJ
randomwalker-info-585	811	8	probability	probability	NN
randomwalker-info-585	811	9	,	,	,
randomwalker-info-585	811	10	the	the	DT
randomwalker-info-585	811	11	number	number	NN
randomwalker-info-585	811	12	of	of	IN
randomwalker-info-585	811	13	blocks	block	NNS
randomwalker-info-585	811	14	found	find	VBN
randomwalker-info-585	811	15	in	in	IN
randomwalker-info-585	811	16	a	a	DT
randomwalker-info-585	811	17	time	time	NN
randomwalker-info-585	811	18	interval	interval	NN
randomwalker-info-585	811	19	of	of	IN
randomwalker-info-585	811	20	length	length	NN
randomwalker-info-585	811	21	n	n	NNP
randomwalker-info-585	811	22	+	+	CC
randomwalker-info-585	811	23	√	√	NNP
randomwalker-info-585	811	24	n	n	RB
randomwalker-info-585	811	25	is	be	VBZ
randomwalker-info-585	811	26	at	at	RB
randomwalker-info-585	811	27	most	most	JJS
randomwalker-info-585	811	28	n.	n.	NN
randomwalker-info-585	811	29	When	when	WRB
randomwalker-info-585	811	30	this	this	DT
randomwalker-info-585	811	31	occurs	occur	VBZ
randomwalker-info-585	811	32	,	,	,
randomwalker-info-585	811	33	there	there	EX
randomwalker-info-585	811	34	is	be	VBZ
randomwalker-info-585	811	35	a	a	DT
randomwalker-info-585	811	36	backlog	backlog	NN
randomwalker-info-585	811	37	of	of	IN
randomwalker-info-585	811	38	at	at	IN
randomwalker-info-585	811	39	least	least	JJS
randomwalker-info-585	811	40	√	√	NN
randomwalker-info-585	811	41	n	n	CC
randomwalker-info-585	811	42	transactions	transaction	NNS
randomwalker-info-585	811	43	at	at	IN
randomwalker-info-585	811	44	time	time	NN
randomwalker-info-585	811	45	n	n	CC
randomwalker-info-585	811	46	+	+	CC
randomwalker-info-585	811	47	√	√	NNP
randomwalker-info-585	811	48	n.	n.	NN
randomwalker-info-585	811	49	Therefore	therefore	RB
randomwalker-info-585	811	50	,	,	,
randomwalker-info-585	811	51	the	the	DT
randomwalker-info-585	811	52	expected	expected	JJ
randomwalker-info-585	811	53	backlog	backlog	NN
randomwalker-info-585	811	54	is	be	VBZ
randomwalker-info-585	811	55	at	at	IN
randomwalker-info-585	811	56	least	least	JJS
randomwalker-info-585	811	57	Θ	Θ	NNP
randomwalker-info-585	811	58	(	(	-LRB-
randomwalker-info-585	811	59	√	√	NNP
randomwalker-info-585	811	60	n	n	CC
randomwalker-info-585	811	61	)	)	-RRB-
randomwalker-info-585	811	62	(	(	-LRB-
randomwalker-info-585	811	63	in	in	IN
randomwalker-info-585	811	64	fact	fact	NN
randomwalker-info-585	811	65	,	,	,
randomwalker-info-585	811	66	it	-PRON-	PRP
randomwalker-info-585	811	67	is	be	VBZ
randomwalker-info-585	811	68	exactly	exactly	RB
randomwalker-info-585	811	69	Θ	Θ	NNP
randomwalker-info-585	811	70	(	(	-LRB-
randomwalker-info-585	811	71	√	√	NNP
randomwalker-info-585	811	72	n	n	NNP
randomwalker-info-585	811	73	)	)	-RRB-
randomwalker-info-585	811	74	)	)	-RRB-
randomwalker-info-585	811	75	.	.	.
randomwalker-info-585	812	1	During	during	IN
randomwalker-info-585	812	2	this	this	DT
randomwalker-info-585	812	3	time	time	NN
randomwalker-info-585	812	4	,	,	,
randomwalker-info-585	812	5	new	new	JJ
randomwalker-info-585	812	6	transactions	transaction	NNS
randomwalker-info-585	812	7	take	take	VBP
randomwalker-info-585	812	8	Θ	Θ	NNP
randomwalker-info-585	812	9	(	(	-LRB-
randomwalker-info-585	812	10	√	√	NNP
randomwalker-info-585	812	11	n	n	CC
randomwalker-info-585	812	12	)	)	-RRB-
randomwalker-info-585	812	13	time	time	NN
randomwalker-info-585	812	14	steps	step	NNS
randomwalker-info-585	812	15	before	before	IN
randomwalker-info-585	812	16	they	-PRON-	PRP
randomwalker-info-585	812	17	are	be	VBP
randomwalker-info-585	812	18	included	include	VBN
randomwalker-info-585	812	19	in	in	IN
randomwalker-info-585	812	20	a	a	DT
randomwalker-info-585	812	21	block	block	NN
randomwalker-info-585	812	22	.	.	.
randomwalker-info-585	813	1	2	2	CD
randomwalker-info-585	813	2	Before	before	IN
randomwalker-info-585	813	3	proving	prove	VBG
randomwalker-info-585	813	4	Lemma	Lemma	NNP
randomwalker-info-585	813	5	C.7	C.7	NNP
randomwalker-info-585	813	6	,	,	,
randomwalker-info-585	813	7	we	-PRON-	PRP
randomwalker-info-585	813	8	recall	recall	VBP
randomwalker-info-585	813	9	the	the	DT
randomwalker-info-585	813	10	Berry	Berry	NNP
randomwalker-info-585	813	11	-	-	HYPH
randomwalker-info-585	813	12	Esseen	Esseen	NNP
randomwalker-info-585	813	13	theorem	theorem	NN
randomwalker-info-585	813	14	:	:	:
randomwalker-info-585	813	15	Theorem	theorem	JJ
randomwalker-info-585	813	16	C.6	c.6	NN
randomwalker-info-585	813	17	(	(	-LRB-
randomwalker-info-585	813	18	Berry	Berry	NNP
randomwalker-info-585	813	19	-	-	HYPH
randomwalker-info-585	813	20	Esseen	Esseen	NNP
randomwalker-info-585	813	21	)	)	-RRB-
randomwalker-info-585	813	22	.	.	.
randomwalker-info-585	814	1	Let	let	VB
randomwalker-info-585	814	2	X1	X1	NNP
randomwalker-info-585	814	3	,	,	,
randomwalker-info-585	814	4	.	.	.
randomwalker-info-585	815	1	.	.	.
randomwalker-info-585	816	1	.	.	.
randomwalker-info-585	817	1	,	,	,
randomwalker-info-585	817	2	Xn	Xn	NNP
randomwalker-info-585	817	3	be	be	VB
randomwalker-info-585	817	4	i.i.d	i.i.d	JJ
randomwalker-info-585	817	5	.	.	.
randomwalker-info-585	818	1	random	random	JJ
randomwalker-info-585	818	2	variables	variable	NNS
randomwalker-info-585	818	3	with	with	IN
randomwalker-info-585	818	4	mean	mean	NNP
randomwalker-info-585	818	5	0	0	CD
randomwalker-info-585	818	6	,	,	,
randomwalker-info-585	818	7	E[X2i	E[X2i	,
randomwalker-info-585	818	8	]	]	-RRB-
randomwalker-info-585	818	9	=	=	SYM
randomwalker-info-585	818	10	σ	σ	NNP
randomwalker-info-585	818	11	2	2	CD
randomwalker-info-585	818	12	,	,	,
randomwalker-info-585	818	13	E[X3i	e[x3i	ADD
randomwalker-info-585	818	14	]	]	-RRB-
randomwalker-info-585	818	15	=	=	NFP
randomwalker-info-585	818	16	ρ	ρ	XX
randomwalker-info-585	818	17	.	.	.
randomwalker-info-585	819	1	Then	then	RB
randomwalker-info-585	819	2	for	for	IN
randomwalker-info-585	819	3	all	all	DT
randomwalker-info-585	819	4	x	x	NN
randomwalker-info-585	819	5	:	:	:
randomwalker-info-585	819	6	Pr	pr	NN
randomwalker-info-585	819	7	[	[	-LRB-
randomwalker-info-585	819	8	∑	∑	.
randomwalker-info-585	819	9	i	i	PRP
randomwalker-info-585	819	10	Xi	Xi	NNP
randomwalker-info-585	819	11	σ	σ	NNP
randomwalker-info-585	819	12	√	√	NNP
randomwalker-info-585	819	13	n	n	CC
randomwalker-info-585	819	14	≥	≥	NN
randomwalker-info-585	819	15	x	x	NN
randomwalker-info-585	819	16	]	]	-RRB-
randomwalker-info-585	819	17	−	−	NNP
randomwalker-info-585	819	18	Φ(x	φ(x	CD
randomwalker-info-585	819	19	)	)	-RRB-
randomwalker-info-585	819	20	=	=	NFP
randomwalker-info-585	819	21	O	o	FW
randomwalker-info-585	819	22	(	(	-LRB-
randomwalker-info-585	819	23	ρ	ρ	NN
randomwalker-info-585	819	24	σ3	σ3	NNP
randomwalker-info-585	819	25	√	√	NNP
randomwalker-info-585	819	26	n	n	NNP
randomwalker-info-585	819	27	)	)	-RRB-
randomwalker-info-585	819	28	,	,	,
randomwalker-info-585	819	29	Where	where	WRB
randomwalker-info-585	819	30	Φ(x	Φ(x	NNS
randomwalker-info-585	819	31	)	)	-RRB-
randomwalker-info-585	819	32	denotes	denote	VBZ
randomwalker-info-585	819	33	the	the	DT
randomwalker-info-585	819	34	probability	probability	NN
randomwalker-info-585	819	35	that	that	IN
randomwalker-info-585	819	36	a	a	DT
randomwalker-info-585	819	37	Gaussian	gaussian	JJ
randomwalker-info-585	819	38	random	random	JJ
randomwalker-info-585	819	39	variable	variable	NN
randomwalker-info-585	819	40	with	with	IN
randomwalker-info-585	819	41	mean	mean	NNP
randomwalker-info-585	819	42	0	0	CD
randomwalker-info-585	819	43	and	and	CC
randomwalker-info-585	819	44	standard	standard	JJ
randomwalker-info-585	819	45	deviation	deviation	NN
randomwalker-info-585	819	46	1	1	CD
randomwalker-info-585	819	47	exceeds	exceed	VBZ
randomwalker-info-585	819	48	x.	x.	NN
randomwalker-info-585	819	49	Lemma	Lemma	NNP
randomwalker-info-585	819	50	C.7	C.7	NNP
randomwalker-info-585	819	51	.	.	.
randomwalker-info-585	820	1	Define	Define	NNP
randomwalker-info-585	820	2	Xi	Xi	NNP
randomwalker-info-585	820	3	to	to	TO
randomwalker-info-585	820	4	be	be	VB
randomwalker-info-585	820	5	an	an	DT
randomwalker-info-585	820	6	exponential	exponential	JJ
randomwalker-info-585	820	7	random	random	JJ
randomwalker-info-585	820	8	variable	variable	NN
randomwalker-info-585	820	9	with	with	IN
randomwalker-info-585	820	10	mean	mean	NNP
randomwalker-info-585	820	11	1	1	CD
randomwalker-info-585	820	12	.	.	.
randomwalker-info-585	821	1	Then	then	RB
randomwalker-info-585	821	2	:	:	:
randomwalker-info-585	821	3	Pr	pr	NN
randomwalker-info-585	821	4	[	[	-LRB-
randomwalker-info-585	821	5	n∑	n∑	NN
randomwalker-info-585	821	6	i=1	i=1	NNS
randomwalker-info-585	821	7	Xi	Xi	NNP
randomwalker-info-585	821	8	>	>	XX
randomwalker-info-585	821	9	n	n	CC
randomwalker-info-585	821	10	+	+	CC
randomwalker-info-585	821	11	√	√	NNP
randomwalker-info-585	821	12	n	n	NN
randomwalker-info-585	821	13	]	]	-RRB-
randomwalker-info-585	821	14	=	=	SYM
randomwalker-info-585	821	15	Θ(1	θ(1	LS
randomwalker-info-585	821	16	)	)	-RRB-
randomwalker-info-585	821	17	.	.	.
randomwalker-info-585	822	1	In	in	IN
randomwalker-info-585	822	2	particular	particular	JJ
randomwalker-info-585	822	3	,	,	,
randomwalker-info-585	822	4	this	this	DT
randomwalker-info-585	822	5	implies	imply	VBZ
randomwalker-info-585	822	6	that	that	IN
randomwalker-info-585	822	7	probability	probability	NN
randomwalker-info-585	822	8	that	that	IN
randomwalker-info-585	822	9	fewer	few	JJR
randomwalker-info-585	822	10	than	than	IN
randomwalker-info-585	822	11	n	n	JJ
randomwalker-info-585	822	12	blocks	block	NNS
randomwalker-info-585	822	13	are	be	VBP
randomwalker-info-585	822	14	found	find	VBN
randomwalker-info-585	822	15	in	in	IN
randomwalker-info-585	822	16	n	n	CC
randomwalker-info-585	822	17	+	+	CC
randomwalker-info-585	822	18	√	√	NN
randomwalker-info-585	822	19	n	n	CD
randomwalker-info-585	822	20	time	time	NN
randomwalker-info-585	822	21	steps	step	NNS
randomwalker-info-585	822	22	is	be	VBZ
randomwalker-info-585	822	23	Θ(1	θ(1	XX
randomwalker-info-585	822	24	)	)	-RRB-
randomwalker-info-585	822	25	.	.	.
randomwalker-info-585	823	1	Proof	proof	NN
randomwalker-info-585	823	2	.	.	.
randomwalker-info-585	824	1	Define	Define	NNP
randomwalker-info-585	824	2	Yi	Yi	NNP
randomwalker-info-585	824	3	=	=	NFP
randomwalker-info-585	824	4	Xi	Xi	NNP
randomwalker-info-585	824	5	−	−	NNP
randomwalker-info-585	824	6	1	1	CD
randomwalker-info-585	824	7	.	.	.
randomwalker-info-585	825	1	Then	then	RB
randomwalker-info-585	825	2	the	the	DT
randomwalker-info-585	825	3	Yi	Yi	NNP
randomwalker-info-585	825	4	are	be	VBP
randomwalker-info-585	825	5	i.i.d	i.i.d	JJ
randomwalker-info-585	825	6	.	.	.
randomwalker-info-585	826	1	random	random	JJ
randomwalker-info-585	826	2	variables	variable	NNS
randomwalker-info-585	826	3	with	with	IN
randomwalker-info-585	826	4	mean	mean	NNP
randomwalker-info-585	826	5	0	0	CD
randomwalker-info-585	826	6	,	,	,
randomwalker-info-585	826	7	E[Y	E[Y	JJR
randomwalker-info-585	826	8	2i	2i	LS
randomwalker-info-585	826	9	]	]	-RRB-
randomwalker-info-585	826	10	=	=	SYM
randomwalker-info-585	826	11	σ	σ	NNP
randomwalker-info-585	826	12	<	<	XX
randomwalker-info-585	826	13	2	2	CD
randomwalker-info-585	826	14	,	,	,
randomwalker-info-585	826	15	and	and	CC
randomwalker-info-585	826	16	E[Y	E[Y	JJR
randomwalker-info-585	826	17	3i	3i	NNPS
randomwalker-info-585	826	18	]	]	-RRB-
randomwalker-info-585	826	19	=	=	NFP
randomwalker-info-585	826	20	ρ	ρ	NNP
randomwalker-info-585	826	21	<	<	XX
randomwalker-info-585	826	22	6	6	CD
randomwalker-info-585	826	23	.	.	.
randomwalker-info-585	827	1	Plugging	plug	VBG
randomwalker-info-585	827	2	into	into	IN
randomwalker-info-585	827	3	Berry	Berry	NNP
randomwalker-info-585	827	4	-	-	HYPH
randomwalker-info-585	827	5	Esseen	Esseen	NNP
randomwalker-info-585	827	6	(	(	-LRB-
randomwalker-info-585	827	7	stated	state	VBN
randomwalker-info-585	827	8	below	below	RB
randomwalker-info-585	827	9	)	)	-RRB-
randomwalker-info-585	827	10	,	,	,
randomwalker-info-585	827	11	we	-PRON-	PRP
randomwalker-info-585	827	12	get	get	VBP
randomwalker-info-585	827	13	:	:	:
randomwalker-info-585	827	14	Pr	pr	NN
randomwalker-info-585	827	15	[	[	-LRB-
randomwalker-info-585	827	16	n∑	n∑	NN
randomwalker-info-585	827	17	i=1	i=1	NNP
randomwalker-info-585	827	18	Yi	Yi	NNP
randomwalker-info-585	827	19	>	>	FW
randomwalker-info-585	827	20	√	√	NNP
randomwalker-info-585	827	21	n	n	CC
randomwalker-info-585	827	22	]	]	-RRB-
randomwalker-info-585	827	23	=	=	NFP
randomwalker-info-585	827	24	Pr	pr	NN
randomwalker-info-585	827	25	[	[	-LRB-
randomwalker-info-585	827	26	∑n	∑n	NN
randomwalker-info-585	827	27	i=1	i=1	UH
randomwalker-info-585	827	28	Yi	Yi	NNP
randomwalker-info-585	827	29	σ	σ	NNP
randomwalker-info-585	827	30	√	√	NNP
randomwalker-info-585	827	31	n	n	IN
randomwalker-info-585	827	32	>	>	NN
randomwalker-info-585	827	33	1	1	CD
randomwalker-info-585	827	34	σ	σ	NNP
randomwalker-info-585	827	35	]	]	-RRB-
randomwalker-info-585	827	36	≥	≥	NN
randomwalker-info-585	827	37	Φ	φ	NN
randomwalker-info-585	827	38	(	(	-LRB-
randomwalker-info-585	827	39	1	1	CD
randomwalker-info-585	827	40	σ	σ	NN
randomwalker-info-585	827	41	)	)	-RRB-
randomwalker-info-585	827	42	−O	−O	NNP
randomwalker-info-585	827	43	(	(	-LRB-
randomwalker-info-585	827	44	1	1	CD
randomwalker-info-585	827	45	√	√	NNP
randomwalker-info-585	827	46	n	n	NN
randomwalker-info-585	827	47	)	)	-RRB-
randomwalker-info-585	827	48	.	.	.
randomwalker-info-585	828	1	As	as	IN
randomwalker-info-585	828	2	σ	σ	NN
randomwalker-info-585	828	3	is	be	VBZ
randomwalker-info-585	828	4	a	a	DT
randomwalker-info-585	828	5	constant	constant	JJ
randomwalker-info-585	828	6	independent	independent	NN
randomwalker-info-585	828	7	of	of	IN
randomwalker-info-585	828	8	n	n	NN
randomwalker-info-585	828	9	,	,	,
randomwalker-info-585	828	10	Φ(σ	φ(σ	JJ
randomwalker-info-585	828	11	)	)	-RRB-
randomwalker-info-585	828	12	is	be	VBZ
randomwalker-info-585	828	13	also	also	RB
randomwalker-info-585	828	14	independent	independent	JJ
randomwalker-info-585	828	15	of	of	IN
randomwalker-info-585	828	16	n	n	NN
randomwalker-info-585	828	17	,	,	,
randomwalker-info-585	828	18	so	so	RB
randomwalker-info-585	828	19	Φ	φ	NN
randomwalker-info-585	828	20	(	(	-LRB-
randomwalker-info-585	828	21	1	1	CD
randomwalker-info-585	828	22	σ	σ	NN
randomwalker-info-585	828	23	)	)	-RRB-
randomwalker-info-585	828	24	−O	−O	NNP
randomwalker-info-585	828	25	(	(	-LRB-
randomwalker-info-585	828	26	1√	1√	CD
randomwalker-info-585	828	27	n	n	CC
randomwalker-info-585	828	28	)	)	-RRB-
randomwalker-info-585	828	29	=	=	NFP
randomwalker-info-585	828	30	Θ(1	θ(1	LS
randomwalker-info-585	828	31	)	)	-RRB-
randomwalker-info-585	828	32	,	,	,
randomwalker-info-585	828	33	as	as	IN
randomwalker-info-585	828	34	desired	desire	VBN
randomwalker-info-585	828	35	.	.	.
randomwalker-info-585	829	1	D.	D.	NNP
randomwalker-info-585	829	2	WHEN	when	WRB
randomwalker-info-585	829	3	DEFAULT	DEFAULT	NNP
randomwalker-info-585	829	4	MINING	MINING	NNP
randomwalker-info-585	829	5	IS	be	VBZ
randomwalker-info-585	829	6	AN	an	DT
randomwalker-info-585	829	7	EQUILIBRIUM	EQUILIBRIUM	NNP
randomwalker-info-585	829	8	FOR	for	IN
randomwalker-info-585	829	9	NON	NON	NNP
randomwalker-info-585	829	10	-	-	NN
randomwalker-info-585	829	11	ATOMIC	atomic	JJ
randomwalker-info-585	829	12	MINERS	miner	NNS
randomwalker-info-585	829	13	In	in	IN
randomwalker-info-585	829	14	the	the	DT
randomwalker-info-585	829	15	absence	absence	NN
randomwalker-info-585	829	16	of	of	IN
randomwalker-info-585	829	17	latency	latency	NN
randomwalker-info-585	829	18	,	,	,
randomwalker-info-585	829	19	default	default	NN
randomwalker-info-585	829	20	mining	mining	NN
randomwalker-info-585	829	21	is	be	VBZ
randomwalker-info-585	829	22	an	an	DT
randomwalker-info-585	829	23	equilibrium	equilibrium	NN
randomwalker-info-585	829	24	for	for	IN
randomwalker-info-585	829	25	non	non	JJ
randomwalker-info-585	829	26	-	-	JJ
randomwalker-info-585	829	27	atomic	atomic	JJ
randomwalker-info-585	829	28	miners	miner	NNS
randomwalker-info-585	829	29	regardless	regardless	RB
randomwalker-info-585	829	30	of	of	IN
randomwalker-info-585	829	31	the	the	DT
randomwalker-info-585	829	32	reward	reward	NN
randomwalker-info-585	829	33	model	model	NN
randomwalker-info-585	829	34	,	,	,
randomwalker-info-585	829	35	and	and	CC
randomwalker-info-585	829	36	the	the	DT
randomwalker-info-585	829	37	reasoning	reasoning	NN
randomwalker-info-585	829	38	is	be	VBZ
randomwalker-info-585	829	39	simple	simple	JJ
randomwalker-info-585	829	40	:	:	:
randomwalker-info-585	829	41	if	if	IN
randomwalker-info-585	829	42	you	-PRON-	PRP
randomwalker-info-585	829	43	do	do	VBP
randomwalker-info-585	829	44	anything	anything	NN
randomwalker-info-585	829	45	except	except	IN
randomwalker-info-585	829	46	extend	extend	VB
randomwalker-info-585	829	47	the	the	DT
randomwalker-info-585	829	48	unique	unique	JJ
randomwalker-info-585	829	49	longest	long	JJS
randomwalker-info-585	829	50	chain	chain	NN
randomwalker-info-585	829	51	,	,	,
randomwalker-info-585	829	52	your	-PRON-	PRP$
randomwalker-info-585	829	53	block	block	NN
randomwalker-info-585	829	54	will	will	MD
randomwalker-info-585	829	55	be	be	VB
randomwalker-info-585	829	56	orphaned	orphan	VBN
randomwalker-info-585	829	57	and	and	CC
randomwalker-info-585	829	58	you	-PRON-	PRP
randomwalker-info-585	829	59	will	will	MD
randomwalker-info-585	829	60	receive	receive	VB
randomwalker-info-585	829	61	reward	reward	NN
randomwalker-info-585	829	62	zero	zero	CD
randomwalker-info-585	829	63	.	.	.
randomwalker-info-585	830	1	If	if	IN
randomwalker-info-585	830	2	you	-PRON-	PRP
randomwalker-info-585	830	3	wait	wait	VBP
randomwalker-info-585	830	4	to	to	TO
randomwalker-info-585	830	5	publish	publish	VB
randomwalker-info-585	830	6	your	-PRON-	PRP$
randomwalker-info-585	830	7	block	block	NN
randomwalker-info-585	830	8	,	,	,
randomwalker-info-585	830	9	you	-PRON-	PRP
randomwalker-info-585	830	10	risk	risk	VBP
randomwalker-info-585	830	11	losing	lose	VBG
randomwalker-info-585	830	12	the	the	DT
randomwalker-info-585	830	13	option	option	NN
randomwalker-info-585	830	14	to	to	TO
randomwalker-info-585	830	15	publish	publish	VB
randomwalker-info-585	830	16	it	-PRON-	PRP
randomwalker-info-585	830	17	without	without	IN
randomwalker-info-585	830	18	being	be	VBG
randomwalker-info-585	830	19	orphaned	orphan	VBN
randomwalker-info-585	830	20	.	.	.
randomwalker-info-585	831	1	All	all	DT
randomwalker-info-585	831	2	other	other	JJ
randomwalker-info-585	831	3	miners	miner	NNS
randomwalker-info-585	831	4	ignore	ignore	VBP
randomwalker-info-585	831	5	the	the	DT
randomwalker-info-585	831	6	transactions	transaction	NNS
randomwalker-info-585	831	7	included	include	VBN
randomwalker-info-585	831	8	in	in	IN
randomwalker-info-585	831	9	your	-PRON-	PRP$
randomwalker-info-585	831	10	block	block	NN
randomwalker-info-585	831	11	when	when	WRB
randomwalker-info-585	831	12	deciding	decide	VBG
randomwalker-info-585	831	13	where	where	WRB
randomwalker-info-585	831	14	to	to	TO
randomwalker-info-585	831	15	extend	extend	VB
randomwalker-info-585	831	16	,	,	,
randomwalker-info-585	831	17	so	so	RB
randomwalker-info-585	831	18	you	-PRON-	PRP
randomwalker-info-585	831	19	may	may	MD
randomwalker-info-585	831	20	as	as	RB
randomwalker-info-585	831	21	well	well	RB
randomwalker-info-585	831	22	include	include	VB
randomwalker-info-585	831	23	as	as	RB
randomwalker-info-585	831	24	many	many	JJ
randomwalker-info-585	831	25	transactions	transaction	NNS
randomwalker-info-585	831	26	as	as	IN
randomwalker-info-585	831	27	possible	possible	JJ
randomwalker-info-585	831	28	.	.	.
randomwalker-info-585	832	1	In	in	IN
randomwalker-info-585	832	2	the	the	DT
randomwalker-info-585	832	3	presence	presence	NN
randomwalker-info-585	832	4	of	of	IN
randomwalker-info-585	832	5	latency	latency	NN
randomwalker-info-585	832	6	,	,	,
randomwalker-info-585	832	7	forks	fork	NNS
randomwalker-info-585	832	8	will	will	MD
randomwalker-info-585	832	9	naturally	naturally	RB
randomwalker-info-585	832	10	occur	occur	VB
randomwalker-info-585	832	11	,	,	,
randomwalker-info-585	832	12	so	so	RB
randomwalker-info-585	832	13	PettyCompliant	PettyCompliant	NNP
randomwalker-info-585	832	14	outperforms	outperform	VBZ
randomwalker-info-585	832	15	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	832	16	in	in	IN
randomwalker-info-585	832	17	the	the	DT
randomwalker-info-585	832	18	trans-	trans-	JJ
randomwalker-info-585	832	19	action	action	NN
randomwalker-info-585	832	20	fees	fee	NNS
randomwalker-info-585	832	21	model	model	NN
randomwalker-info-585	832	22	.	.	.
randomwalker-info-585	833	1	In	in	IN
randomwalker-info-585	833	2	the	the	DT
randomwalker-info-585	833	3	fixed	fixed	JJ
randomwalker-info-585	833	4	reward	reward	NN
randomwalker-info-585	833	5	model	model	NN
randomwalker-info-585	833	6	,	,	,
randomwalker-info-585	833	7	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	833	8	remains	remain	VBZ
randomwalker-info-585	833	9	an	an	DT
randomwalker-info-585	833	10	equilibrium	equilibrium	NN
randomwalker-info-585	833	11	under	under	IN
randomwalker-info-585	833	12	quite	quite	RB
randomwalker-info-585	833	13	general	general	JJ
randomwalker-info-585	833	14	models	model	NNS
randomwalker-info-585	833	15	of	of	IN
randomwalker-info-585	833	16	latency	latency	NN
randomwalker-info-585	833	17	(	(	-LRB-
randomwalker-info-585	833	18	still	still	RB
randomwalker-info-585	833	19	assuming	assume	VBG
randomwalker-info-585	833	20	non	non	JJ
randomwalker-info-585	833	21	-	-	JJ
randomwalker-info-585	833	22	atomic	atomic	JJ
randomwalker-info-585	833	23	miners	miner	NNS
randomwalker-info-585	833	24	)	)	-RRB-
randomwalker-info-585	833	25	.	.	.
randomwalker-info-585	834	1	Consider	consider	VB
randomwalker-info-585	834	2	,	,	,
randomwalker-info-585	834	3	for	for	IN
randomwalker-info-585	834	4	instance	instance	NN
randomwalker-info-585	834	5	,	,	,
randomwalker-info-585	834	6	any	any	DT
randomwalker-info-585	834	7	model	model	NN
randomwalker-info-585	834	8	of	of	IN
randomwalker-info-585	834	9	latency	latency	NN
randomwalker-info-585	834	10	with	with	IN
randomwalker-info-585	834	11	the	the	DT
randomwalker-info-585	834	12	following	follow	VBG
randomwalker-info-585	834	13	property	property	NN
randomwalker-info-585	834	14	.	.	.
randomwalker-info-585	835	1	When-	When-	NNP
randomwalker-info-585	835	2	ever	ever	RB
randomwalker-info-585	835	3	miner	miner	NNP
randomwalker-info-585	835	4	m	m	NNP
randomwalker-info-585	835	5	finds	find	VBZ
randomwalker-info-585	835	6	a	a	DT
randomwalker-info-585	835	7	block	block	NN
randomwalker-info-585	835	8	,	,	,
randomwalker-info-585	835	9	and	and	CC
randomwalker-info-585	835	10	miner	miner	NN
randomwalker-info-585	835	11	m′	m′	NNP
randomwalker-info-585	835	12	finds	find	VBZ
randomwalker-info-585	835	13	a	a	DT
randomwalker-info-585	835	14	block	block	NN
randomwalker-info-585	835	15	at	at	IN
randomwalker-info-585	835	16	a	a	DT
randomwalker-info-585	835	17	later	later	JJ
randomwalker-info-585	835	18	time	time	NN
randomwalker-info-585	835	19	,	,	,
randomwalker-info-585	835	20	we	-PRON-	PRP
randomwalker-info-585	835	21	have	have	VBP
randomwalker-info-585	835	22	Bm	Bm	NNP
randomwalker-info-585	835	23	⊆	⊆	ADD
randomwalker-info-585	835	24	Bm′	Bm′	NNP
randomwalker-info-585	835	25	,	,	,
randomwalker-info-585	835	26	where	where	WRB
randomwalker-info-585	835	27	Bm	Bm	NNP
randomwalker-info-585	835	28	denotes	denote	VBZ
randomwalker-info-585	835	29	the	the	DT
randomwalker-info-585	835	30	set	set	NN
randomwalker-info-585	835	31	of	of	IN
randomwalker-info-585	835	32	blocks	block	NNS
randomwalker-info-585	835	33	that	that	WDT
randomwalker-info-585	835	34	miner	miner	NN
randomwalker-info-585	835	35	m	m	NNP
randomwalker-info-585	835	36	had	have	VBD
randomwalker-info-585	835	37	heard	hear	VBN
randomwalker-info-585	835	38	of	of	IN
randomwalker-info-585	835	39	when	when	WRB
randomwalker-info-585	835	40	they	-PRON-	PRP
randomwalker-info-585	835	41	found	find	VBD
randomwalker-info-585	835	42	their	-PRON-	PRP$
randomwalker-info-585	835	43	block	block	NN
randomwalker-info-585	835	44	.	.	.
randomwalker-info-585	836	1	In	in	IN
randomwalker-info-585	836	2	other	other	JJ
randomwalker-info-585	836	3	words	word	NNS
randomwalker-info-585	836	4	,	,	,
randomwalker-info-585	836	5	by	by	IN
randomwalker-info-585	836	6	the	the	DT
randomwalker-info-585	836	7	time	time	NN
randomwalker-info-585	836	8	miner	miner	NN
randomwalker-info-585	836	9	m′	m′	NNP
randomwalker-info-585	836	10	solves	solve	VBZ
randomwalker-info-585	836	11	their	-PRON-	PRP$
randomwalker-info-585	836	12	block	block	NN
randomwalker-info-585	836	13	,	,	,
randomwalker-info-585	836	14	they	-PRON-	PRP
randomwalker-info-585	836	15	have	have	VBP
randomwalker-info-585	836	16	become	become	VBN
randomwalker-info-585	836	17	aware	aware	JJ
randomwalker-info-585	836	18	of	of	IN
randomwalker-info-585	836	19	at	at	IN
randomwalker-info-585	836	20	least	least	JJS
randomwalker-info-585	836	21	every	every	DT
randomwalker-info-585	836	22	block	block	NN
randomwalker-info-585	836	23	that	that	WDT
randomwalker-info-585	836	24	m	m	NNP
randomwalker-info-585	836	25	was	be	VBD
randomwalker-info-585	836	26	aware	aware	JJ
randomwalker-info-585	836	27	of	of	IN
randomwalker-info-585	836	28	when	when	WRB
randomwalker-info-585	836	29	they	-PRON-	PRP
randomwalker-info-585	836	30	solved	solve	VBD
randomwalker-info-585	836	31	their	-PRON-	PRP$
randomwalker-info-585	836	32	block	block	NN
randomwalker-info-585	836	33	earlier	early	RBR
randomwalker-info-585	836	34	(	(	-LRB-
randomwalker-info-585	836	35	but	but	CC
randomwalker-info-585	836	36	perhaps	perhaps	RB
randomwalker-info-585	836	37	not	not	RB
randomwalker-info-585	836	38	m	m	NN
randomwalker-info-585	836	39	’s	’s	POS
randomwalker-info-585	836	40	block	block	NN
randomwalker-info-585	836	41	,	,	,
randomwalker-info-585	836	42	nor	nor	CC
randomwalker-info-585	836	43	any	any	DT
randomwalker-info-585	836	44	blocks	block	NNS
randomwalker-info-585	836	45	that	that	WDT
randomwalker-info-585	836	46	m	m	NNP
randomwalker-info-585	836	47	was	be	VBD
randomwalker-info-585	836	48	not	not	RB
randomwalker-info-585	836	49	herself	-PRON-	PRP
randomwalker-info-585	836	50	aware	aware	JJ
randomwalker-info-585	836	51	of	of	IN
randomwalker-info-585	836	52	)	)	-RRB-
randomwalker-info-585	836	53	.	.	.
randomwalker-info-585	837	1	It	-PRON-	PRP
randomwalker-info-585	837	2	is	be	VBZ
randomwalker-info-585	837	3	easy	easy	JJ
randomwalker-info-585	837	4	to	to	TO
randomwalker-info-585	837	5	see	see	VB
randomwalker-info-585	837	6	that	that	DT
randomwalker-info-585	837	7	simple	simple	JJ
randomwalker-info-585	837	8	latency	latency	NN
randomwalker-info-585	837	9	models	model	NNS
randomwalker-info-585	837	10	(	(	-LRB-
randomwalker-info-585	837	11	such	such	JJ
randomwalker-info-585	837	12	as	as	IN
randomwalker-info-585	837	13	all	all	DT
randomwalker-info-585	837	14	announcements	announcement	NNS
randomwalker-info-585	837	15	being	be	VBG
randomwalker-info-585	837	16	grouped	group	VBN
randomwalker-info-585	837	17	into	into	IN
randomwalker-info-585	837	18	chunks	chunk	NNS
randomwalker-info-585	837	19	of	of	IN
randomwalker-info-585	837	20	λ	λ	DT
randomwalker-info-585	837	21	seconds	second	NNS
randomwalker-info-585	837	22	)	)	-RRB-
randomwalker-info-585	837	23	have	have	VBP
randomwalker-info-585	837	24	this	this	DT
randomwalker-info-585	837	25	property	property	NN
randomwalker-info-585	837	26	,	,	,
randomwalker-info-585	837	27	as	as	RB
randomwalker-info-585	837	28	well	well	RB
randomwalker-info-585	837	29	as	as	IN
randomwalker-info-585	837	30	much	much	RB
randomwalker-info-585	837	31	more	more	RBR
randomwalker-info-585	837	32	general	general	JJ
randomwalker-info-585	837	33	latency	latency	NN
randomwalker-info-585	837	34	models	model	NNS
randomwalker-info-585	837	35	.	.	.
randomwalker-info-585	838	1	It	-PRON-	PRP
randomwalker-info-585	838	2	is	be	VBZ
randomwalker-info-585	838	3	also	also	RB
randomwalker-info-585	838	4	easy	easy	JJ
randomwalker-info-585	838	5	to	to	TO
randomwalker-info-585	838	6	see	see	VB
randomwalker-info-585	838	7	that	that	IN
randomwalker-info-585	838	8	in	in	IN
randomwalker-info-585	838	9	the	the	DT
randomwalker-info-585	838	10	transaction	transaction	NN
randomwalker-info-585	838	11	fees	fee	NNS
randomwalker-info-585	838	12	model	model	NN
randomwalker-info-585	838	13	,	,	,
randomwalker-info-585	838	14	the	the	DT
randomwalker-info-585	838	15	simple	simple	JJ
randomwalker-info-585	838	16	latency	latency	NN
randomwalker-info-585	838	17	model	model	NN
randomwalker-info-585	838	18	where	where	WRB
randomwalker-info-585	838	19	announcements	announcement	NNS
randomwalker-info-585	838	20	are	be	VBP
randomwalker-info-585	838	21	grouped	group	VBN
randomwalker-info-585	838	22	into	into	IN
randomwalker-info-585	838	23	chunks	chunk	NNS
randomwalker-info-585	838	24	of	of	IN
randomwalker-info-585	838	25	λ	λ	DT
randomwalker-info-585	838	26	seconds	second	NNS
randomwalker-info-585	838	27	is	be	VBZ
randomwalker-info-585	838	28	rich	rich	JJ
randomwalker-info-585	838	29	enough	enough	RB
randomwalker-info-585	838	30	so	so	IN
randomwalker-info-585	838	31	that	that	IN
randomwalker-info-585	838	32	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	838	33	is	be	VBZ
randomwalker-info-585	838	34	strictly	strictly	RB
randomwalker-info-585	838	35	outperformed	outperform	VBN
randomwalker-info-585	838	36	by	by	IN
randomwalker-info-585	838	37	PettyCompliant	PettyCompliant	NNP
randomwalker-info-585	838	38	and	and	CC
randomwalker-info-585	838	39	therefore	therefore	RB
randomwalker-info-585	838	40	not	not	RB
randomwalker-info-585	838	41	an	an	DT
randomwalker-info-585	838	42	equilibrium	equilibrium	NN
randomwalker-info-585	838	43	.	.	.
randomwalker-info-585	839	1	Proposition	proposition	NN
randomwalker-info-585	839	2	D.1	D.1	NNP
randomwalker-info-585	839	3	.	.	.
randomwalker-info-585	840	1	When	when	WRB
randomwalker-info-585	840	2	miners	miner	NNS
randomwalker-info-585	840	3	are	be	VBP
randomwalker-info-585	840	4	non	non	JJ
randomwalker-info-585	840	5	-	-	JJ
randomwalker-info-585	840	6	atomic	atomic	JJ
randomwalker-info-585	840	7	,	,	,
randomwalker-info-585	840	8	even	even	RB
randomwalker-info-585	840	9	in	in	IN
randomwalker-info-585	840	10	the	the	DT
randomwalker-info-585	840	11	presence	presence	NN
randomwalker-info-585	840	12	of	of	IN
randomwalker-info-585	840	13	any	any	DT
randomwalker-info-585	840	14	latency	latency	NN
randomwalker-info-585	840	15	of	of	IN
randomwalker-info-585	840	16	the	the	DT
randomwalker-info-585	840	17	form	form	NN
randomwalker-info-585	840	18	described	describe	VBN
randomwalker-info-585	840	19	above	above	RB
randomwalker-info-585	840	20	,	,	,
randomwalker-info-585	840	21	it	-PRON-	PRP
randomwalker-info-585	840	22	is	be	VBZ
randomwalker-info-585	840	23	an	an	DT
randomwalker-info-585	840	24	equilibrium	equilibrium	NN
randomwalker-info-585	840	25	for	for	IN
randomwalker-info-585	840	26	every	every	DT
randomwalker-info-585	840	27	miner	miner	NN
randomwalker-info-585	840	28	to	to	TO
randomwalker-info-585	840	29	use	use	VB
randomwalker-info-585	840	30	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	840	31	.	.	.
randomwalker-info-585	841	1	Proof	proof	NN
randomwalker-info-585	841	2	.	.	.
randomwalker-info-585	842	1	The	the	DT
randomwalker-info-585	842	2	proof	proof	NN
randomwalker-info-585	842	3	is	be	VBZ
randomwalker-info-585	842	4	actually	actually	RB
randomwalker-info-585	842	5	very	very	RB
randomwalker-info-585	842	6	straight	straight	RB
randomwalker-info-585	842	7	-	-	HYPH
randomwalker-info-585	842	8	forward	forward	RB
randomwalker-info-585	842	9	:	:	:
randomwalker-info-585	842	10	assuming	assume	VBG
randomwalker-info-585	842	11	that	that	IN
randomwalker-info-585	842	12	all	all	DT
randomwalker-info-585	842	13	other	other	JJ
randomwalker-info-585	842	14	miners	miner	NNS
randomwalker-info-585	842	15	are	be	VBP
randomwalker-info-585	842	16	DefaultCompliant	defaultcompliant	JJ
randomwalker-info-585	842	17	,	,	,
randomwalker-info-585	842	18	mining	mine	VBG
randomwalker-info-585	842	19	anywhere	anywhere	RB
randomwalker-info-585	842	20	except	except	IN
randomwalker-info-585	842	21	on	on	IN
randomwalker-info-585	842	22	top	top	NN
randomwalker-info-585	842	23	of	of	IN
randomwalker-info-585	842	24	a	a	DT
randomwalker-info-585	842	25	longest	long	JJS
randomwalker-info-585	842	26	chain	chain	NN
randomwalker-info-585	842	27	guarantees	guarantee	NNS
randomwalker-info-585	842	28	that	that	IN
randomwalker-info-585	842	29	your	-PRON-	PRP$
randomwalker-info-585	842	30	block	block	NN
randomwalker-info-585	842	31	will	will	MD
randomwalker-info-585	842	32	be	be	VB
randomwalker-info-585	842	33	orphaned	orphan	VBN
randomwalker-info-585	842	34	and	and	CC
randomwalker-info-585	842	35	you	-PRON-	PRP
randomwalker-info-585	842	36	will	will	MD
randomwalker-info-585	842	37	receive	receive	VB
randomwalker-info-585	842	38	a	a	DT
randomwalker-info-585	842	39	reward	reward	NN
randomwalker-info-585	842	40	of	of	IN
randomwalker-info-585	842	41	zero	zero	CD
randomwalker-info-585	842	42	(	(	-LRB-
randomwalker-info-585	842	43	because	because	IN
randomwalker-info-585	842	44	our	-PRON-	PRP$
randomwalker-info-585	842	45	latency	latency	NN
randomwalker-info-585	842	46	assumptions	assumption	NNS
randomwalker-info-585	842	47	guarantee	guarantee	VBP
randomwalker-info-585	842	48	that	that	IN
randomwalker-info-585	842	49	the	the	DT
randomwalker-info-585	842	50	next	next	JJ
randomwalker-info-585	842	51	miner	miner	NN
randomwalker-info-585	842	52	and	and	CC
randomwalker-info-585	842	53	all	all	DT
randomwalker-info-585	842	54	future	future	JJ
randomwalker-info-585	842	55	miners	miner	NNS
randomwalker-info-585	842	56	will	will	MD
randomwalker-info-585	842	57	have	have	VB
randomwalker-info-585	842	58	heard	hear	VBN
randomwalker-info-585	842	59	about	about	IN
randomwalker-info-585	842	60	the	the	DT
randomwalker-info-585	842	61	blocks	block	NNS
randomwalker-info-585	842	62	you	-PRON-	PRP
randomwalker-info-585	842	63	chose	choose	VBD
randomwalker-info-585	842	64	to	to	TO
randomwalker-info-585	842	65	undercut	undercut	VB
randomwalker-info-585	842	66	before	before	IN
randomwalker-info-585	842	67	yours	-PRON-	PRP
randomwalker-info-585	842	68	,	,	,
randomwalker-info-585	842	69	and	and	CC
randomwalker-info-585	842	70	they	-PRON-	PRP
randomwalker-info-585	842	71	are	be	VBP
randomwalker-info-585	842	72	all	all	DT
randomwalker-info-585	842	73	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	842	74	)	)	-RRB-
randomwalker-info-585	842	75	.	.	.
randomwalker-info-585	843	1	So	so	RB
randomwalker-info-585	843	2	the	the	DT
randomwalker-info-585	843	3	only	only	JJ
randomwalker-info-585	843	4	choices	choice	NNS
randomwalker-info-585	843	5	are	be	VBP
randomwalker-info-585	843	6	how	how	WRB
randomwalker-info-585	843	7	to	to	TO
randomwalker-info-585	843	8	tie	tie	VB
randomwalker-info-585	843	9	-	-	HYPH
randomwalker-info-585	843	10	break	break	NN
randomwalker-info-585	843	11	among	among	IN
randomwalker-info-585	843	12	multiple	multiple	JJ
randomwalker-info-585	843	13	longest	long	JJS
randomwalker-info-585	843	14	chains	chain	NNS
randomwalker-info-585	843	15	.	.	.
randomwalker-info-585	844	1	But	but	CC
randomwalker-info-585	844	2	this	this	DT
randomwalker-info-585	844	3	choice	choice	NN
randomwalker-info-585	844	4	neither	neither	DT
randomwalker-info-585	844	5	affects	affect	VBZ
randomwalker-info-585	844	6	your	-PRON-	PRP$
randomwalker-info-585	844	7	rewards	reward	NNS
randomwalker-info-585	844	8	(	(	-LRB-
randomwalker-info-585	844	9	they	-PRON-	PRP
randomwalker-info-585	844	10	are	be	VBP
randomwalker-info-585	844	11	fixed	fix	VBN
randomwalker-info-585	844	12	!	!	.
randomwalker-info-585	845	1	)	)	-RRB-
randomwalker-info-585	845	2	,	,	,
randomwalker-info-585	845	3	nor	nor	CC
randomwalker-info-585	845	4	the	the	DT
randomwalker-info-585	845	5	likelihood	likelihood	NN
randomwalker-info-585	845	6	that	that	IN
randomwalker-info-585	845	7	your	-PRON-	PRP$
randomwalker-info-585	845	8	block	block	NN
randomwalker-info-585	845	9	will	will	MD
randomwalker-info-585	845	10	be	be	VB
randomwalker-info-585	845	11	chosen	choose	VBN
randomwalker-info-585	845	12	by	by	IN
randomwalker-info-585	845	13	the	the	DT
randomwalker-info-585	845	14	next	next	JJ
randomwalker-info-585	845	15	miner	miner	NN
randomwalker-info-585	845	16	(	(	-LRB-
randomwalker-info-585	845	17	as	as	IN
randomwalker-info-585	845	18	this	this	DT
randomwalker-info-585	845	19	depends	depend	VBZ
randomwalker-info-585	845	20	only	only	RB
randomwalker-info-585	845	21	on	on	RB
randomwalker-info-585	845	22	how	how	WRB
randomwalker-info-585	845	23	quickly	quickly	RB
randomwalker-info-585	845	24	they	-PRON-	PRP
randomwalker-info-585	845	25	hear	hear	VBP
randomwalker-info-585	845	26	about	about	IN
randomwalker-info-585	845	27	your	-PRON-	PRP$
randomwalker-info-585	845	28	block	block	NN
randomwalker-info-585	845	29	and	and	CC
randomwalker-info-585	845	30	not	not	RB
randomwalker-info-585	845	31	on	on	IN
randomwalker-info-585	845	32	its	-PRON-	PRP$
randomwalker-info-585	845	33	contents	content	NNS
randomwalker-info-585	845	34	)	)	-RRB-
randomwalker-info-585	845	35	.	.	.
randomwalker-info-585	846	1	So	so	RB
randomwalker-info-585	846	2	tie	tie	NN
randomwalker-info-585	846	3	-	-	HYPH
randomwalker-info-585	846	4	breaking	breaking	NN
randomwalker-info-585	846	5	in	in	IN
randomwalker-info-585	846	6	favor	favor	NN
randomwalker-info-585	846	7	of	of	IN
randomwalker-info-585	846	8	the	the	DT
randomwalker-info-585	846	9	earliest	early	JJS
randomwalker-info-585	846	10	chain	chain	NN
randomwalker-info-585	846	11	is	be	VBZ
randomwalker-info-585	846	12	at	at	IN
randomwalker-info-585	846	13	least	least	JJS
randomwalker-info-585	846	14	as	as	RB
randomwalker-info-585	846	15	good	good	JJ
randomwalker-info-585	846	16	as	as	IN
randomwalker-info-585	846	17	any	any	DT
randomwalker-info-585	846	18	other	other	JJ
randomwalker-info-585	846	19	tie	tie	NN
randomwalker-info-585	846	20	-	-	HYPH
randomwalker-info-585	846	21	breaking	break	VBG
randomwalker-info-585	846	22	rule	rule	NN
randomwalker-info-585	846	23	.	.	.
randomwalker-info-585	847	1	Finally	finally	RB
randomwalker-info-585	847	2	,	,	,
randomwalker-info-585	847	3	it	-PRON-	PRP
randomwalker-info-585	847	4	is	be	VBZ
randomwalker-info-585	847	5	also	also	RB
randomwalker-info-585	847	6	easy	easy	JJ
randomwalker-info-585	847	7	to	to	TO
randomwalker-info-585	847	8	see	see	VB
randomwalker-info-585	847	9	that	that	DT
randomwalker-info-585	847	10	publishing	publishing	NN
randomwalker-info-585	847	11	as	as	RB
randomwalker-info-585	847	12	soon	soon	RB
randomwalker-info-585	847	13	as	as	IN
randomwalker-info-585	847	14	possible	possible	JJ
randomwalker-info-585	847	15	is	be	VBZ
randomwalker-info-585	847	16	optimal	optimal	JJ
randomwalker-info-585	847	17	,	,	,
randomwalker-info-585	847	18	as	as	IN
randomwalker-info-585	847	19	this	this	DT
randomwalker-info-585	847	20	maximizes	maximize	VBZ
randomwalker-info-585	847	21	the	the	DT
randomwalker-info-585	847	22	likelihood	likelihood	NN
randomwalker-info-585	847	23	that	that	IN
randomwalker-info-585	847	24	your	-PRON-	PRP$
randomwalker-info-585	847	25	block	block	NN
randomwalker-info-585	847	26	is	be	VBZ
randomwalker-info-585	847	27	chosen	choose	VBN
randomwalker-info-585	847	28	to	to	TO
randomwalker-info-585	847	29	be	be	VB
randomwalker-info-585	847	30	extended	extend	VBN
randomwalker-info-585	847	31	.	.	.
randomwalker-info-585	848	1	The	the	DT
randomwalker-info-585	848	2	point	point	NN
randomwalker-info-585	848	3	of	of	IN
randomwalker-info-585	848	4	Proposition	Proposition	NNP
randomwalker-info-585	848	5	D.1	D.1	NNP
randomwalker-info-585	848	6	is	be	VBZ
randomwalker-info-585	848	7	again	again	RB
randomwalker-info-585	848	8	just	just	RB
randomwalker-info-585	848	9	to	to	TO
randomwalker-info-585	848	10	contrast	contrast	VB
randomwalker-info-585	848	11	the	the	DT
randomwalker-info-585	848	12	difference	difference	NN
randomwalker-info-585	848	13	between	between	IN
randomwalker-info-585	848	14	transaction	transaction	NN
randomwalker-info-585	848	15	fees	fee	NNS
randomwalker-info-585	848	16	and	and	CC
randomwalker-info-585	848	17	fixed	fix	VBN
randomwalker-info-585	848	18	rewards	reward	NNS
randomwalker-info-585	848	19	.	.	.
randomwalker-info-585	849	1	In	in	IN
randomwalker-info-585	849	2	the	the	DT
randomwalker-info-585	849	3	non-	non-	NNP
randomwalker-info-585	849	4	atomic	atomic	NNP
randomwalker-info-585	849	5	regime	regime	NN
randomwalker-info-585	849	6	,	,	,
randomwalker-info-585	849	7	even	even	RB
randomwalker-info-585	849	8	in	in	IN
randomwalker-info-585	849	9	quite	quite	RB
randomwalker-info-585	849	10	general	general	JJ
randomwalker-info-585	849	11	latency	latency	NN
randomwalker-info-585	849	12	models	model	NNS
randomwalker-info-585	849	13	,	,	,
randomwalker-info-585	849	14	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	849	15	mining	mining	NN
randomwalker-info-585	849	16	is	be	VBZ
randomwalker-info-585	849	17	an	an	DT
randomwalker-info-585	849	18	equilibrium	equilibrium	NN
randomwalker-info-585	849	19	in	in	IN
randomwalker-info-585	849	20	the	the	DT
randomwalker-info-585	849	21	fixed	fix	VBN
randomwalker-info-585	849	22	-	-	HYPH
randomwalker-info-585	849	23	reward	reward	NN
randomwalker-info-585	849	24	model	model	NN
randomwalker-info-585	849	25	.	.	.
randomwalker-info-585	850	1	The	the	DT
randomwalker-info-585	850	2	proof	proof	NN
randomwalker-info-585	850	3	is	be	VBZ
randomwalker-info-585	850	4	simple	simple	JJ
randomwalker-info-585	850	5	and	and	CC
randomwalker-info-585	850	6	matches	match	VBZ
randomwalker-info-585	850	7	exactly	exactly	RB
randomwalker-info-585	850	8	our	-PRON-	PRP$
randomwalker-info-585	850	9	intuition	intuition	NN
randomwalker-info-585	850	10	for	for	IN
randomwalker-info-585	850	11	why	why	WRB
randomwalker-info-585	850	12	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	850	13	should	should	MD
randomwalker-info-585	850	14	make	make	VB
randomwalker-info-585	850	15	sense	sense	NN
randomwalker-info-585	850	16	.	.	.
randomwalker-info-585	851	1	But	but	CC
randomwalker-info-585	851	2	in	in	IN
randomwalker-info-585	851	3	the	the	DT
randomwalker-info-585	851	4	transaction	transaction	NN
randomwalker-info-585	851	5	fees	fee	NNS
randomwalker-info-585	851	6	model	model	NN
randomwalker-info-585	851	7	,	,	,
randomwalker-info-585	851	8	whenever	whenever	WRB
randomwalker-info-585	851	9	there	there	EX
randomwalker-info-585	851	10	exists	exist	VBZ
randomwalker-info-585	851	11	a	a	DT
randomwalker-info-585	851	12	possibility	possibility	NN
randomwalker-info-585	851	13	for	for	IN
randomwalker-info-585	851	14	forks	fork	NNS
randomwalker-info-585	851	15	,	,	,
randomwalker-info-585	851	16	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	851	17	is	be	VBZ
randomwalker-info-585	851	18	strictly	strictly	RB
randomwalker-info-585	851	19	outperformed	outperform	VBN
randomwalker-info-585	851	20	by	by	IN
randomwalker-info-585	851	21	PettyCompliant	PettyCompliant	NNP
randomwalker-info-585	851	22	,	,	,
randomwalker-info-585	851	23	and	and	CC
randomwalker-info-585	851	24	the	the	DT
randomwalker-info-585	851	25	space	space	NN
randomwalker-info-585	851	26	of	of	IN
randomwalker-info-585	851	27	equilibria	equilibria	NNP
randomwalker-info-585	851	28	is	be	VBZ
randomwalker-info-585	851	29	therefore	therefore	RB
randomwalker-info-585	851	30	much	much	RB
randomwalker-info-585	851	31	more	more	RBR
randomwalker-info-585	851	32	complex	complex	JJ
randomwalker-info-585	851	33	.	.	.
randomwalker-info-585	852	1	In	in	IN
randomwalker-info-585	852	2	particular	particular	JJ
randomwalker-info-585	852	3	,	,	,
randomwalker-info-585	852	4	it	-PRON-	PRP
randomwalker-info-585	852	5	would	would	MD
randomwalker-info-585	852	6	be	be	VB
randomwalker-info-585	852	7	interesting	interesting	JJ
randomwalker-info-585	852	8	for	for	IN
randomwalker-info-585	852	9	future	future	JJ
randomwalker-info-585	852	10	work	work	NN
randomwalker-info-585	852	11	to	to	TO
randomwalker-info-585	852	12	identify	identify	VB
randomwalker-info-585	852	13	an	an	DT
randomwalker-info-585	852	14	equilibrium	equilibrium	NN
randomwalker-info-585	852	15	for	for	IN
randomwalker-info-585	852	16	non	non	JJ
randomwalker-info-585	852	17	-	-	JJ
randomwalker-info-585	852	18	atomic	atomic	JJ
randomwalker-info-585	852	19	miners	miner	NNS
randomwalker-info-585	852	20	in	in	IN
randomwalker-info-585	852	21	the	the	DT
randomwalker-info-585	852	22	transaction	transaction	NN
randomwalker-info-585	852	23	fees	fee	NNS
randomwalker-info-585	852	24	model	model	NN
randomwalker-info-585	852	25	in	in	IN
randomwalker-info-585	852	26	any	any	DT
randomwalker-info-585	852	27	non	non	JJ
randomwalker-info-585	852	28	-	-	JJ
randomwalker-info-585	852	29	trivial	trivial	JJ
randomwalker-info-585	852	30	latency	latency	NN
randomwalker-info-585	852	31	model	model	NN
randomwalker-info-585	852	32	.	.	.
randomwalker-info-585	853	1	E.	E.	NNP
randomwalker-info-585	853	2	SELFISH	SELFISH	NNP
randomwalker-info-585	853	3	MINING	mining	NN
randomwalker-info-585	853	4	E.1	E.1	NNP
randomwalker-info-585	853	5	Classic	Classic	NNP
randomwalker-info-585	853	6	Selfish	Selfish	NNP
randomwalker-info-585	853	7	Mining	Mining	NNP
randomwalker-info-585	853	8	with	with	IN
randomwalker-info-585	853	9	transaction	transaction	NN
randomwalker-info-585	853	10	fees	fee	NNS
randomwalker-info-585	853	11	Here	here	RB
randomwalker-info-585	853	12	we	-PRON-	PRP
randomwalker-info-585	853	13	provide	provide	VBP
randomwalker-info-585	853	14	details	detail	NNS
randomwalker-info-585	853	15	on	on	IN
randomwalker-info-585	853	16	how	how	WRB
randomwalker-info-585	853	17	to	to	TO
randomwalker-info-585	853	18	analyze	analyze	VB
randomwalker-info-585	853	19	selfish	selfish	JJ
randomwalker-info-585	853	20	mining	mining	NN
randomwalker-info-585	853	21	in	in	IN
randomwalker-info-585	853	22	the	the	DT
randomwalker-info-585	853	23	transaction	transaction	NN
randomwalker-info-585	853	24	fee	fee	NN
randomwalker-info-585	853	25	regime	regime	NN
randomwalker-info-585	853	26	.	.	.
randomwalker-info-585	854	1	Recall	recall	VB
randomwalker-info-585	854	2	that	that	IN
randomwalker-info-585	854	3	Eyal	Eyal	NNP
randomwalker-info-585	854	4	and	and	CC
randomwalker-info-585	854	5	Sirer	Sirer	NNP
randomwalker-info-585	854	6	[	[	-LRB-
randomwalker-info-585	854	7	9	9	CD
randomwalker-info-585	854	8	]	]	-RRB-
randomwalker-info-585	854	9	have	have	VBP
randomwalker-info-585	854	10	already	already	RB
randomwalker-info-585	854	11	computed	compute	VBN
randomwalker-info-585	854	12	ps	ps	NNP
randomwalker-info-585	854	13	for	for	IN
randomwalker-info-585	854	14	all	all	DT
randomwalker-info-585	854	15	s	s	NNPS
randomwalker-info-585	854	16	,	,	,
randomwalker-info-585	854	17	the	the	DT
randomwalker-info-585	854	18	probability	probability	NN
randomwalker-info-585	854	19	that	that	WDT
randomwalker-info-585	854	20	the	the	DT
randomwalker-info-585	854	21	block	block	NN
randomwalker-info-585	854	22	chain	chain	NN
randomwalker-info-585	854	23	is	be	VBZ
randomwalker-info-585	854	24	in	in	IN
randomwalker-info-585	854	25	state	state	NN
randomwalker-info-585	854	26	s.	s.	NN
randomwalker-info-585	854	27	Below	below	RB
randomwalker-info-585	854	28	we	-PRON-	PRP
randomwalker-info-585	854	29	compute	compute	VBP
randomwalker-info-585	854	30	fs	f	NNS
randomwalker-info-585	854	31	for	for	IN
randomwalker-info-585	854	32	all	all	DT
randomwalker-info-585	854	33	states	state	NNS
randomwalker-info-585	854	34	s	s	POS
randomwalker-info-585	854	35	,	,	,
randomwalker-info-585	854	36	the	the	DT
randomwalker-info-585	854	37	probability	probability	NN
randomwalker-info-585	854	38	that	that	IN
randomwalker-info-585	854	39	a	a	DT
randomwalker-info-585	854	40	transaction	transaction	NN
randomwalker-info-585	854	41	winds	wind	VBZ
randomwalker-info-585	854	42	up	up	RP
randomwalker-info-585	854	43	with	with	IN
randomwalker-info-585	854	44	the	the	DT
randomwalker-info-585	854	45	selfish	selfish	JJ
randomwalker-info-585	854	46	miner	miner	NN
randomwalker-info-585	854	47	conditioned	condition	VBN
randomwalker-info-585	854	48	on	on	IN
randomwalker-info-585	854	49	that	that	DT
randomwalker-info-585	854	50	transaction	transaction	NN
randomwalker-info-585	854	51	arriving	arrive	VBG
randomwalker-info-585	854	52	while	while	IN
randomwalker-info-585	854	53	the	the	DT
randomwalker-info-585	854	54	blockchain	blockchain	NNP
randomwalker-info-585	854	55	is	be	VBZ
randomwalker-info-585	854	56	in	in	IN
randomwalker-info-585	854	57	state	state	NN
randomwalker-info-585	854	58	s.	s.	NNP
randomwalker-info-585	854	59	Computing	Computing	NNP
randomwalker-info-585	854	60	f0	f0	NN
randomwalker-info-585	854	61	:	:	:
randomwalker-info-585	854	62	Let	let	VB
randomwalker-info-585	854	63	’s	-PRON-	PRP
randomwalker-info-585	854	64	consider	consider	VB
randomwalker-info-585	854	65	the	the	DT
randomwalker-info-585	854	66	possible	possible	JJ
randomwalker-info-585	854	67	outcomes	outcome	NNS
randomwalker-info-585	854	68	when	when	WRB
randomwalker-info-585	854	69	a	a	DT
randomwalker-info-585	854	70	transaction	transaction	NN
randomwalker-info-585	854	71	arrives	arrive	VBZ
randomwalker-info-585	854	72	in	in	IN
randomwalker-info-585	854	73	state	state	NN
randomwalker-info-585	854	74	0	0	CD
randomwalker-info-585	854	75	:	:	:
randomwalker-info-585	854	76	•	•	XX
randomwalker-info-585	854	77	If	if	IN
randomwalker-info-585	854	78	a	a	DT
randomwalker-info-585	854	79	default	default	NN
randomwalker-info-585	854	80	miner	miner	NN
randomwalker-info-585	854	81	mines	mine	NNS
randomwalker-info-585	854	82	the	the	DT
randomwalker-info-585	854	83	next	next	JJ
randomwalker-info-585	854	84	block	block	NN
randomwalker-info-585	854	85	,	,	,
randomwalker-info-585	854	86	it	-PRON-	PRP
randomwalker-info-585	854	87	will	will	MD
randomwalker-info-585	854	88	contain	contain	VB
randomwalker-info-585	854	89	this	this	DT
randomwalker-info-585	854	90	transaction	transaction	NN
randomwalker-info-585	854	91	,	,	,
randomwalker-info-585	854	92	and	and	CC
randomwalker-info-585	854	93	this	this	DT
randomwalker-info-585	854	94	block	block	NN
randomwalker-info-585	854	95	will	will	MD
randomwalker-info-585	854	96	definitely	definitely	RB
randomwalker-info-585	854	97	be	be	VB
randomwalker-info-585	854	98	in	in	IN
randomwalker-info-585	854	99	the	the	DT
randomwalker-info-585	854	100	eventual	eventual	JJ
randomwalker-info-585	854	101	longest	long	JJS
randomwalker-info-585	854	102	chain	chain	NN
randomwalker-info-585	854	103	.	.	.
randomwalker-info-585	855	1	This	this	DT
randomwalker-info-585	855	2	happens	happen	VBZ
randomwalker-info-585	855	3	with	with	IN
randomwalker-info-585	855	4	probability	probability	NN
randomwalker-info-585	855	5	(	(	-LRB-
randomwalker-info-585	855	6	1	1	CD
randomwalker-info-585	855	7	−α	−α	CD
randomwalker-info-585	855	8	)	)	-RRB-
randomwalker-info-585	855	9	.	.	.
randomwalker-info-585	856	1	•	•	NNP
randomwalker-info-585	856	2	Alternatively	alternatively	RB
randomwalker-info-585	856	3	,	,	,
randomwalker-info-585	856	4	the	the	DT
randomwalker-info-585	856	5	selfish	selfish	JJ
randomwalker-info-585	856	6	miner	miner	NN
randomwalker-info-585	856	7	could	could	MD
randomwalker-info-585	856	8	find	find	VB
randomwalker-info-585	856	9	the	the	DT
randomwalker-info-585	856	10	next	next	JJ
randomwalker-info-585	856	11	block	block	NN
randomwalker-info-585	856	12	.	.	.
randomwalker-info-585	857	1	If	if	IN
randomwalker-info-585	857	2	the	the	DT
randomwalker-info-585	857	3	selfish	selfish	JJ
randomwalker-info-585	857	4	miner	miner	NN
randomwalker-info-585	857	5	finds	find	VBZ
randomwalker-info-585	857	6	the	the	DT
randomwalker-info-585	857	7	next	next	JJ
randomwalker-info-585	857	8	block	block	NN
randomwalker-info-585	857	9	,	,	,
randomwalker-info-585	857	10	they	-PRON-	PRP
randomwalker-info-585	857	11	will	will	MD
randomwalker-info-585	857	12	include	include	VB
randomwalker-info-585	857	13	the	the	DT
randomwalker-info-585	857	14	transaction	transaction	NN
randomwalker-info-585	857	15	in	in	IN
randomwalker-info-585	857	16	their	-PRON-	PRP$
randomwalker-info-585	857	17	block	block	NN
randomwalker-info-585	857	18	,	,	,
randomwalker-info-585	857	19	but	but	CC
randomwalker-info-585	857	20	they	-PRON-	PRP
randomwalker-info-585	857	21	keep	keep	VBP
randomwalker-info-585	857	22	this	this	DT
randomwalker-info-585	857	23	block	block	NN
randomwalker-info-585	857	24	private	private	JJ
randomwalker-info-585	857	25	after	after	IN
randomwalker-info-585	857	26	they	-PRON-	PRP
randomwalker-info-585	857	27	find	find	VBP
randomwalker-info-585	857	28	it	-PRON-	PRP
randomwalker-info-585	857	29	.	.	.
randomwalker-info-585	858	1	This	this	DT
randomwalker-info-585	858	2	happens	happen	VBZ
randomwalker-info-585	858	3	with	with	IN
randomwalker-info-585	858	4	probability	probability	NN
randomwalker-info-585	858	5	α	α	XX
randomwalker-info-585	858	6	,	,	,
randomwalker-info-585	858	7	but	but	CC
randomwalker-info-585	858	8	this	this	DT
randomwalker-info-585	858	9	block	block	NN
randomwalker-info-585	858	10	is	be	VBZ
randomwalker-info-585	858	11	not	not	RB
randomwalker-info-585	858	12	guaranteed	guarantee	VBN
randomwalker-info-585	858	13	to	to	TO
randomwalker-info-585	858	14	make	make	VB
randomwalker-info-585	858	15	it	-PRON-	PRP
randomwalker-info-585	858	16	into	into	IN
randomwalker-info-585	858	17	the	the	DT
randomwalker-info-585	858	18	eventual	eventual	JJ
randomwalker-info-585	858	19	longest	long	JJS
randomwalker-info-585	858	20	chain	chain	NN
randomwalker-info-585	858	21	,	,	,
randomwalker-info-585	858	22	yet	yet	RB
randomwalker-info-585	858	23	.	.	.
randomwalker-info-585	859	1	•	•	VB
randomwalker-info-585	859	2	From	from	IN
randomwalker-info-585	859	3	here	here	RB
randomwalker-info-585	859	4	,	,	,
randomwalker-info-585	859	5	maybe	maybe	RB
randomwalker-info-585	859	6	the	the	DT
randomwalker-info-585	859	7	selfish	selfish	JJ
randomwalker-info-585	859	8	miner	miner	NN
randomwalker-info-585	859	9	finds	find	VBZ
randomwalker-info-585	859	10	the	the	DT
randomwalker-info-585	859	11	next	next	JJ
randomwalker-info-585	859	12	block	block	NN
randomwalker-info-585	859	13	as	as	RB
randomwalker-info-585	859	14	well	well	RB
randomwalker-info-585	859	15	.	.	.
randomwalker-info-585	860	1	This	this	DT
randomwalker-info-585	860	2	happens	happen	VBZ
randomwalker-info-585	860	3	with	with	IN
randomwalker-info-585	860	4	probability	probability	NN
randomwalker-info-585	860	5	α	α	XX
randomwalker-info-585	860	6	.	.	.
randomwalker-info-585	861	1	Once	once	IN
randomwalker-info-585	861	2	this	this	DT
randomwalker-info-585	861	3	happens	happen	VBZ
randomwalker-info-585	861	4	,	,	,
randomwalker-info-585	861	5	both	both	DT
randomwalker-info-585	861	6	blocks	block	NNS
randomwalker-info-585	861	7	are	be	VBP
randomwalker-info-585	861	8	guaranteed	guarantee	VBN
randomwalker-info-585	861	9	to	to	TO
randomwalker-info-585	861	10	be	be	VB
randomwalker-info-585	861	11	in	in	IN
randomwalker-info-585	861	12	the	the	DT
randomwalker-info-585	861	13	eventual	eventual	JJ
randomwalker-info-585	861	14	longest	long	JJS
randomwalker-info-585	861	15	chain	chain	NN
randomwalker-info-585	861	16	.	.	.
randomwalker-info-585	862	1	So	so	RB
randomwalker-info-585	862	2	this	this	DT
randomwalker-info-585	862	3	event	event	NN
randomwalker-info-585	862	4	contributes	contribute	VBZ
randomwalker-info-585	862	5	a	a	DT
randomwalker-info-585	862	6	probability	probability	NN
randomwalker-info-585	862	7	α2	α2	XX
randomwalker-info-585	862	8	that	that	IN
randomwalker-info-585	862	9	the	the	DT
randomwalker-info-585	862	10	transaction	transaction	NN
randomwalker-info-585	862	11	winds	wind	VBZ
randomwalker-info-585	862	12	up	up	RP
randomwalker-info-585	862	13	in	in	IN
randomwalker-info-585	862	14	the	the	DT
randomwalker-info-585	862	15	selfish	selfish	JJ
randomwalker-info-585	862	16	miner	miner	NN
randomwalker-info-585	862	17	’s	’s	POS
randomwalker-info-585	862	18	block	block	NN
randomwalker-info-585	862	19	.	.	.
randomwalker-info-585	863	1	•	•	NNP
randomwalker-info-585	863	2	Alternatively	alternatively	RB
randomwalker-info-585	863	3	,	,	,
randomwalker-info-585	863	4	a	a	DT
randomwalker-info-585	863	5	default	default	NN
randomwalker-info-585	863	6	miner	miner	NN
randomwalker-info-585	863	7	might	may	MD
randomwalker-info-585	863	8	find	find	VB
randomwalker-info-585	863	9	the	the	DT
randomwalker-info-585	863	10	next	next	JJ
randomwalker-info-585	863	11	block	block	NN
randomwalker-info-585	863	12	,	,	,
randomwalker-info-585	863	13	which	which	WDT
randomwalker-info-585	863	14	triggers	trigger	VBZ
randomwalker-info-585	863	15	a	a	DT
randomwalker-info-585	863	16	race	race	NN
randomwalker-info-585	863	17	.	.	.
randomwalker-info-585	864	1	This	this	DT
randomwalker-info-585	864	2	happens	happen	VBZ
randomwalker-info-585	864	3	with	with	IN
randomwalker-info-585	864	4	probability	probability	NN
randomwalker-info-585	864	5	(	(	-LRB-
randomwalker-info-585	864	6	1−α	1−α	CD
randomwalker-info-585	864	7	)	)	-RRB-
randomwalker-info-585	864	8	.	.	.
randomwalker-info-585	865	1	Both	both	DT
randomwalker-info-585	865	2	racing	racing	NN
randomwalker-info-585	865	3	blocks	block	NNS
randomwalker-info-585	865	4	contain	contain	VBP
randomwalker-info-585	865	5	the	the	DT
randomwalker-info-585	865	6	transaction	transaction	NN
randomwalker-info-585	865	7	being	be	VBG
randomwalker-info-585	865	8	considered	consider	VBN
randomwalker-info-585	865	9	,	,	,
randomwalker-info-585	865	10	so	so	CC
randomwalker-info-585	865	11	whoever	whoever	WP
randomwalker-info-585	865	12	wins	win	VBZ
randomwalker-info-585	865	13	the	the	DT
randomwalker-info-585	865	14	race	race	NN
randomwalker-info-585	865	15	receives	receive	VBZ
randomwalker-info-585	865	16	the	the	DT
randomwalker-info-585	865	17	corresponding	correspond	VBG
randomwalker-info-585	865	18	transaction	transaction	NN
randomwalker-info-585	865	19	fees	fee	NNS
randomwalker-info-585	865	20	.	.	.
randomwalker-info-585	866	1	The	the	DT
randomwalker-info-585	866	2	selfish	selfish	JJ
randomwalker-info-585	866	3	miner	miner	NN
randomwalker-info-585	866	4	wins	win	VBZ
randomwalker-info-585	866	5	the	the	DT
randomwalker-info-585	866	6	race	race	NN
randomwalker-info-585	866	7	with	with	IN
randomwalker-info-585	866	8	probability	probability	NN
randomwalker-info-585	866	9	α	α	CD
randomwalker-info-585	866	10	+	+	CC
randomwalker-info-585	866	11	γ(1	γ(1	$
randomwalker-info-585	866	12	−α	−α	XX
randomwalker-info-585	866	13	)	)	-RRB-
randomwalker-info-585	866	14	,	,	,
randomwalker-info-585	866	15	so	so	CC
randomwalker-info-585	866	16	this	this	DT
randomwalker-info-585	866	17	event	event	NN
randomwalker-info-585	866	18	contributes	contribute	VBZ
randomwalker-info-585	866	19	α(1	α(1	ADD
randomwalker-info-585	866	20	−α)(α	−α)(α	NNP
randomwalker-info-585	866	21	+	+	NFP
randomwalker-info-585	866	22	γ(1	γ(1	$
randomwalker-info-585	866	23	−α	−α	XX
randomwalker-info-585	866	24	)	)	-RRB-
randomwalker-info-585	866	25	)	)	-RRB-
randomwalker-info-585	866	26	in	in	IN
randomwalker-info-585	866	27	total	total	NN
randomwalker-info-585	866	28	.	.	.
randomwalker-info-585	867	1	Therefore	therefore	RB
randomwalker-info-585	867	2	,	,	,
randomwalker-info-585	867	3	we	-PRON-	PRP
randomwalker-info-585	867	4	see	see	VBP
randomwalker-info-585	867	5	that	that	DT
randomwalker-info-585	867	6	:	:	:
randomwalker-info-585	867	7	f0	f0	NN
randomwalker-info-585	867	8	=	=	SYM
randomwalker-info-585	867	9	α	α	NNP
randomwalker-info-585	867	10	2	2	CD
randomwalker-info-585	867	11	+	+	SYM
randomwalker-info-585	867	12	α(1	α(1	NFP
randomwalker-info-585	867	13	−α	−α	CD
randomwalker-info-585	867	14	)	)	-RRB-
randomwalker-info-585	867	15	(	(	-LRB-
randomwalker-info-585	867	16	α	α	NNP
randomwalker-info-585	867	17	+	+	SYM
randomwalker-info-585	867	18	γ(1	γ(1	$
randomwalker-info-585	867	19	−α	−α	CD
randomwalker-info-585	867	20	)	)	-RRB-
randomwalker-info-585	867	21	)	)	-RRB-
randomwalker-info-585	867	22	(	(	-LRB-
randomwalker-info-585	867	23	4	4	LS
randomwalker-info-585	867	24	)	)	-RRB-
randomwalker-info-585	867	25	Computing	computing	NN
randomwalker-info-585	867	26	f0′	f0′	NN
randomwalker-info-585	867	27	:	:	:
randomwalker-info-585	867	28	If	if	IN
randomwalker-info-585	867	29	a	a	DT
randomwalker-info-585	867	30	new	new	JJ
randomwalker-info-585	867	31	transaction	transaction	NN
randomwalker-info-585	867	32	is	be	VBZ
randomwalker-info-585	867	33	announced	announce	VBN
randomwalker-info-585	867	34	in	in	IN
randomwalker-info-585	867	35	state	state	NN
randomwalker-info-585	867	36	0	0	CD
randomwalker-info-585	867	37	′	′	XX
randomwalker-info-585	867	38	,	,	,
randomwalker-info-585	867	39	then	then	RB
randomwalker-info-585	867	40	the	the	DT
randomwalker-info-585	867	41	next	next	JJ
randomwalker-info-585	867	42	block	block	NN
randomwalker-info-585	867	43	found	find	VBN
randomwalker-info-585	867	44	is	be	VBZ
randomwalker-info-585	867	45	certainly	certainly	RB
randomwalker-info-585	867	46	contained	contain	VBN
randomwalker-info-585	867	47	in	in	IN
randomwalker-info-585	867	48	the	the	DT
randomwalker-info-585	867	49	eventual	eventual	JJ
randomwalker-info-585	867	50	longest	long	JJS
randomwalker-info-585	867	51	chain	chain	NN
randomwalker-info-585	867	52	because	because	IN
randomwalker-info-585	867	53	it	-PRON-	PRP
randomwalker-info-585	867	54	is	be	VBZ
randomwalker-info-585	867	55	always	always	RB
randomwalker-info-585	867	56	announced	announce	VBN
randomwalker-info-585	867	57	and	and	CC
randomwalker-info-585	867	58	every	every	DT
randomwalker-info-585	867	59	miner	miner	NN
randomwalker-info-585	867	60	chooses	choose	VBZ
randomwalker-info-585	867	61	to	to	IN
randomwalker-info-585	867	62	mine	-PRON-	PRP
randomwalker-info-585	867	63	on	on	IN
randomwalker-info-585	867	64	top	top	NN
randomwalker-info-585	867	65	of	of	IN
randomwalker-info-585	867	66	it	-PRON-	PRP
randomwalker-info-585	867	67	.	.	.
randomwalker-info-585	868	1	So	so	RB
randomwalker-info-585	868	2	this	this	DT
randomwalker-info-585	868	3	transaction	transaction	NN
randomwalker-info-585	868	4	is	be	VBZ
randomwalker-info-585	868	5	won	win	VBN
randomwalker-info-585	868	6	by	by	IN
randomwalker-info-585	868	7	whichever	whichever	WDT
randomwalker-info-585	868	8	miner	miner	NN
randomwalker-info-585	868	9	finds	find	VBZ
randomwalker-info-585	868	10	the	the	DT
randomwalker-info-585	868	11	next	next	JJ
randomwalker-info-585	868	12	block	block	NN
randomwalker-info-585	868	13	,	,	,
randomwalker-info-585	868	14	which	which	WDT
randomwalker-info-585	868	15	is	be	VBZ
randomwalker-info-585	868	16	the	the	DT
randomwalker-info-585	868	17	selfish	selfish	JJ
randomwalker-info-585	868	18	miner	miner	NN
randomwalker-info-585	868	19	with	with	IN
randomwalker-info-585	868	20	probability	probability	NN
randomwalker-info-585	868	21	α	α	NNP
randomwalker-info-585	868	22	.	.	.
randomwalker-info-585	869	1	Therefore	therefore	RB
randomwalker-info-585	869	2	:	:	:
randomwalker-info-585	869	3	f0′	f0′	NN
randomwalker-info-585	869	4	=	=	SYM
randomwalker-info-585	869	5	α	α	FW
randomwalker-info-585	869	6	(	(	-LRB-
randomwalker-info-585	869	7	5	5	CD
randomwalker-info-585	869	8	)	)	-RRB-
randomwalker-info-585	869	9	f1	f1	NNP
randomwalker-info-585	869	10	:	:	:
randomwalker-info-585	869	11	Consider	consider	VB
randomwalker-info-585	869	12	now	now	RB
randomwalker-info-585	869	13	a	a	DT
randomwalker-info-585	869	14	transaction	transaction	NN
randomwalker-info-585	869	15	announced	announce	VBN
randomwalker-info-585	869	16	in	in	IN
randomwalker-info-585	869	17	state	state	NN
randomwalker-info-585	869	18	1	1	CD
randomwalker-info-585	869	19	,	,	,
randomwalker-info-585	869	20	and	and	CC
randomwalker-info-585	869	21	where	where	WRB
randomwalker-info-585	869	22	it	-PRON-	PRP
randomwalker-info-585	869	23	might	may	MD
randomwalker-info-585	869	24	wind	wind	VB
randomwalker-info-585	869	25	up	up	RP
randomwalker-info-585	869	26	:	:	:
randomwalker-info-585	869	27	•	•	VB
randomwalker-info-585	869	28	If	if	IN
randomwalker-info-585	869	29	the	the	DT
randomwalker-info-585	869	30	selfish	selfish	JJ
randomwalker-info-585	869	31	miner	miner	NN
randomwalker-info-585	869	32	finds	find	VBZ
randomwalker-info-585	869	33	the	the	DT
randomwalker-info-585	869	34	next	next	JJ
randomwalker-info-585	869	35	block	block	NN
randomwalker-info-585	869	36	,	,	,
randomwalker-info-585	869	37	they	-PRON-	PRP
randomwalker-info-585	869	38	will	will	MD
randomwalker-info-585	869	39	have	have	VB
randomwalker-info-585	869	40	a	a	DT
randomwalker-info-585	869	41	private	private	JJ
randomwalker-info-585	869	42	chain	chain	NN
randomwalker-info-585	869	43	of	of	IN
randomwalker-info-585	869	44	length	length	NN
randomwalker-info-585	869	45	2	2	CD
randomwalker-info-585	869	46	,	,	,
randomwalker-info-585	869	47	in	in	IN
randomwalker-info-585	869	48	which	which	WDT
randomwalker-info-585	869	49	case	case	NN
randomwalker-info-585	869	50	both	both	DT
randomwalker-info-585	869	51	blocks	block	NNS
randomwalker-info-585	869	52	are	be	VBP
randomwalker-info-585	869	53	guaranteed	guarantee	VBN
randomwalker-info-585	869	54	to	to	TO
randomwalker-info-585	869	55	make	make	VB
randomwalker-info-585	869	56	it	-PRON-	PRP
randomwalker-info-585	869	57	into	into	IN
randomwalker-info-585	869	58	the	the	DT
randomwalker-info-585	869	59	final	final	JJ
randomwalker-info-585	869	60	block	block	NN
randomwalker-info-585	869	61	chain	chain	NN
randomwalker-info-585	869	62	.	.	.
randomwalker-info-585	870	1	Therefore	therefore	RB
randomwalker-info-585	870	2	,	,	,
randomwalker-info-585	870	3	this	this	DT
randomwalker-info-585	870	4	transaction	transaction	NN
randomwalker-info-585	870	5	will	will	MD
randomwalker-info-585	870	6	certainly	certainly	RB
randomwalker-info-585	870	7	wind	wind	VB
randomwalker-info-585	870	8	up	up	RP
randomwalker-info-585	870	9	in	in	IN
randomwalker-info-585	870	10	a	a	DT
randomwalker-info-585	870	11	block	block	NN
randomwalker-info-585	870	12	mined	mine	VBN
randomwalker-info-585	870	13	by	by	IN
randomwalker-info-585	870	14	the	the	DT
randomwalker-info-585	870	15	selfish	selfish	JJ
randomwalker-info-585	870	16	miner	miner	NN
randomwalker-info-585	870	17	.	.	.
randomwalker-info-585	871	1	This	this	DT
randomwalker-info-585	871	2	happens	happen	VBZ
randomwalker-info-585	871	3	with	with	IN
randomwalker-info-585	871	4	probability	probability	NN
randomwalker-info-585	871	5	α	α	XX
randomwalker-info-585	871	6	.	.	.
randomwalker-info-585	872	1	•	•	NNP
randomwalker-info-585	872	2	Alternatively	alternatively	RB
randomwalker-info-585	872	3	,	,	,
randomwalker-info-585	872	4	the	the	DT
randomwalker-info-585	872	5	rest	rest	NN
randomwalker-info-585	872	6	of	of	IN
randomwalker-info-585	872	7	the	the	DT
randomwalker-info-585	872	8	network	network	NN
randomwalker-info-585	872	9	might	may	MD
randomwalker-info-585	872	10	find	find	VB
randomwalker-info-585	872	11	the	the	DT
randomwalker-info-585	872	12	next	next	JJ
randomwalker-info-585	872	13	block	block	NN
randomwalker-info-585	872	14	.	.	.
randomwalker-info-585	873	1	This	this	DT
randomwalker-info-585	873	2	happens	happen	VBZ
randomwalker-info-585	873	3	with	with	IN
randomwalker-info-585	873	4	probability	probability	NN
randomwalker-info-585	873	5	(	(	-LRB-
randomwalker-info-585	873	6	1−α	1−α	CD
randomwalker-info-585	873	7	)	)	-RRB-
randomwalker-info-585	873	8	.	.	.
randomwalker-info-585	874	1	But	but	CC
randomwalker-info-585	874	2	we	-PRON-	PRP
randomwalker-info-585	874	3	do	do	VBP
randomwalker-info-585	874	4	n’t	not	RB
randomwalker-info-585	874	5	yet	yet	RB
randomwalker-info-585	874	6	know	know	VB
randomwalker-info-585	874	7	whether	whether	IN
randomwalker-info-585	874	8	or	or	CC
randomwalker-info-585	874	9	not	not	RB
randomwalker-info-585	874	10	this	this	DT
randomwalker-info-585	874	11	block	block	NN
randomwalker-info-585	874	12	will	will	MD
randomwalker-info-585	874	13	make	make	VB
randomwalker-info-585	874	14	it	-PRON-	PRP
randomwalker-info-585	874	15	in	in	IN
randomwalker-info-585	874	16	the	the	DT
randomwalker-info-585	874	17	eventual	eventual	JJ
randomwalker-info-585	874	18	longest	long	JJS
randomwalker-info-585	874	19	chain	chain	NN
randomwalker-info-585	874	20	because	because	IN
randomwalker-info-585	874	21	this	this	DT
randomwalker-info-585	874	22	triggers	trigger	VBZ
randomwalker-info-585	874	23	the	the	DT
randomwalker-info-585	874	24	“	"	``
randomwalker-info-585	874	25	race	race	NN
randomwalker-info-585	874	26	,	,	,
randomwalker-info-585	874	27	”	"	''
randomwalker-info-585	874	28	and	and	CC
randomwalker-info-585	874	29	puts	put	VBZ
randomwalker-info-585	874	30	us	-PRON-	PRP
randomwalker-info-585	874	31	in	in	IN
randomwalker-info-585	874	32	state	state	NN
randomwalker-info-585	874	33	0′.	0′.	CD
randomwalker-info-585	875	1	Note	note	VB
randomwalker-info-585	875	2	though	though	IN
randomwalker-info-585	875	3	that	that	IN
randomwalker-info-585	875	4	the	the	DT
randomwalker-info-585	875	5	racing	race	VBG
randomwalker-info-585	875	6	selfish	selfish	JJ
randomwalker-info-585	875	7	block	block	NN
randomwalker-info-585	875	8	does	do	VBZ
randomwalker-info-585	875	9	not	not	RB
randomwalker-info-585	875	10	contain	contain	VB
randomwalker-info-585	875	11	this	this	DT
randomwalker-info-585	875	12	transaction	transaction	NN
randomwalker-info-585	875	13	that	that	WDT
randomwalker-info-585	875	14	arrived	arrive	VBD
randomwalker-info-585	875	15	once	once	IN
randomwalker-info-585	875	16	we	-PRON-	PRP
randomwalker-info-585	875	17	were	be	VBD
randomwalker-info-585	875	18	already	already	RB
randomwalker-info-585	875	19	in	in	IN
randomwalker-info-585	875	20	state	state	NN
randomwalker-info-585	875	21	1	1	CD
randomwalker-info-585	875	22	.	.	.
randomwalker-info-585	876	1	Therefore	therefore	RB
randomwalker-info-585	876	2	,	,	,
randomwalker-info-585	876	3	even	even	RB
randomwalker-info-585	876	4	if	if	IN
randomwalker-info-585	876	5	the	the	DT
randomwalker-info-585	876	6	selfish	selfish	JJ
randomwalker-info-585	876	7	miner	miner	NN
randomwalker-info-585	876	8	wins	win	VBZ
randomwalker-info-585	876	9	the	the	DT
randomwalker-info-585	876	10	race	race	NN
randomwalker-info-585	876	11	,	,	,
randomwalker-info-585	876	12	but	but	CC
randomwalker-info-585	876	13	because	because	IN
randomwalker-info-585	876	14	a	a	DT
randomwalker-info-585	876	15	default	default	NN
randomwalker-info-585	876	16	miner	miner	NN
randomwalker-info-585	876	17	chose	choose	VBD
randomwalker-info-585	876	18	their	-PRON-	PRP$
randomwalker-info-585	876	19	block	block	NN
randomwalker-info-585	876	20	,	,	,
randomwalker-info-585	876	21	the	the	DT
randomwalker-info-585	876	22	selfish	selfish	JJ
randomwalker-info-585	876	23	miner	miner	NN
randomwalker-info-585	876	24	will	will	MD
randomwalker-info-585	876	25	not	not	RB
randomwalker-info-585	876	26	get	get	VB
randomwalker-info-585	876	27	this	this	DT
randomwalker-info-585	876	28	transaction	transaction	NN
randomwalker-info-585	876	29	.	.	.
randomwalker-info-585	877	1	So	so	RB
randomwalker-info-585	877	2	the	the	DT
randomwalker-info-585	877	3	only	only	JJ
randomwalker-info-585	877	4	way	way	NN
randomwalker-info-585	877	5	for	for	IN
randomwalker-info-585	877	6	the	the	DT
randomwalker-info-585	877	7	selfish	selfish	JJ
randomwalker-info-585	877	8	miner	miner	NN
randomwalker-info-585	877	9	to	to	TO
randomwalker-info-585	877	10	win	win	VB
randomwalker-info-585	877	11	this	this	DT
randomwalker-info-585	877	12	transaction	transaction	NN
randomwalker-info-585	877	13	is	be	VBZ
randomwalker-info-585	877	14	to	to	TO
randomwalker-info-585	877	15	find	find	VB
randomwalker-info-585	877	16	the	the	DT
randomwalker-info-585	877	17	block	block	NN
randomwalker-info-585	877	18	that	that	WDT
randomwalker-info-585	877	19	ends	end	VBZ
randomwalker-info-585	877	20	the	the	DT
randomwalker-info-585	877	21	race	race	NN
randomwalker-info-585	877	22	.	.	.
randomwalker-info-585	878	1	This	this	DT
randomwalker-info-585	878	2	happens	happen	VBZ
randomwalker-info-585	878	3	with	with	IN
randomwalker-info-585	878	4	probability	probability	NN
randomwalker-info-585	878	5	α	α	NNP
randomwalker-info-585	878	6	.	.	.
randomwalker-info-585	878	7	f1	f1	NNP
randomwalker-info-585	878	8	=	=	SYM
randomwalker-info-585	878	9	α	α	NNP
randomwalker-info-585	878	10	+	+	SYM
randomwalker-info-585	878	11	(	(	-LRB-
randomwalker-info-585	878	12	1	1	CD
randomwalker-info-585	878	13	−α)α	−α)α	NNS
randomwalker-info-585	878	14	=	=	SYM
randomwalker-info-585	878	15	α(2	α(2	$
randomwalker-info-585	878	16	−α	−α	CD
randomwalker-info-585	878	17	)	)	-RRB-
randomwalker-info-585	878	18	.	.	.
randomwalker-info-585	879	1	(	(	-LRB-
randomwalker-info-585	879	2	6	6	LS
randomwalker-info-585	879	3	)	)	-RRB-
randomwalker-info-585	879	4	Computing	computing	NN
randomwalker-info-585	879	5	fi	fi	NN
randomwalker-info-585	879	6	:	:	:
randomwalker-info-585	879	7	Finally	finally	RB
randomwalker-info-585	879	8	,	,	,
randomwalker-info-585	879	9	consider	consider	VB
randomwalker-info-585	879	10	a	a	DT
randomwalker-info-585	879	11	transaction	transaction	NN
randomwalker-info-585	879	12	arriving	arrive	VBG
randomwalker-info-585	879	13	to	to	IN
randomwalker-info-585	879	14	the	the	DT
randomwalker-info-585	879	15	system	system	NN
randomwalker-info-585	879	16	in	in	IN
randomwalker-info-585	879	17	state	state	NN
randomwalker-info-585	879	18	i	i	NNP
randomwalker-info-585	879	19	,	,	,
randomwalker-info-585	879	20	i	i	PRP
randomwalker-info-585	879	21	>	>	XX
randomwalker-info-585	879	22	1	1	CD
randomwalker-info-585	879	23	.	.	.
randomwalker-info-585	880	1	In	in	IN
randomwalker-info-585	880	2	these	these	DT
randomwalker-info-585	880	3	states	state	NNS
randomwalker-info-585	880	4	,	,	,
randomwalker-info-585	880	5	it	-PRON-	PRP
randomwalker-info-585	880	6	is	be	VBZ
randomwalker-info-585	880	7	easier	easy	JJR
randomwalker-info-585	880	8	to	to	TO
randomwalker-info-585	880	9	consider	consider	VB
randomwalker-info-585	880	10	what	what	WP
randomwalker-info-585	880	11	must	must	MD
randomwalker-info-585	880	12	happen	happen	VB
randomwalker-info-585	880	13	in	in	IN
randomwalker-info-585	880	14	order	order	NN
randomwalker-info-585	880	15	for	for	IN
randomwalker-info-585	880	16	the	the	DT
randomwalker-info-585	880	17	transaction	transaction	NN
randomwalker-info-585	880	18	to	to	TO
randomwalker-info-585	880	19	not	not	RB
randomwalker-info-585	880	20	end	end	VB
randomwalker-info-585	880	21	up	up	RP
randomwalker-info-585	880	22	in	in	IN
randomwalker-info-585	880	23	a	a	DT
randomwalker-info-585	880	24	block	block	NN
randomwalker-info-585	880	25	the	the	DT
randomwalker-info-585	880	26	selfish	selfish	JJ
randomwalker-info-585	880	27	miner	miner	NN
randomwalker-info-585	880	28	owns	own	VBZ
randomwalker-info-585	880	29	.	.	.
randomwalker-info-585	881	1	For	for	IN
randomwalker-info-585	881	2	the	the	DT
randomwalker-info-585	881	3	transaction	transaction	NN
randomwalker-info-585	881	4	to	to	TO
randomwalker-info-585	881	5	wind	wind	VB
randomwalker-info-585	881	6	up	up	RP
randomwalker-info-585	881	7	in	in	IN
randomwalker-info-585	881	8	a	a	DT
randomwalker-info-585	881	9	default	default	NN
randomwalker-info-585	881	10	miner	miner	NN
randomwalker-info-585	881	11	’s	’s	POS
randomwalker-info-585	881	12	block	block	NN
randomwalker-info-585	881	13	,	,	,
randomwalker-info-585	881	14	it	-PRON-	PRP
randomwalker-info-585	881	15	needs	need	VBZ
randomwalker-info-585	881	16	to	to	TO
randomwalker-info-585	881	17	be	be	VB
randomwalker-info-585	881	18	the	the	DT
randomwalker-info-585	881	19	case	case	NN
randomwalker-info-585	881	20	that	that	IN
randomwalker-info-585	881	21	the	the	DT
randomwalker-info-585	881	22	selfish	selfish	JJ
randomwalker-info-585	881	23	miner	miner	NN
randomwalker-info-585	881	24	releases	release	VBZ
randomwalker-info-585	881	25	their	-PRON-	PRP$
randomwalker-info-585	881	26	entire	entire	JJ
randomwalker-info-585	881	27	private	private	JJ
randomwalker-info-585	881	28	chain	chain	NN
randomwalker-info-585	881	29	before	before	IN
randomwalker-info-585	881	30	mining	mine	VBG
randomwalker-info-585	881	31	a	a	DT
randomwalker-info-585	881	32	new	new	JJ
randomwalker-info-585	881	33	block	block	NN
randomwalker-info-585	881	34	(	(	-LRB-
randomwalker-info-585	881	35	which	which	WDT
randomwalker-info-585	881	36	would	would	MD
randomwalker-info-585	881	37	contain	contain	VB
randomwalker-info-585	881	38	this	this	DT
randomwalker-info-585	881	39	transaction	transaction	NN
randomwalker-info-585	881	40	)	)	-RRB-
randomwalker-info-585	881	41	.	.	.
randomwalker-info-585	882	1	This	this	DT
randomwalker-info-585	882	2	is	be	VBZ
randomwalker-info-585	882	3	because	because	IN
randomwalker-info-585	882	4	any	any	DT
randomwalker-info-585	882	5	blocks	block	NNS
randomwalker-info-585	882	6	found	find	VBN
randomwalker-info-585	882	7	by	by	IN
randomwalker-info-585	882	8	default	default	NN
randomwalker-info-585	882	9	miners	miner	NNS
randomwalker-info-585	882	10	before	before	IN
randomwalker-info-585	882	11	this	this	DT
randomwalker-info-585	882	12	trigger	trigger	NN
randomwalker-info-585	882	13	are	be	VBP
randomwalker-info-585	882	14	all	all	RB
randomwalker-info-585	882	15	orphaned	orphan	VBN
randomwalker-info-585	882	16	.	.	.
randomwalker-info-585	883	1	For	for	IN
randomwalker-info-585	883	2	a	a	DT
randomwalker-info-585	883	3	release	release	NN
randomwalker-info-585	883	4	to	to	TO
randomwalker-info-585	883	5	be	be	VB
randomwalker-info-585	883	6	triggered	trigger	VBN
randomwalker-info-585	883	7	,	,	,
randomwalker-info-585	883	8	a	a	DT
randomwalker-info-585	883	9	default	default	NN
randomwalker-info-585	883	10	miner	miner	NN
randomwalker-info-585	883	11	must	must	MD
randomwalker-info-585	883	12	find	find	VB
randomwalker-info-585	883	13	each	each	DT
randomwalker-info-585	883	14	of	of	IN
randomwalker-info-585	883	15	the	the	DT
randomwalker-info-585	883	16	next	next	JJ
randomwalker-info-585	883	17	i−	i−	NNP
randomwalker-info-585	883	18	1	1	CD
randomwalker-info-585	883	19	blocks	block	NNS
randomwalker-info-585	883	20	,	,	,
randomwalker-info-585	883	21	which	which	WDT
randomwalker-info-585	883	22	happens	happen	VBZ
randomwalker-info-585	883	23	with	with	IN
randomwalker-info-585	883	24	probability	probability	NN
randomwalker-info-585	883	25	(	(	-LRB-
randomwalker-info-585	883	26	1	1	CD
randomwalker-info-585	883	27	−α)i−1	−α)i−1	NNP
randomwalker-info-585	883	28	.	.	.
randomwalker-info-585	884	1	If	if	IN
randomwalker-info-585	884	2	this	this	DT
randomwalker-info-585	884	3	happens	happen	VBZ
randomwalker-info-585	884	4	,	,	,
randomwalker-info-585	884	5	we	-PRON-	PRP
randomwalker-info-585	884	6	still	still	RB
randomwalker-info-585	884	7	do	do	VBP
randomwalker-info-585	884	8	n’t	not	RB
randomwalker-info-585	884	9	know	know	VB
randomwalker-info-585	884	10	where	where	WRB
randomwalker-info-585	884	11	this	this	DT
randomwalker-info-585	884	12	transaction	transaction	NN
randomwalker-info-585	884	13	winds	wind	VBZ
randomwalker-info-585	884	14	up	up	RP
randomwalker-info-585	884	15	,	,	,
randomwalker-info-585	884	16	because	because	IN
randomwalker-info-585	884	17	each	each	DT
randomwalker-info-585	884	18	of	of	IN
randomwalker-info-585	884	19	the	the	DT
randomwalker-info-585	884	20	i−1	i−1	NN
randomwalker-info-585	884	21	blocks	block	NNS
randomwalker-info-585	884	22	found	find	VBN
randomwalker-info-585	884	23	will	will	MD
randomwalker-info-585	884	24	be	be	VB
randomwalker-info-585	884	25	orphaned	orphan	VBN
randomwalker-info-585	884	26	.	.	.
randomwalker-info-585	885	1	But	but	CC
randomwalker-info-585	885	2	we	-PRON-	PRP
randomwalker-info-585	885	3	have	have	VBP
randomwalker-info-585	885	4	now	now	RB
randomwalker-info-585	885	5	returned	return	VBN
randomwalker-info-585	885	6	to	to	IN
randomwalker-info-585	885	7	state	state	NN
randomwalker-info-585	885	8	0	0	CD
randomwalker-info-585	885	9	,	,	,
randomwalker-info-585	885	10	and	and	CC
randomwalker-info-585	885	11	the	the	DT
randomwalker-info-585	885	12	remainder	remainder	NN
randomwalker-info-585	885	13	of	of	IN
randomwalker-info-585	885	14	the	the	DT
randomwalker-info-585	885	15	analysis	analysis	NN
randomwalker-info-585	885	16	concludes	conclude	VBZ
randomwalker-info-585	885	17	as	as	IN
randomwalker-info-585	885	18	if	if	IN
randomwalker-info-585	885	19	the	the	DT
randomwalker-info-585	885	20	transaction	transaction	NN
randomwalker-info-585	885	21	had	have	VBD
randomwalker-info-585	885	22	been	be	VBN
randomwalker-info-585	885	23	announced	announce	VBN
randomwalker-info-585	885	24	during	during	IN
randomwalker-info-585	885	25	state	state	NN
randomwalker-info-585	885	26	0	0	CD
randomwalker-info-585	885	27	.	.	.
randomwalker-info-585	886	1	So	so	RB
randomwalker-info-585	886	2	the	the	DT
randomwalker-info-585	886	3	probability	probability	NN
randomwalker-info-585	886	4	that	that	IN
randomwalker-info-585	886	5	a	a	DT
randomwalker-info-585	886	6	default	default	NN
randomwalker-info-585	886	7	miner	miner	NN
randomwalker-info-585	886	8	winds	wind	VBZ
randomwalker-info-585	886	9	up	up	RP
randomwalker-info-585	886	10	with	with	IN
randomwalker-info-585	886	11	a	a	DT
randomwalker-info-585	886	12	transaction	transaction	NN
randomwalker-info-585	886	13	arriving	arrive	VBG
randomwalker-info-585	886	14	in	in	IN
randomwalker-info-585	886	15	state	state	NN
randomwalker-info-585	886	16	i	i	PRP
randomwalker-info-585	886	17	is	be	VBZ
randomwalker-info-585	886	18	(	(	-LRB-
randomwalker-info-585	886	19	1	1	CD
randomwalker-info-585	886	20	−α)i−1(1	−α)i−1(1	NNP
randomwalker-info-585	886	21	−f0	−f0	NNP
randomwalker-info-585	886	22	)	)	-RRB-
randomwalker-info-585	886	23	,	,	,
randomwalker-info-585	886	24	and	and	CC
randomwalker-info-585	886	25	therefore	therefore	RB
randomwalker-info-585	886	26	:	:	:
randomwalker-info-585	886	27	fi	fi	NN
randomwalker-info-585	886	28	=	=	SYM
randomwalker-info-585	886	29	1	1	CD
randomwalker-info-585	886	30	−	−	NNP
randomwalker-info-585	886	31	(	(	-LRB-
randomwalker-info-585	886	32	(	(	-LRB-
randomwalker-info-585	886	33	1	1	CD
randomwalker-info-585	886	34	−α)i−1(1	−α)i−1(1	NNP
randomwalker-info-585	886	35	−f0	−f0	NNP
randomwalker-info-585	886	36	)	)	-RRB-
randomwalker-info-585	886	37	)	)	-RRB-
randomwalker-info-585	886	38	(	(	-LRB-
randomwalker-info-585	886	39	7	7	LS
randomwalker-info-585	886	40	)	)	-RRB-
randomwalker-info-585	886	41	Summing	sum	VBG
randomwalker-info-585	886	42	everything	everything	NN
randomwalker-info-585	886	43	together	together	RB
randomwalker-info-585	886	44	,	,	,
randomwalker-info-585	886	45	we	-PRON-	PRP
randomwalker-info-585	886	46	get	get	VBP
randomwalker-info-585	886	47	the	the	DT
randomwalker-info-585	886	48	following	follow	VBG
randomwalker-info-585	886	49	:	:	:
randomwalker-info-585	886	50	Theorem	theorem	NN
randomwalker-info-585	886	51	E.1	E.1	NNP
randomwalker-info-585	886	52	.	.	.
randomwalker-info-585	887	1	If	if	IN
randomwalker-info-585	887	2	all	all	DT
randomwalker-info-585	887	3	other	other	JJ
randomwalker-info-585	887	4	miners	miner	NNS
randomwalker-info-585	887	5	remain	remain	VBP
randomwalker-info-585	887	6	DefaultCompliant	DefaultCompliant	NNP
randomwalker-info-585	887	7	,	,	,
randomwalker-info-585	887	8	a	a	DT
randomwalker-info-585	887	9	selfish	selfish	JJ
randomwalker-info-585	887	10	miner	miner	NN
randomwalker-info-585	887	11	in	in	IN
randomwalker-info-585	887	12	the	the	DT
randomwalker-info-585	887	13	transaction	transaction	NN
randomwalker-info-585	887	14	fees	fee	NNS
randomwalker-info-585	887	15	model	model	NN
randomwalker-info-585	887	16	with	with	IN
randomwalker-info-585	887	17	an	an	DT
randomwalker-info-585	887	18	α	α	XX
randomwalker-info-585	887	19	∈	∈	NNP
randomwalker-info-585	887	20	(	(	-LRB-
randomwalker-info-585	887	21	0	0	NFP
randomwalker-info-585	887	22	,	,	,
randomwalker-info-585	887	23	.5	.5	NFP
randomwalker-info-585	887	24	)	)	-RRB-
randomwalker-info-585	887	25	fraction	fraction	NN
randomwalker-info-585	887	26	of	of	IN
randomwalker-info-585	887	27	the	the	DT
randomwalker-info-585	887	28	mining	mining	NN
randomwalker-info-585	887	29	power	power	NN
randomwalker-info-585	887	30	and	and	CC
randomwalker-info-585	887	31	racing	racing	NN
randomwalker-info-585	887	32	parameter	parameter	NN
randomwalker-info-585	887	33	γ	γ	NN
randomwalker-info-585	887	34	∈	∈	NNP
randomwalker-info-585	887	35	[	[	-LRB-
randomwalker-info-585	887	36	0	0	CD
randomwalker-info-585	887	37	,	,	,
randomwalker-info-585	887	38	1	1	LS
randomwalker-info-585	887	39	]	]	-RRB-
randomwalker-info-585	887	40	achieves	achieve	VBZ
randomwalker-info-585	887	41	reward	reward	VBP
randomwalker-info-585	887	42	Reward(α	Reward(α	NNP
randomwalker-info-585	887	43	,	,	,
randomwalker-info-585	887	44	γ	γ	NNP
randomwalker-info-585	887	45	)	)	-RRB-
randomwalker-info-585	887	46	with	with	IN
randomwalker-info-585	887	47	:	:	:
randomwalker-info-585	887	48	Reward(α	Reward(α	NNP
randomwalker-info-585	887	49	,	,	,
randomwalker-info-585	887	50	γ	γ	NNP
randomwalker-info-585	887	51	)	)	-RRB-
randomwalker-info-585	887	52	=	=	SYM
randomwalker-info-585	887	53	5α2	5α2	CD
randomwalker-info-585	887	54	−	−	NNP
randomwalker-info-585	887	55	12α3	12α3	CD
randomwalker-info-585	887	56	+	+	SYM
randomwalker-info-585	887	57	9α4	9α4	CD
randomwalker-info-585	887	58	−	−	NNP
randomwalker-info-585	887	59	2α5	2α5	CD
randomwalker-info-585	887	60	+	+	SYM
randomwalker-info-585	887	61	γ(α−	γ(α−	NNP
randomwalker-info-585	887	62	4α2	4α2	CD
randomwalker-info-585	887	63	+	+	SYM
randomwalker-info-585	887	64	6α3	6α3	CD
randomwalker-info-585	887	65	−	−	NNP
randomwalker-info-585	887	66	5α4	5α4	CD
randomwalker-info-585	887	67	+	+	SYM
randomwalker-info-585	887	68	2α5	2α5	CD
randomwalker-info-585	887	69	)	)	-RRB-
randomwalker-info-585	887	70	2α3	2α3	CD
randomwalker-info-585	887	71	−	−	NNP
randomwalker-info-585	887	72	4α2	4α2	CD
randomwalker-info-585	887	73	+	+	SYM
randomwalker-info-585	887	74	1	1	CD
randomwalker-info-585	887	75	Proof	proof	NN
randomwalker-info-585	887	76	.	.	.
randomwalker-info-585	888	1	The	the	DT
randomwalker-info-585	888	2	only	only	RB
randomwalker-info-585	888	3	remaining	remain	VBG
randomwalker-info-585	888	4	part	part	NN
randomwalker-info-585	888	5	of	of	IN
randomwalker-info-585	888	6	the	the	DT
randomwalker-info-585	888	7	proof	proof	NN
randomwalker-info-585	888	8	is	be	VBZ
randomwalker-info-585	888	9	summing	sum	VBG
randomwalker-info-585	888	10	p0f0	p0f0	NN
randomwalker-info-585	888	11	+	+	NNS
randomwalker-info-585	888	12	p0′f0′	p0′f0′	NN
randomwalker-info-585	888	13	+	+	SYM
randomwalker-info-585	888	14	p1f1	p1f1	NN
randomwalker-info-585	888	15	+	+	SYM
randomwalker-info-585	888	16	∑	∑	.
randomwalker-info-585	888	17	i>1	i>1	NN
randomwalker-info-585	888	18	pifi	pifi	VBD
randomwalker-info-585	888	19	.	.	.
randomwalker-info-585	889	1	p0f0	p0f0	NNP
randomwalker-info-585	889	2	=	=	SYM
randomwalker-info-585	889	3	1	1	CD
randomwalker-info-585	889	4	−	−	NNP
randomwalker-info-585	889	5	2α	2α	CD
randomwalker-info-585	889	6	2α3	2α3	CD
randomwalker-info-585	889	7	−	−	NNP
randomwalker-info-585	889	8	4α2	4α2	CD
randomwalker-info-585	889	9	+	+	SYM
randomwalker-info-585	889	10	1	1	CD
randomwalker-info-585	889	11	·	·	NFP
randomwalker-info-585	889	12	(	(	-LRB-
randomwalker-info-585	889	13	α	α	DT
randomwalker-info-585	889	14	2	2	CD
randomwalker-info-585	889	15	+	+	SYM
randomwalker-info-585	889	16	α(1	α(1	ADD
randomwalker-info-585	889	17	−α)(α	−α)(α	ADD
randomwalker-info-585	889	18	+	+	NFP
randomwalker-info-585	889	19	(	(	-LRB-
randomwalker-info-585	889	20	1	1	CD
randomwalker-info-585	889	21	−α)γ	−α)γ	NNP
randomwalker-info-585	889	22	)	)	-RRB-
randomwalker-info-585	889	23	)	)	-RRB-
randomwalker-info-585	889	24	=	=	NFP
randomwalker-info-585	889	25	2α2	2α2	CD
randomwalker-info-585	889	26	−	−	NNP
randomwalker-info-585	889	27	5α3	5α3	CD
randomwalker-info-585	889	28	+	+	CC
randomwalker-info-585	889	29	2α4	2α4	CD
randomwalker-info-585	889	30	+	+	SYM
randomwalker-info-585	889	31	αγ	αγ	NNP
randomwalker-info-585	889	32	−	−	NNP
randomwalker-info-585	889	33	4α2γ	4α2γ	NNP
randomwalker-info-585	889	34	+	+	SYM
randomwalker-info-585	889	35	5α3γ	5α3γ	CD
randomwalker-info-585	889	36	−	−	NNP
randomwalker-info-585	889	37	2α4γ	2α4γ	CD
randomwalker-info-585	889	38	2α3	2α3	CD
randomwalker-info-585	889	39	−	−	NNP
randomwalker-info-585	889	40	4α2	4α2	CD
randomwalker-info-585	889	41	+	+	SYM
randomwalker-info-585	889	42	1	1	CD
randomwalker-info-585	889	43	p0′f0′	p0′f0′	NNS
randomwalker-info-585	889	44	=	=	SYM
randomwalker-info-585	889	45	(	(	-LRB-
randomwalker-info-585	889	46	1	1	CD
randomwalker-info-585	889	47	−α)(α−	−α)(α−	JJ
randomwalker-info-585	889	48	2α2	2α2	CD
randomwalker-info-585	889	49	)	)	-RRB-
randomwalker-info-585	889	50	2α3	2α3	CD
randomwalker-info-585	889	51	−	−	NNP
randomwalker-info-585	889	52	4α2	4α2	CD
randomwalker-info-585	889	53	+	+	SYM
randomwalker-info-585	889	54	1	1	CD
randomwalker-info-585	889	55	·	·	SYM
randomwalker-info-585	889	56	α	α	XX
randomwalker-info-585	889	57	=	=	SYM
randomwalker-info-585	889	58	α2	α2	NN
randomwalker-info-585	889	59	−	−	NNP
randomwalker-info-585	889	60	3α3	3α3	CD
randomwalker-info-585	889	61	+	+	CC
randomwalker-info-585	889	62	2α4	2α4	CD
randomwalker-info-585	889	63	2α3	2α3	CD
randomwalker-info-585	889	64	−	−	NNP
randomwalker-info-585	889	65	4α2	4α2	CD
randomwalker-info-585	889	66	+	+	SYM
randomwalker-info-585	889	67	1	1	CD
randomwalker-info-585	889	68	p1f1	p1f1	NNS
randomwalker-info-585	889	69	=	=	SYM
randomwalker-info-585	889	70	α−	α−	NNP
randomwalker-info-585	889	71	2α2	2α2	CD
randomwalker-info-585	889	72	2α3	2α3	CD
randomwalker-info-585	889	73	−	−	NNP
randomwalker-info-585	889	74	4α2	4α2	CD
randomwalker-info-585	889	75	+	+	SYM
randomwalker-info-585	889	76	1	1	CD
randomwalker-info-585	889	77	·	·	SYM
randomwalker-info-585	889	78	α(2	α(2	$
randomwalker-info-585	889	79	−α	−α	CD
randomwalker-info-585	889	80	)	)	-RRB-
randomwalker-info-585	889	81	=	=	NFP
randomwalker-info-585	889	82	2α2	2α2	CD
randomwalker-info-585	889	83	−	−	NNP
randomwalker-info-585	889	84	5α3	5α3	CD
randomwalker-info-585	889	85	+	+	SYM
randomwalker-info-585	889	86	2α4	2α4	CD
randomwalker-info-585	889	87	2α3	2α3	CD
randomwalker-info-585	889	88	−	−	NNP
randomwalker-info-585	889	89	4α2	4α2	CD
randomwalker-info-585	889	90	+	+	SYM
randomwalker-info-585	889	91	1	1	CD
randomwalker-info-585	889	92	pifi	pifi	NN
randomwalker-info-585	889	93	=	=	SYM
randomwalker-info-585	889	94	(	(	-LRB-
randomwalker-info-585	889	95	α	α	DT
randomwalker-info-585	889	96	1	1	CD
randomwalker-info-585	889	97	−α	−α	CD
randomwalker-info-585	889	98	)	)	-RRB-
randomwalker-info-585	889	99	i−1	i−1	NNP
randomwalker-info-585	889	100	α−	α−	NNP
randomwalker-info-585	889	101	2α2	2α2	CD
randomwalker-info-585	889	102	2α3	2α3	CD
randomwalker-info-585	889	103	−	−	NNP
randomwalker-info-585	889	104	4α2	4α2	CD
randomwalker-info-585	889	105	+	+	SYM
randomwalker-info-585	889	106	1	1	CD
randomwalker-info-585	889	107	−αi−1(1	−αi−1(1	NNP
randomwalker-info-585	889	108	−f0	−f0	NNP
randomwalker-info-585	889	109	)	)	-RRB-
randomwalker-info-585	889	110	α−	α−	NNP
randomwalker-info-585	889	111	2α2	2α2	CD
randomwalker-info-585	889	112	2α3	2α3	CD
randomwalker-info-585	889	113	−	−	NNP
randomwalker-info-585	889	114	4α2	4α2	CD
randomwalker-info-585	889	115	+	+	SYM
randomwalker-info-585	889	116	1∑	1∑	CD
randomwalker-info-585	889	117	i>1	i>1	NN
randomwalker-info-585	889	118	(	(	-LRB-
randomwalker-info-585	889	119	α	α	NNP
randomwalker-info-585	889	120	1	1	CD
randomwalker-info-585	889	121	−α	−α	CD
randomwalker-info-585	889	122	)	)	-RRB-
randomwalker-info-585	889	123	i−1	i−1	NNP
randomwalker-info-585	889	124	=	=	SYM
randomwalker-info-585	889	125	α	α	NNP
randomwalker-info-585	889	126	1	1	CD
randomwalker-info-585	889	127	−	−	NNP
randomwalker-info-585	889	128	2α	2α	CD
randomwalker-info-585	889	129	⇒	⇒	CD
randomwalker-info-585	889	130	∑	∑	.
randomwalker-info-585	889	131	i>1	i>1	NN
randomwalker-info-585	889	132	pifi	pifi	NN
randomwalker-info-585	889	133	=	=	SYM
randomwalker-info-585	889	134	α2	α2	NNP
randomwalker-info-585	889	135	2α3	2α3	CD
randomwalker-info-585	889	136	−	−	NNP
randomwalker-info-585	889	137	4α2	4α2	CD
randomwalker-info-585	889	138	+	+	SYM
randomwalker-info-585	889	139	1	1	CD
randomwalker-info-585	889	140	−	−	NNP
randomwalker-info-585	889	141	∑	∑	.
randomwalker-info-585	889	142	i>1	i>1	NN
randomwalker-info-585	889	143	α	α	NNP
randomwalker-info-585	889	144	i−1	i−1	NNP
randomwalker-info-585	889	145	(	(	-LRB-
randomwalker-info-585	889	146	1	1	CD
randomwalker-info-585	889	147	−f0	−f0	CD
randomwalker-info-585	889	148	)	)	-RRB-
randomwalker-info-585	889	149	α−	α−	NNP
randomwalker-info-585	889	150	2α2	2α2	CD
randomwalker-info-585	889	151	2α3	2α3	CD
randomwalker-info-585	889	152	−	−	NNP
randomwalker-info-585	889	153	4α2	4α2	CD
randomwalker-info-585	889	154	+	+	SYM
randomwalker-info-585	889	155	1∑	1∑	CD
randomwalker-info-585	889	156	i>1	i>1	NN
randomwalker-info-585	889	157	α	α	NNP
randomwalker-info-585	889	158	i−1	i−1	NNP
randomwalker-info-585	889	159	=	=	SYM
randomwalker-info-585	889	160	α	α	NNP
randomwalker-info-585	889	161	1	1	CD
randomwalker-info-585	889	162	−α	−α	CD
randomwalker-info-585	889	163	⇒	⇒	CD
randomwalker-info-585	889	164	∑	∑	.
randomwalker-info-585	889	165	i>1	i>1	NN
randomwalker-info-585	889	166	pifi	pifi	NN
randomwalker-info-585	889	167	=	=	SYM
randomwalker-info-585	889	168	α2	α2	NNP
randomwalker-info-585	889	169	2α3	2α3	CD
randomwalker-info-585	889	170	−	−	NNP
randomwalker-info-585	889	171	4α2	4α2	CD
randomwalker-info-585	889	172	+	+	SYM
randomwalker-info-585	889	173	1	1	CD
randomwalker-info-585	889	174	−	−	NNP
randomwalker-info-585	889	175	α(1	α(1	:
randomwalker-info-585	889	176	−α	−α	CD
randomwalker-info-585	889	177	+	+	CC
randomwalker-info-585	889	178	α(1	α(1	NFP
randomwalker-info-585	889	179	−α)2(1	−α)2(1	NNP
randomwalker-info-585	889	180	−γ))(α−	−γ))(α−	NNP
randomwalker-info-585	889	181	2α2	2α2	CD
randomwalker-info-585	889	182	)	)	-RRB-
randomwalker-info-585	889	183	(	(	-LRB-
randomwalker-info-585	889	184	1	1	CD
randomwalker-info-585	889	185	−α)2α3	−α)2α3	NNP
randomwalker-info-585	889	186	−	−	NNP
randomwalker-info-585	889	187	4α2	4α2	CD
randomwalker-info-585	889	188	+	+	SYM
randomwalker-info-585	889	189	1	1	CD
randomwalker-info-585	889	190	=	=	SYM
randomwalker-info-585	889	191	α2	α2	NN
randomwalker-info-585	889	192	−α(1	−α(1	NNP
randomwalker-info-585	889	193	+	+	SYM
randomwalker-info-585	889	194	α(1	α(1	NFP
randomwalker-info-585	889	195	−α)(1	−α)(1	CD
randomwalker-info-585	889	196	−γ))(α−	−γ))(α−	NNP
randomwalker-info-585	889	197	2α2	2α2	CD
randomwalker-info-585	889	198	)	)	-RRB-
randomwalker-info-585	889	199	2α3	2α3	CD
randomwalker-info-585	889	200	−	−	NNP
randomwalker-info-585	889	201	4α2	4α2	CD
randomwalker-info-585	889	202	+	+	SYM
randomwalker-info-585	889	203	1	1	CD
randomwalker-info-585	889	204	.	.	.
randomwalker-info-585	890	1	=	=	NFP
randomwalker-info-585	890	2	2α3	2α3	CD
randomwalker-info-585	890	3	−α2(α−	−α2(α−	NNP
randomwalker-info-585	890	4	2α2	2α2	CD
randomwalker-info-585	890	5	−α2	−α2	NN
randomwalker-info-585	890	6	+	+	SYM
randomwalker-info-585	890	7	2α3	2α3	CD
randomwalker-info-585	890	8	−γα	−γα	CD
randomwalker-info-585	890	9	+	+	SYM
randomwalker-info-585	890	10	2γα2	2γα2	CD
randomwalker-info-585	890	11	+	+	CC
randomwalker-info-585	890	12	γα2	γα2	NN
randomwalker-info-585	890	13	−	−	NNP
randomwalker-info-585	890	14	2γα3	2γα3	CD
randomwalker-info-585	890	15	)	)	-RRB-
randomwalker-info-585	890	16	2α3	2α3	CD
randomwalker-info-585	890	17	−	−	NNP
randomwalker-info-585	890	18	4α2	4α2	CD
randomwalker-info-585	890	19	+	+	SYM
randomwalker-info-585	890	20	1	1	CD
randomwalker-info-585	890	21	=	=	SYM
randomwalker-info-585	890	22	α3	α3	NN
randomwalker-info-585	890	23	+	+	CC
randomwalker-info-585	890	24	3α4	3α4	CD
randomwalker-info-585	890	25	−	−	NNP
randomwalker-info-585	890	26	2α5	2α5	CD
randomwalker-info-585	890	27	+	+	SYM
randomwalker-info-585	890	28	γα3	γα3	NNS
randomwalker-info-585	890	29	−	−	NNP
randomwalker-info-585	890	30	3γα4	3γα4	CD
randomwalker-info-585	890	31	+	+	CC
randomwalker-info-585	890	32	2γα5	2γα5	CD
randomwalker-info-585	890	33	2α3	2α3	CD
randomwalker-info-585	890	34	−	−	NNP
randomwalker-info-585	890	35	4α2	4α2	CD
randomwalker-info-585	890	36	+	+	SYM
randomwalker-info-585	890	37	1	1	CD
randomwalker-info-585	890	38	The	the	DT
randomwalker-info-585	890	39	proof	proof	NN
randomwalker-info-585	890	40	concludes	conclude	VBZ
randomwalker-info-585	890	41	by	by	IN
randomwalker-info-585	890	42	just	just	RB
randomwalker-info-585	890	43	summing	sum	VBG
randomwalker-info-585	890	44	the	the	DT
randomwalker-info-585	890	45	four	four	CD
randomwalker-info-585	890	46	terms	term	NNS
randomwalker-info-585	890	47	.	.	.
randomwalker-info-585	891	1	E.2	E.2	NNP
randomwalker-info-585	891	2	Improved	Improved	NNP
randomwalker-info-585	891	3	Selfish	Selfish	NNP
randomwalker-info-585	891	4	Mining	Mining	NNP
randomwalker-info-585	891	5	with	with	IN
randomwalker-info-585	891	6	a	a	DT
randomwalker-info-585	891	7	cutoff	cutoff	NN
randomwalker-info-585	891	8	In	in	IN
randomwalker-info-585	891	9	this	this	DT
randomwalker-info-585	891	10	section	section	NN
randomwalker-info-585	891	11	,	,	,
randomwalker-info-585	891	12	we	-PRON-	PRP
randomwalker-info-585	891	13	complete	complete	VBP
randomwalker-info-585	891	14	our	-PRON-	PRP$
randomwalker-info-585	891	15	analysis	analysis	NN
randomwalker-info-585	891	16	of	of	IN
randomwalker-info-585	891	17	our	-PRON-	PRP$
randomwalker-info-585	891	18	improved	improved	JJ
randomwalker-info-585	891	19	selfish	selfish	JJ
randomwalker-info-585	891	20	mining	mining	NN
randomwalker-info-585	891	21	with	with	IN
randomwalker-info-585	891	22	a	a	DT
randomwalker-info-585	891	23	cutoff	cutoff	NN
randomwalker-info-585	891	24	.	.	.
randomwalker-info-585	892	1	In	in	IN
randomwalker-info-585	892	2	order	order	NN
randomwalker-info-585	892	3	to	to	TO
randomwalker-info-585	892	4	keep	keep	VB
randomwalker-info-585	892	5	the	the	DT
randomwalker-info-585	892	6	analysis	analysis	NN
randomwalker-info-585	892	7	of	of	IN
randomwalker-info-585	892	8	this	this	DT
randomwalker-info-585	892	9	strategy	strategy	NN
randomwalker-info-585	892	10	tractable	tractable	NN
randomwalker-info-585	892	11	,	,	,
randomwalker-info-585	892	12	we	-PRON-	PRP
randomwalker-info-585	892	13	choose	choose	VBP
randomwalker-info-585	892	14	to	to	TO
randomwalker-info-585	892	15	slightly	slightly	RB
randomwalker-info-585	892	16	tweak	tweak	VB
randomwalker-info-585	892	17	our	-PRON-	PRP$
randomwalker-info-585	892	18	analysis	analysis	NN
randomwalker-info-585	892	19	(	(	-LRB-
randomwalker-info-585	892	20	but	but	CC
randomwalker-info-585	892	21	our	-PRON-	PRP$
randomwalker-info-585	892	22	theory	theory	NN
randomwalker-info-585	892	23	-	-	HYPH
randomwalker-info-585	892	24	matches	match	NNS
randomwalker-info-585	892	25	-	-	HYPH
randomwalker-info-585	892	26	simulation	simulation	NN
randomwalker-info-585	892	27	plot	plot	NN
randomwalker-info-585	892	28	in	in	IN
randomwalker-info-585	892	29	Figure	Figure	NNP
randomwalker-info-585	892	30	6.2	6.2	CD
randomwalker-info-585	892	31	shows	show	VBZ
randomwalker-info-585	892	32	that	that	IN
randomwalker-info-585	892	33	this	this	DT
randomwalker-info-585	892	34	tweak	tweak	NN
randomwalker-info-585	892	35	is	be	VBZ
randomwalker-info-585	892	36	essentially	essentially	RB
randomwalker-info-585	892	37	irrelevant	irrelevant	JJ
randomwalker-info-585	892	38	)	)	-RRB-
randomwalker-info-585	892	39	.	.	.
randomwalker-info-585	893	1	The	the	DT
randomwalker-info-585	893	2	only	only	JJ
randomwalker-info-585	893	3	tweak	tweak	NN
randomwalker-info-585	893	4	we	-PRON-	PRP
randomwalker-info-585	893	5	make	make	VBP
randomwalker-info-585	893	6	is	be	VBZ
randomwalker-info-585	893	7	that	that	DT
randomwalker-info-585	893	8	right	right	RB
randomwalker-info-585	893	9	after	after	IN
randomwalker-info-585	893	10	the	the	DT
randomwalker-info-585	893	11	selfish	selfish	JJ
randomwalker-info-585	893	12	miner	miner	NN
randomwalker-info-585	893	13	releases	release	VBZ
randomwalker-info-585	893	14	a	a	DT
randomwalker-info-585	893	15	chain	chain	NN
randomwalker-info-585	893	16	of	of	IN
randomwalker-info-585	893	17	length	length	NN
randomwalker-info-585	893	18	two	two	CD
randomwalker-info-585	893	19	simultaneously	simultaneously	RB
randomwalker-info-585	893	20	,	,	,
randomwalker-info-585	893	21	they	-PRON-	PRP
randomwalker-info-585	893	22	immediately	immediately	RB
randomwalker-info-585	893	23	publish	publish	VBP
randomwalker-info-585	893	24	the	the	DT
randomwalker-info-585	893	25	next	next	JJ
randomwalker-info-585	893	26	block	block	NN
randomwalker-info-585	893	27	(	(	-LRB-
randomwalker-info-585	893	28	if	if	IN
randomwalker-info-585	893	29	they	-PRON-	PRP
randomwalker-info-585	893	30	find	find	VBP
randomwalker-info-585	893	31	it	-PRON-	PRP
randomwalker-info-585	893	32	)	)	-RRB-
randomwalker-info-585	893	33	,	,	,
randomwalker-info-585	893	34	and	and	CC
randomwalker-info-585	893	35	then	then	RB
randomwalker-info-585	893	36	return	return	VB
randomwalker-info-585	893	37	to	to	IN
randomwalker-info-585	893	38	selfish	selfish	JJ
randomwalker-info-585	893	39	mining	mining	NN
randomwalker-info-585	893	40	.	.	.
randomwalker-info-585	894	1	In	in	IN
randomwalker-info-585	894	2	the	the	DT
randomwalker-info-585	894	3	language	language	NN
randomwalker-info-585	894	4	of	of	IN
randomwalker-info-585	894	5	Eyal	Eyal	NNP
randomwalker-info-585	894	6	and	and	CC
randomwalker-info-585	894	7	Sirer	Sirer	NNP
randomwalker-info-585	894	8	,	,	,
randomwalker-info-585	894	9	this	this	DT
randomwalker-info-585	894	10	is	be	VBZ
randomwalker-info-585	894	11	like	like	IN
randomwalker-info-585	894	12	adding	add	VBG
randomwalker-info-585	894	13	an	an	DT
randomwalker-info-585	894	14	additional	additional	JJ
randomwalker-info-585	894	15	state	state	NN
randomwalker-info-585	894	16	0′′	0′′	CD
randomwalker-info-585	894	17	where	where	WRB
randomwalker-info-585	894	18	the	the	DT
randomwalker-info-585	894	19	selfish	selfish	JJ
randomwalker-info-585	894	20	miner	miner	NN
randomwalker-info-585	894	21	honestly	honestly	RB
randomwalker-info-585	894	22	mines	mine	NNS
randomwalker-info-585	894	23	.	.	.
randomwalker-info-585	895	1	No	no	RB
randomwalker-info-585	895	2	matter	matter	RB
randomwalker-info-585	895	3	who	who	WP
randomwalker-info-585	895	4	finds	find	VBZ
randomwalker-info-585	895	5	a	a	DT
randomwalker-info-585	895	6	block	block	NN
randomwalker-info-585	895	7	in	in	IN
randomwalker-info-585	895	8	this	this	DT
randomwalker-info-585	895	9	state	state	NN
randomwalker-info-585	895	10	,	,	,
randomwalker-info-585	895	11	the	the	DT
randomwalker-info-585	895	12	next	next	JJ
randomwalker-info-585	895	13	state	state	NN
randomwalker-info-585	895	14	is	be	VBZ
randomwalker-info-585	895	15	0	0	CD
randomwalker-info-585	895	16	.	.	.
randomwalker-info-585	896	1	The	the	DT
randomwalker-info-585	896	2	only	only	JJ
randomwalker-info-585	896	3	transition	transition	NN
randomwalker-info-585	896	4	into	into	IN
randomwalker-info-585	896	5	this	this	DT
randomwalker-info-585	896	6	state	state	NN
randomwalker-info-585	896	7	is	be	VBZ
randomwalker-info-585	896	8	when	when	WRB
randomwalker-info-585	896	9	the	the	DT
randomwalker-info-585	896	10	honest	honest	JJ
randomwalker-info-585	896	11	portion	portion	NN
randomwalker-info-585	896	12	of	of	IN
randomwalker-info-585	896	13	the	the	DT
randomwalker-info-585	896	14	network	network	NN
randomwalker-info-585	896	15	finds	find	VBZ
randomwalker-info-585	896	16	a	a	DT
randomwalker-info-585	896	17	block	block	NN
randomwalker-info-585	896	18	when	when	WRB
randomwalker-info-585	896	19	the	the	DT
randomwalker-info-585	896	20	selfish	selfish	JJ
randomwalker-info-585	896	21	miner	miner	NN
randomwalker-info-585	896	22	has	have	VBZ
randomwalker-info-585	896	23	a	a	DT
randomwalker-info-585	896	24	lead	lead	NN
randomwalker-info-585	896	25	of	of	IN
randomwalker-info-585	896	26	2	2	CD
randomwalker-info-585	896	27	13	13	CD
randomwalker-info-585	896	28	shows	show	VBZ
randomwalker-info-585	896	29	an	an	DT
randomwalker-info-585	896	30	updated	update	VBN
randomwalker-info-585	896	31	Markov	Markov	NNP
randomwalker-info-585	896	32	chain	chain	NN
randomwalker-info-585	896	33	with	with	IN
randomwalker-info-585	896	34	state	state	NN
randomwalker-info-585	896	35	0′′.	0′′.	.
randomwalker-info-585	897	1	Again	again	RB
randomwalker-info-585	897	2	,	,	,
randomwalker-info-585	897	3	note	note	VB
randomwalker-info-585	897	4	that	that	IN
randomwalker-info-585	897	5	this	this	DT
randomwalker-info-585	897	6	modification	modification	NN
randomwalker-info-585	897	7	is	be	VBZ
randomwalker-info-585	897	8	just	just	RB
randomwalker-info-585	897	9	for	for	IN
randomwalker-info-585	897	10	analysis	analysis	NN
randomwalker-info-585	897	11	.	.	.
randomwalker-info-585	898	1	The	the	DT
randomwalker-info-585	898	2	selfish	selfish	JJ
randomwalker-info-585	898	3	mining	mining	NN
randomwalker-info-585	898	4	with	with	IN
randomwalker-info-585	898	5	cutoff	cutoff	NN
randomwalker-info-585	898	6	that	that	WDT
randomwalker-info-585	898	7	is	be	VBZ
randomwalker-info-585	898	8	implemented	implement	VBN
randomwalker-info-585	898	9	in	in	IN
randomwalker-info-585	898	10	our	-PRON-	PRP$
randomwalker-info-585	898	11	simulator	simulator	NN
randomwalker-info-585	898	12	is	be	VBZ
randomwalker-info-585	898	13	as	as	RB
randomwalker-info-585	898	14	described	describe	VBN
randomwalker-info-585	898	15	in	in	IN
randomwalker-info-585	898	16	the	the	DT
randomwalker-info-585	898	17	body	body	NN
randomwalker-info-585	898	18	.	.	.
randomwalker-info-585	899	1	In	in	IN
randomwalker-info-585	899	2	order	order	NN
randomwalker-info-585	899	3	to	to	TO
randomwalker-info-585	899	4	calculate	calculate	VB
randomwalker-info-585	899	5	the	the	DT
randomwalker-info-585	899	6	selfish	selfish	JJ
randomwalker-info-585	899	7	miner	miner	NN
randomwalker-info-585	899	8	’s	’s	POS
randomwalker-info-585	899	9	expected	expect	VBN
randomwalker-info-585	899	10	revenue	revenue	NN
randomwalker-info-585	899	11	,	,	,
randomwalker-info-585	899	12	we	-PRON-	PRP
randomwalker-info-585	899	13	must	must	MD
randomwalker-info-585	899	14	again	again	RB
randomwalker-info-585	899	15	calculate	calculate	VB
randomwalker-info-585	899	16	the	the	DT
randomwalker-info-585	899	17	probability	probability	NN
randomwalker-info-585	899	18	of	of	IN
randomwalker-info-585	899	19	the	the	DT
randomwalker-info-585	899	20	system	system	NN
randomwalker-info-585	899	21	being	be	VBG
randomwalker-info-585	899	22	in	in	IN
randomwalker-info-585	899	23	any	any	DT
randomwalker-info-585	899	24	given	give	VBN
randomwalker-info-585	899	25	state	state	NN
randomwalker-info-585	899	26	,	,	,
randomwalker-info-585	899	27	and	and	CC
randomwalker-info-585	899	28	the	the	DT
randomwalker-info-585	899	29	chance	chance	NN
randomwalker-info-585	899	30	that	that	IN
randomwalker-info-585	899	31	a	a	DT
randomwalker-info-585	899	32	transaction	transaction	NN
randomwalker-info-585	899	33	arriving	arrive	VBG
randomwalker-info-585	899	34	to	to	IN
randomwalker-info-585	899	35	the	the	DT
randomwalker-info-585	899	36	system	system	NN
randomwalker-info-585	899	37	while	while	IN
randomwalker-info-585	899	38	in	in	IN
randomwalker-info-585	899	39	one	one	CD
randomwalker-info-585	899	40	of	of	IN
randomwalker-info-585	899	41	these	these	DT
randomwalker-info-585	899	42	states	state	NNS
randomwalker-info-585	899	43	eventually	eventually	RB
randomwalker-info-585	899	44	ends	end	VBZ
randomwalker-info-585	899	45	up	up	RP
randomwalker-info-585	899	46	in	in	IN
randomwalker-info-585	899	47	a	a	DT
randomwalker-info-585	899	48	block	block	NN
randomwalker-info-585	899	49	mined	mine	VBN
randomwalker-info-585	899	50	by	by	IN
randomwalker-info-585	899	51	the	the	DT
randomwalker-info-585	899	52	selfish	selfish	JJ
randomwalker-info-585	899	53	miner	miner	NN
randomwalker-info-585	899	54	.	.	.
randomwalker-info-585	900	1	From	from	IN
randomwalker-info-585	900	2	looking	look	VBG
randomwalker-info-585	900	3	at	at	IN
randomwalker-info-585	900	4	the	the	DT
randomwalker-info-585	900	5	state	state	NN
randomwalker-info-585	900	6	transitions	transition	NNS
randomwalker-info-585	900	7	in	in	IN
randomwalker-info-585	900	8	Figure	Figure	NNP
randomwalker-info-585	900	9	13	13	CD
randomwalker-info-585	900	10	,	,	,
randomwalker-info-585	900	11	we	-PRON-	PRP
randomwalker-info-585	900	12	can	can	MD
randomwalker-info-585	900	13	derive	derive	VB
randomwalker-info-585	900	14	the	the	DT
randomwalker-info-585	900	15	following	follow	VBG
randomwalker-info-585	900	16	formulas	formula	NNS
randomwalker-info-585	900	17	relating	relate	VBG
randomwalker-info-585	900	18	the	the	DT
randomwalker-info-585	900	19	probabilities	probability	NNS
randomwalker-info-585	900	20	of	of	IN
randomwalker-info-585	900	21	being	be	VBG
randomwalker-info-585	900	22	in	in	IN
randomwalker-info-585	900	23	each	each	DT
randomwalker-info-585	900	24	state	state	NN
randomwalker-info-585	900	25	:	:	:
randomwalker-info-585	900	26	piα	piα	NN
randomwalker-info-585	900	27	=	=	NFP
randomwalker-info-585	900	28	pi+1(1	pi+1(1	CD
randomwalker-info-585	900	29	−α	−α	CD
randomwalker-info-585	900	30	)	)	-RRB-
randomwalker-info-585	900	31	(	(	-LRB-
randomwalker-info-585	900	32	8)	8)	CD
randomwalker-info-585	900	33	=	=	SYM
randomwalker-info-585	900	34	⇒	⇒	NNP
randomwalker-info-585	900	35	pi	pi	NN
randomwalker-info-585	900	36	=	=	SYM
randomwalker-info-585	900	37	(	(	-LRB-
randomwalker-info-585	900	38	α	α	DT
randomwalker-info-585	900	39	1	1	CD
randomwalker-info-585	900	40	−α	−α	CD
randomwalker-info-585	900	41	)	)	-RRB-
randomwalker-info-585	900	42	i−1	i−1	NNP
randomwalker-info-585	900	43	p1	p1	NN
randomwalker-info-585	900	44	(	(	-LRB-
randomwalker-info-585	900	45	9	9	CD
randomwalker-info-585	900	46	)	)	-RRB-
randomwalker-info-585	900	47	p0′′	p0′′	NNP
randomwalker-info-585	900	48	=	=	SYM
randomwalker-info-585	900	49	(	(	-LRB-
randomwalker-info-585	900	50	1	1	CD
randomwalker-info-585	900	51	−α)p2	−α)p2	NNP
randomwalker-info-585	900	52	=	=	SYM
randomwalker-info-585	900	53	αp1	αp1	NNP
randomwalker-info-585	900	54	(	(	-LRB-
randomwalker-info-585	900	55	10	10	CD
randomwalker-info-585	900	56	)	)	-RRB-
randomwalker-info-585	900	57	p0′	p0′	NNP
randomwalker-info-585	900	58	=	=	NNS
randomwalker-info-585	900	59	(	(	-LRB-
randomwalker-info-585	900	60	1	1	CD
randomwalker-info-585	900	61	−α)p1	−α)p1	NN
randomwalker-info-585	900	62	(	(	-LRB-
randomwalker-info-585	900	63	11	11	CD
randomwalker-info-585	900	64	)	)	-RRB-
randomwalker-info-585	900	65	Figure	figure	NN
randomwalker-info-585	900	66	13	13	CD
randomwalker-info-585	900	67	:	:	:
randomwalker-info-585	900	68	State	state	NN
randomwalker-info-585	900	69	machine	machine	NN
randomwalker-info-585	900	70	for	for	IN
randomwalker-info-585	900	71	selfish	selfish	JJ
randomwalker-info-585	900	72	mining	mining	NN
randomwalker-info-585	900	73	with	with	IN
randomwalker-info-585	900	74	a	a	DT
randomwalker-info-585	900	75	cutoff	cutoff	NN
randomwalker-info-585	900	76	,	,	,
randomwalker-info-585	900	77	introducing	introduce	VBG
randomwalker-info-585	900	78	state	state	NN
randomwalker-info-585	900	79	0′′.	0′′.	.
randomwalker-info-585	901	1	p0	p0	NN
randomwalker-info-585	901	2	=	=	SYM
randomwalker-info-585	901	3	p1	p1	NN
randomwalker-info-585	901	4	α(1	α(1	NFP
randomwalker-info-585	901	5	−e−β	−e−β	NN
randomwalker-info-585	901	6	)	)	-RRB-
randomwalker-info-585	901	7	(	(	-LRB-
randomwalker-info-585	901	8	12	12	CD
randomwalker-info-585	901	9	)	)	-RRB-
randomwalker-info-585	901	10	We	-PRON-	PRP
randomwalker-info-585	901	11	also	also	RB
randomwalker-info-585	901	12	know	know	VBP
randomwalker-info-585	901	13	that	that	IN
randomwalker-info-585	901	14	the	the	DT
randomwalker-info-585	901	15	system	system	NN
randomwalker-info-585	901	16	is	be	VBZ
randomwalker-info-585	901	17	guaranteed	guarantee	VBN
randomwalker-info-585	901	18	to	to	TO
randomwalker-info-585	901	19	be	be	VB
randomwalker-info-585	901	20	in	in	IN
randomwalker-info-585	901	21	some	some	DT
randomwalker-info-585	901	22	state	state	NN
randomwalker-info-585	901	23	,	,	,
randomwalker-info-585	901	24	which	which	WDT
randomwalker-info-585	901	25	means	mean	VBZ
randomwalker-info-585	901	26	the	the	DT
randomwalker-info-585	901	27	following	following	NN
randomwalker-info-585	901	28	.	.	.
randomwalker-info-585	902	1	p0	p0	NN
randomwalker-info-585	902	2	+	+	SYM
randomwalker-info-585	902	3	p0′	p0′	NN
randomwalker-info-585	902	4	+	+	CC
randomwalker-info-585	902	5	p0′′	p0′′	NN
randomwalker-info-585	902	6	+	+	SYM
randomwalker-info-585	902	7	i=∞∑	i=∞∑	NN
randomwalker-info-585	902	8	i=1	i=1	NNPS
randomwalker-info-585	902	9	pi	pi	NN
randomwalker-info-585	902	10	=	=	SYM
randomwalker-info-585	902	11	1	1	CD
randomwalker-info-585	902	12	(	(	-LRB-
randomwalker-info-585	902	13	13	13	CD
randomwalker-info-585	902	14	)	)	-RRB-
randomwalker-info-585	902	15	Which	which	WDT
randomwalker-info-585	902	16	together	together	RB
randomwalker-info-585	902	17	imply	imply	VBP
randomwalker-info-585	902	18	that	that	DT
randomwalker-info-585	902	19	p1	p1	NN
randomwalker-info-585	902	20	=	=	NFP
randomwalker-info-585	902	21	α(2α−	α(2α−	NNP
randomwalker-info-585	902	22	1)(eβ	1)(eβ	CD
randomwalker-info-585	902	23	−	−	NNP
randomwalker-info-585	902	24	1	1	CD
randomwalker-info-585	902	25	)	)	-RRB-
randomwalker-info-585	902	26	3α2(eβ	3α2(eβ	CD
randomwalker-info-585	902	27	−	−	NNP
randomwalker-info-585	902	28	1	1	CD
randomwalker-info-585	902	29	)	)	-RRB-
randomwalker-info-585	902	30	+	+	CC
randomwalker-info-585	902	31	2α−eβ	2α−eβ	CD
randomwalker-info-585	902	32	(	(	-LRB-
randomwalker-info-585	902	33	14	14	CD
randomwalker-info-585	902	34	)	)	-RRB-
randomwalker-info-585	902	35	With	with	IN
randomwalker-info-585	902	36	equations	equation	NNS
randomwalker-info-585	902	37	9	9	CD
randomwalker-info-585	902	38	-	-	SYM
randomwalker-info-585	902	39	12	12	CD
randomwalker-info-585	902	40	,	,	,
randomwalker-info-585	902	41	this	this	DT
randomwalker-info-585	902	42	gives	give	VBZ
randomwalker-info-585	902	43	expressions	expression	NNS
randomwalker-info-585	902	44	for	for	IN
randomwalker-info-585	902	45	the	the	DT
randomwalker-info-585	902	46	probabilities	probability	NNS
randomwalker-info-585	902	47	of	of	IN
randomwalker-info-585	902	48	all	all	PDT
randomwalker-info-585	902	49	the	the	DT
randomwalker-info-585	902	50	possible	possible	JJ
randomwalker-info-585	902	51	states	state	NNS
randomwalker-info-585	902	52	the	the	DT
randomwalker-info-585	902	53	system	system	NN
randomwalker-info-585	902	54	could	could	MD
randomwalker-info-585	902	55	be	be	VB
randomwalker-info-585	902	56	in	in	IN
randomwalker-info-585	902	57	.	.	.
randomwalker-info-585	903	1	Now	now	RB
randomwalker-info-585	903	2	we	-PRON-	PRP
randomwalker-info-585	903	3	need	need	VBP
randomwalker-info-585	903	4	to	to	TO
randomwalker-info-585	903	5	compute	compute	VB
randomwalker-info-585	903	6	the	the	DT
randomwalker-info-585	903	7	probability	probability	NN
randomwalker-info-585	903	8	that	that	IN
randomwalker-info-585	903	9	a	a	DT
randomwalker-info-585	903	10	transaction	transaction	NN
randomwalker-info-585	903	11	that	that	WDT
randomwalker-info-585	903	12	arrives	arrive	VBZ
randomwalker-info-585	903	13	when	when	WRB
randomwalker-info-585	903	14	the	the	DT
randomwalker-info-585	903	15	system	system	NN
randomwalker-info-585	903	16	is	be	VBZ
randomwalker-info-585	903	17	in	in	IN
randomwalker-info-585	903	18	state	state	NN
randomwalker-info-585	903	19	s	s	POS
randomwalker-info-585	903	20	winds	wind	VBZ
randomwalker-info-585	903	21	up	up	RP
randomwalker-info-585	903	22	with	with	IN
randomwalker-info-585	903	23	the	the	DT
randomwalker-info-585	903	24	selfish	selfish	JJ
randomwalker-info-585	903	25	miner	miner	NN
randomwalker-info-585	903	26	.	.	.
randomwalker-info-585	904	1	Unfortunately	unfortunately	RB
randomwalker-info-585	904	2	,	,	,
randomwalker-info-585	904	3	this	this	DT
randomwalker-info-585	904	4	is	be	VBZ
randomwalker-info-585	904	5	not	not	RB
randomwalker-info-585	904	6	a	a	DT
randomwalker-info-585	904	7	clean	clean	JJ
randomwalker-info-585	904	8	approach	approach	NN
randomwalker-info-585	904	9	:	:	:
randomwalker-info-585	904	10	because	because	IN
randomwalker-info-585	904	11	in	in	IN
randomwalker-info-585	904	12	state	state	NN
randomwalker-info-585	904	13	0	0	NFP
randomwalker-info-585	904	14	the	the	DT
randomwalker-info-585	904	15	selfish	selfish	JJ
randomwalker-info-585	904	16	miner	miner	NN
randomwalker-info-585	904	17	will	will	MD
randomwalker-info-585	904	18	sometimes	sometimes	RB
randomwalker-info-585	904	19	publish	publish	VB
randomwalker-info-585	904	20	and	and	CC
randomwalker-info-585	904	21	sometimes	sometimes	RB
randomwalker-info-585	904	22	hide	hide	VB
randomwalker-info-585	904	23	their	-PRON-	PRP$
randomwalker-info-585	904	24	block	block	NN
randomwalker-info-585	904	25	,	,	,
randomwalker-info-585	904	26	depending	depend	VBG
randomwalker-info-585	904	27	on	on	IN
randomwalker-info-585	904	28	how	how	WRB
randomwalker-info-585	904	29	much	much	JJ
randomwalker-info-585	904	30	time	time	NN
randomwalker-info-585	904	31	has	have	VBZ
randomwalker-info-585	904	32	passed	pass	VBN
randomwalker-info-585	904	33	since	since	IN
randomwalker-info-585	904	34	the	the	DT
randomwalker-info-585	904	35	last	last	JJ
randomwalker-info-585	904	36	block	block	NN
randomwalker-info-585	904	37	was	be	VBD
randomwalker-info-585	904	38	found	find	VBN
randomwalker-info-585	904	39	,	,	,
randomwalker-info-585	904	40	we	-PRON-	PRP
randomwalker-info-585	904	41	need	need	VBP
randomwalker-info-585	904	42	actually	actually	RB
randomwalker-info-585	904	43	to	to	TO
randomwalker-info-585	904	44	introduce	introduce	VB
randomwalker-info-585	904	45	a	a	DT
randomwalker-info-585	904	46	continuum	continuum	NN
randomwalker-info-585	904	47	of	of	IN
randomwalker-info-585	904	48	states	state	NNS
randomwalker-info-585	904	49	for	for	IN
randomwalker-info-585	904	50	each	each	DT
randomwalker-info-585	904	51	amount	amount	NN
randomwalker-info-585	904	52	of	of	IN
randomwalker-info-585	904	53	time	time	NN
randomwalker-info-585	904	54	x	x	NNS
randomwalker-info-585	904	55	for	for	IN
randomwalker-info-585	904	56	the	the	DT
randomwalker-info-585	904	57	size	size	NN
randomwalker-info-585	904	58	of	of	IN
randomwalker-info-585	904	59	the	the	DT
randomwalker-info-585	904	60	block	block	NN
randomwalker-info-585	904	61	that	that	WDT
randomwalker-info-585	904	62	is	be	VBZ
randomwalker-info-585	904	63	building	build	VBG
randomwalker-info-585	904	64	during	during	IN
randomwalker-info-585	904	65	state	state	NN
randomwalker-info-585	904	66	0	0	CD
randomwalker-info-585	904	67	.	.	.
randomwalker-info-585	905	1	So	so	RB
randomwalker-info-585	905	2	let	let	VB
randomwalker-info-585	905	3	’s	-PRON-	PRP
randomwalker-info-585	905	4	define	define	VB
randomwalker-info-585	905	5	a	a	DT
randomwalker-info-585	905	6	new	new	JJ
randomwalker-info-585	905	7	variable	variable	NN
randomwalker-info-585	905	8	,	,	,
randomwalker-info-585	905	9	p0(x	p0(x	NNP
randomwalker-info-585	905	10	)	)	-RRB-
randomwalker-info-585	905	11	which	which	WDT
randomwalker-info-585	905	12	denotes	denote	VBZ
randomwalker-info-585	905	13	the	the	DT
randomwalker-info-585	905	14	probability	probability	NN
randomwalker-info-585	905	15	that	that	IN
randomwalker-info-585	905	16	the	the	DT
randomwalker-info-585	905	17	system	system	NN
randomwalker-info-585	905	18	is	be	VBZ
randomwalker-info-585	905	19	in	in	IN
randomwalker-info-585	905	20	state	state	NN
randomwalker-info-585	905	21	0	0	CD
randomwalker-info-585	905	22	and	and	CC
randomwalker-info-585	905	23	x	x	SYM
randomwalker-info-585	905	24	units	unit	NNS
randomwalker-info-585	905	25	of	of	IN
randomwalker-info-585	905	26	time	time	NN
randomwalker-info-585	905	27	have	have	VBP
randomwalker-info-585	905	28	passed	pass	VBN
randomwalker-info-585	905	29	since	since	IN
randomwalker-info-585	905	30	the	the	DT
randomwalker-info-585	905	31	system	system	NN
randomwalker-info-585	905	32	entered	enter	VBD
randomwalker-info-585	905	33	state	state	NN
randomwalker-info-585	905	34	0	0	CD
randomwalker-info-585	905	35	.	.	.
randomwalker-info-585	906	1	Because	because	IN
randomwalker-info-585	906	2	we	-PRON-	PRP
randomwalker-info-585	906	3	introduced	introduce	VBD
randomwalker-info-585	906	4	this	this	DT
randomwalker-info-585	906	5	new	new	JJ
randomwalker-info-585	906	6	state	state	NN
randomwalker-info-585	906	7	0′′	0′′	NNP
randomwalker-info-585	906	8	,	,	,
randomwalker-info-585	906	9	whenever	whenever	WRB
randomwalker-info-585	906	10	we	-PRON-	PRP
randomwalker-info-585	906	11	enter	enter	VBP
randomwalker-info-585	906	12	state	state	NN
randomwalker-info-585	906	13	0	0	CD
randomwalker-info-585	906	14	,	,	,
randomwalker-info-585	906	15	the	the	DT
randomwalker-info-585	906	16	initial	initial	JJ
randomwalker-info-585	906	17	block	block	NN
randomwalker-info-585	906	18	is	be	VBZ
randomwalker-info-585	906	19	empty	empty	JJ
randomwalker-info-585	906	20	.	.	.
randomwalker-info-585	907	1	Therefore	therefore	RB
randomwalker-info-585	907	2	,	,	,
randomwalker-info-585	907	3	the	the	DT
randomwalker-info-585	907	4	probability	probability	NN
randomwalker-info-585	907	5	that	that	WDT
randomwalker-info-585	907	6	we	-PRON-	PRP
randomwalker-info-585	907	7	wind	wind	VBP
randomwalker-info-585	907	8	up	up	RP
randomwalker-info-585	907	9	in	in	IN
randomwalker-info-585	907	10	state	state	NN
randomwalker-info-585	907	11	0	0	CD
randomwalker-info-585	907	12	with	with	IN
randomwalker-info-585	907	13	a	a	DT
randomwalker-info-585	907	14	block	block	NN
randomwalker-info-585	907	15	of	of	IN
randomwalker-info-585	907	16	size	size	NN
randomwalker-info-585	907	17	at	at	IN
randomwalker-info-585	907	18	least	least	JJS
randomwalker-info-585	907	19	x	x	NN
randomwalker-info-585	907	20	is	be	VBZ
randomwalker-info-585	907	21	p0e	p0e	NNP
randomwalker-info-585	907	22	−x	−x	CD
randomwalker-info-585	907	23	,	,	,
randomwalker-info-585	907	24	and	and	CC
randomwalker-info-585	907	25	we	-PRON-	PRP
randomwalker-info-585	907	26	have	have	VBP
randomwalker-info-585	907	27	:	:	:
randomwalker-info-585	907	28	p0(x	p0(x	ADD
randomwalker-info-585	907	29	)	)	-RRB-
randomwalker-info-585	907	30	=	=	NFP
randomwalker-info-585	907	31	p0e	p0e	ADD
randomwalker-info-585	907	32	−x	−x	CD
randomwalker-info-585	907	33	dx	dx	NNP
randomwalker-info-585	907	34	(	(	-LRB-
randomwalker-info-585	907	35	15	15	CD
randomwalker-info-585	907	36	)	)	-RRB-
randomwalker-info-585	907	37	We	-PRON-	PRP
randomwalker-info-585	907	38	must	must	MD
randomwalker-info-585	907	39	now	now	RB
randomwalker-info-585	907	40	calculate	calculate	VB
randomwalker-info-585	907	41	the	the	DT
randomwalker-info-585	907	42	associated	associated	JJ
randomwalker-info-585	907	43	fs	fs	NNP
randomwalker-info-585	907	44	(	(	-LRB-
randomwalker-info-585	907	45	probability	probability	NN
randomwalker-info-585	907	46	that	that	IN
randomwalker-info-585	907	47	a	a	DT
randomwalker-info-585	907	48	transaction	transaction	NN
randomwalker-info-585	907	49	winds	wind	VBZ
randomwalker-info-585	907	50	up	up	RP
randomwalker-info-585	907	51	with	with	IN
randomwalker-info-585	907	52	the	the	DT
randomwalker-info-585	907	53	selfish	selfish	JJ
randomwalker-info-585	907	54	miner	miner	NN
randomwalker-info-585	907	55	conditioned	condition	VBN
randomwalker-info-585	907	56	on	on	IN
randomwalker-info-585	907	57	arriving	arrive	VBG
randomwalker-info-585	907	58	during	during	IN
randomwalker-info-585	907	59	state	state	NN
randomwalker-info-585	907	60	s	s	NNPS
randomwalker-info-585	907	61	)	)	-RRB-
randomwalker-info-585	907	62	in	in	IN
randomwalker-info-585	907	63	order	order	NN
randomwalker-info-585	907	64	to	to	TO
randomwalker-info-585	907	65	calculate	calculate	VB
randomwalker-info-585	907	66	the	the	DT
randomwalker-info-585	907	67	expected	expect	VBN
randomwalker-info-585	907	68	fraction	fraction	NN
randomwalker-info-585	907	69	of	of	IN
randomwalker-info-585	907	70	the	the	DT
randomwalker-info-585	907	71	rewards	reward	NNS
randomwalker-info-585	907	72	claimed	claim	VBN
randomwalker-info-585	907	73	by	by	IN
randomwalker-info-585	907	74	the	the	DT
randomwalker-info-585	907	75	selfish	selfish	JJ
randomwalker-info-585	907	76	miner	miner	NN
randomwalker-info-585	907	77	.	.	.
randomwalker-info-585	908	1	Computing	Computing	NNP
randomwalker-info-585	908	2	f0(x	f0(x	NNP
randomwalker-info-585	908	3	)	)	-RRB-
randomwalker-info-585	908	4	.	.	.
randomwalker-info-585	909	1	If	if	IN
randomwalker-info-585	909	2	a	a	DT
randomwalker-info-585	909	3	new	new	JJ
randomwalker-info-585	909	4	transaction	transaction	NN
randomwalker-info-585	909	5	arrives	arrive	VBZ
randomwalker-info-585	909	6	in	in	IN
randomwalker-info-585	909	7	state	state	NN
randomwalker-info-585	909	8	0	0	CD
randomwalker-info-585	909	9	,	,	,
randomwalker-info-585	909	10	let	let	VB
randomwalker-info-585	909	11	’s	-PRON-	PRP
randomwalker-info-585	909	12	look	look	VB
randomwalker-info-585	909	13	at	at	IN
randomwalker-info-585	909	14	where	where	WRB
randomwalker-info-585	909	15	this	this	DT
randomwalker-info-585	909	16	transaction	transaction	NN
randomwalker-info-585	909	17	might	may	MD
randomwalker-info-585	909	18	wind	wind	VB
randomwalker-info-585	909	19	up	up	RP
randomwalker-info-585	909	20	.	.	.
randomwalker-info-585	910	1	Note	note	VB
randomwalker-info-585	910	2	that	that	IN
randomwalker-info-585	910	3	this	this	DT
randomwalker-info-585	910	4	depends	depend	VBZ
randomwalker-info-585	910	5	on	on	IN
randomwalker-info-585	910	6	how	how	WRB
randomwalker-info-585	910	7	long	long	JJ
randomwalker-info-585	910	8	it	-PRON-	PRP
randomwalker-info-585	910	9	’s	’	VBZ
randomwalker-info-585	910	10	been	be	VBN
randomwalker-info-585	910	11	(	(	-LRB-
randomwalker-info-585	910	12	x	x	LS
randomwalker-info-585	910	13	)	)	-RRB-
randomwalker-info-585	910	14	since	since	IN
randomwalker-info-585	910	15	the	the	DT
randomwalker-info-585	910	16	last	last	JJ
randomwalker-info-585	910	17	block	block	NN
randomwalker-info-585	910	18	was	be	VBD
randomwalker-info-585	910	19	found	find	VBN
randomwalker-info-585	910	20	.	.	.
randomwalker-info-585	911	1	•	•	VB
randomwalker-info-585	911	2	If	if	IN
randomwalker-info-585	911	3	the	the	DT
randomwalker-info-585	911	4	next	next	JJ
randomwalker-info-585	911	5	block	block	NN
randomwalker-info-585	911	6	is	be	VBZ
randomwalker-info-585	911	7	found	find	VBN
randomwalker-info-585	911	8	by	by	IN
randomwalker-info-585	911	9	the	the	DT
randomwalker-info-585	911	10	honest	honest	JJ
randomwalker-info-585	911	11	miner	miner	NN
randomwalker-info-585	911	12	,	,	,
randomwalker-info-585	911	13	then	then	RB
randomwalker-info-585	911	14	this	this	DT
randomwalker-info-585	911	15	transaction	transaction	NN
randomwalker-info-585	911	16	will	will	MD
randomwalker-info-585	911	17	certainly	certainly	RB
randomwalker-info-585	911	18	wind	wind	VB
randomwalker-info-585	911	19	up	up	RP
randomwalker-info-585	911	20	with	with	IN
randomwalker-info-585	911	21	the	the	DT
randomwalker-info-585	911	22	honest	honest	JJ
randomwalker-info-585	911	23	miners	miner	NNS
randomwalker-info-585	911	24	.	.	.
randomwalker-info-585	912	1	This	this	DT
randomwalker-info-585	912	2	happens	happen	VBZ
randomwalker-info-585	912	3	with	with	IN
randomwalker-info-585	912	4	probability	probability	NN
randomwalker-info-585	912	5	1	1	CD
randomwalker-info-585	912	6	−α	−α	CD
randomwalker-info-585	912	7	.	.	.
randomwalker-info-585	913	1	•	•	VB
randomwalker-info-585	913	2	If	if	IN
randomwalker-info-585	913	3	x	x	LS
randomwalker-info-585	913	4	≥	≥	UH
randomwalker-info-585	913	5	β	β	NN
randomwalker-info-585	913	6	,	,	,
randomwalker-info-585	913	7	and	and	CC
randomwalker-info-585	913	8	the	the	DT
randomwalker-info-585	913	9	next	next	JJ
randomwalker-info-585	913	10	block	block	NN
randomwalker-info-585	913	11	is	be	VBZ
randomwalker-info-585	913	12	found	find	VBN
randomwalker-info-585	913	13	by	by	IN
randomwalker-info-585	913	14	the	the	DT
randomwalker-info-585	913	15	selfish	selfish	JJ
randomwalker-info-585	913	16	miner	miner	NN
randomwalker-info-585	913	17	,	,	,
randomwalker-info-585	913	18	then	then	RB
randomwalker-info-585	913	19	it	-PRON-	PRP
randomwalker-info-585	913	20	certainly	certainly	RB
randomwalker-info-585	913	21	winds	wind	VBZ
randomwalker-info-585	913	22	up	up	RP
randomwalker-info-585	913	23	with	with	IN
randomwalker-info-585	913	24	the	the	DT
randomwalker-info-585	913	25	selfish	selfish	JJ
randomwalker-info-585	913	26	miner	miner	NN
randomwalker-info-585	913	27	.	.	.
randomwalker-info-585	914	1	This	this	DT
randomwalker-info-585	914	2	happens	happen	VBZ
randomwalker-info-585	914	3	with	with	IN
randomwalker-info-585	914	4	probability	probability	NN
randomwalker-info-585	914	5	α	α	XX
randomwalker-info-585	914	6	.	.	.
randomwalker-info-585	915	1	•	•	VB
randomwalker-info-585	915	2	If	if	IN
randomwalker-info-585	915	3	x	x	NNS
randomwalker-info-585	915	4	<	<	XX
randomwalker-info-585	915	5	β	β	XX
randomwalker-info-585	915	6	,	,	,
randomwalker-info-585	915	7	and	and	CC
randomwalker-info-585	915	8	the	the	DT
randomwalker-info-585	915	9	next	next	JJ
randomwalker-info-585	915	10	block	block	NN
randomwalker-info-585	915	11	is	be	VBZ
randomwalker-info-585	915	12	found	find	VBN
randomwalker-info-585	915	13	by	by	IN
randomwalker-info-585	915	14	the	the	DT
randomwalker-info-585	915	15	selfish	selfish	JJ
randomwalker-info-585	915	16	miner	miner	NN
randomwalker-info-585	915	17	after	after	IN
randomwalker-info-585	915	18	time	time	NN
randomwalker-info-585	915	19	β−x	β−x	VBD
randomwalker-info-585	915	20	as	as	IN
randomwalker-info-585	915	21	passed	pass	VBN
randomwalker-info-585	915	22	,	,	,
randomwalker-info-585	915	23	then	then	RB
randomwalker-info-585	915	24	it	-PRON-	PRP
randomwalker-info-585	915	25	certainly	certainly	RB
randomwalker-info-585	915	26	winds	wind	VBZ
randomwalker-info-585	915	27	up	up	RP
randomwalker-info-585	915	28	with	with	IN
randomwalker-info-585	915	29	the	the	DT
randomwalker-info-585	915	30	selfish	selfish	JJ
randomwalker-info-585	915	31	miner	miner	NN
randomwalker-info-585	915	32	.	.	.
randomwalker-info-585	916	1	This	this	DT
randomwalker-info-585	916	2	happens	happen	VBZ
randomwalker-info-585	916	3	with	with	IN
randomwalker-info-585	916	4	probability	probability	NN
randomwalker-info-585	916	5	αe−β+x	αe−β+x	NNP
randomwalker-info-585	916	6	.	.	.
randomwalker-info-585	917	1	•	•	VB
randomwalker-info-585	917	2	If	if	IN
randomwalker-info-585	917	3	x	x	NNS
randomwalker-info-585	917	4	<	<	XX
randomwalker-info-585	917	5	β	β	XX
randomwalker-info-585	917	6	,	,	,
randomwalker-info-585	917	7	and	and	CC
randomwalker-info-585	917	8	the	the	DT
randomwalker-info-585	917	9	next	next	JJ
randomwalker-info-585	917	10	block	block	NN
randomwalker-info-585	917	11	is	be	VBZ
randomwalker-info-585	917	12	found	find	VBN
randomwalker-info-585	917	13	by	by	IN
randomwalker-info-585	917	14	the	the	DT
randomwalker-info-585	917	15	selfish	selfish	JJ
randomwalker-info-585	917	16	miner	miner	NN
randomwalker-info-585	917	17	within	within	IN
randomwalker-info-585	917	18	β	β	NNP
randomwalker-info-585	917	19	−x	−x	CD
randomwalker-info-585	917	20	time	time	NN
randomwalker-info-585	917	21	,	,	,
randomwalker-info-585	917	22	then	then	RB
randomwalker-info-585	917	23	this	this	DT
randomwalker-info-585	917	24	transaction	transaction	NN
randomwalker-info-585	917	25	is	be	VBZ
randomwalker-info-585	917	26	n’t	not	RB
randomwalker-info-585	917	27	determined	determine	VBN
randomwalker-info-585	917	28	yet	yet	RB
randomwalker-info-585	917	29	because	because	IN
randomwalker-info-585	917	30	the	the	DT
randomwalker-info-585	917	31	selfish	selfish	JJ
randomwalker-info-585	917	32	miner	miner	NN
randomwalker-info-585	917	33	chooses	choose	VBZ
randomwalker-info-585	917	34	to	to	TO
randomwalker-info-585	917	35	hide	hide	VB
randomwalker-info-585	917	36	that	that	DT
randomwalker-info-585	917	37	block	block	NN
randomwalker-info-585	917	38	.	.	.
randomwalker-info-585	918	1	But	but	CC
randomwalker-info-585	918	2	this	this	DT
randomwalker-info-585	918	3	happens	happen	VBZ
randomwalker-info-585	918	4	with	with	IN
randomwalker-info-585	918	5	probability	probability	NN
randomwalker-info-585	918	6	α(1	α(1	NNP
randomwalker-info-585	918	7	−e−β+x	−e−β+x	NNP
randomwalker-info-585	918	8	)	)	-RRB-
randomwalker-info-585	918	9	.	.	.
randomwalker-info-585	919	1	•	•	VB
randomwalker-info-585	919	2	If	if	IN
randomwalker-info-585	919	3	both	both	DT
randomwalker-info-585	919	4	of	of	IN
randomwalker-info-585	919	5	the	the	DT
randomwalker-info-585	919	6	next	next	JJ
randomwalker-info-585	919	7	two	two	CD
randomwalker-info-585	919	8	blocks	block	NNS
randomwalker-info-585	919	9	are	be	VBP
randomwalker-info-585	919	10	found	find	VBN
randomwalker-info-585	919	11	by	by	IN
randomwalker-info-585	919	12	the	the	DT
randomwalker-info-585	919	13	selfish	selfish	JJ
randomwalker-info-585	919	14	miner	miner	NN
randomwalker-info-585	919	15	,	,	,
randomwalker-info-585	919	16	than	than	IN
randomwalker-info-585	919	17	this	this	DT
randomwalker-info-585	919	18	transaction	transaction	NN
randomwalker-info-585	919	19	is	be	VBZ
randomwalker-info-585	919	20	contained	contain	VBN
randomwalker-info-585	919	21	in	in	IN
randomwalker-info-585	919	22	a	a	DT
randomwalker-info-585	919	23	block	block	NN
randomwalker-info-585	919	24	of	of	IN
randomwalker-info-585	919	25	the	the	DT
randomwalker-info-585	919	26	selfish	selfish	JJ
randomwalker-info-585	919	27	miner	miner	NN
randomwalker-info-585	919	28	that	that	WDT
randomwalker-info-585	919	29	will	will	MD
randomwalker-info-585	919	30	certainly	certainly	RB
randomwalker-info-585	919	31	be	be	VB
randomwalker-info-585	919	32	included	include	VBN
randomwalker-info-585	919	33	in	in	IN
randomwalker-info-585	919	34	the	the	DT
randomwalker-info-585	919	35	eventual	eventual	JJ
randomwalker-info-585	919	36	longest	long	JJS
randomwalker-info-585	919	37	chain	chain	NN
randomwalker-info-585	919	38	.	.	.
randomwalker-info-585	920	1	This	this	DT
randomwalker-info-585	920	2	happens	happen	VBZ
randomwalker-info-585	920	3	with	with	IN
randomwalker-info-585	920	4	probability	probability	NN
randomwalker-info-585	920	5	α2(1	α2(1	NNP
randomwalker-info-585	920	6	−e−β+x	−e−β+x	NNP
randomwalker-info-585	920	7	)	)	-RRB-
randomwalker-info-585	920	8	.	.	.
randomwalker-info-585	921	1	•	•	VB
randomwalker-info-585	921	2	If	if	IN
randomwalker-info-585	921	3	the	the	DT
randomwalker-info-585	921	4	next	next	JJ
randomwalker-info-585	921	5	block	block	NN
randomwalker-info-585	921	6	is	be	VBZ
randomwalker-info-585	921	7	found	find	VBN
randomwalker-info-585	921	8	by	by	IN
randomwalker-info-585	921	9	the	the	DT
randomwalker-info-585	921	10	selfish	selfish	JJ
randomwalker-info-585	921	11	miner	miner	NN
randomwalker-info-585	921	12	,	,	,
randomwalker-info-585	921	13	followed	follow	VBN
randomwalker-info-585	921	14	by	by	IN
randomwalker-info-585	921	15	a	a	DT
randomwalker-info-585	921	16	block	block	NN
randomwalker-info-585	921	17	by	by	IN
randomwalker-info-585	921	18	the	the	DT
randomwalker-info-585	921	19	honest	honest	JJ
randomwalker-info-585	921	20	miner	miner	NN
randomwalker-info-585	921	21	,	,	,
randomwalker-info-585	921	22	then	then	RB
randomwalker-info-585	921	23	a	a	DT
randomwalker-info-585	921	24	race	race	NN
randomwalker-info-585	921	25	is	be	VBZ
randomwalker-info-585	921	26	triggered	trigger	VBN
randomwalker-info-585	921	27	.	.	.
randomwalker-info-585	922	1	This	this	DT
randomwalker-info-585	922	2	transaction	transaction	NN
randomwalker-info-585	922	3	is	be	VBZ
randomwalker-info-585	922	4	contained	contain	VBN
randomwalker-info-585	922	5	in	in	IN
randomwalker-info-585	922	6	the	the	DT
randomwalker-info-585	922	7	two	two	CD
randomwalker-info-585	922	8	racing	racing	NN
randomwalker-info-585	922	9	blocks	block	NNS
randomwalker-info-585	922	10	,	,	,
randomwalker-info-585	922	11	so	so	CC
randomwalker-info-585	922	12	whoever	whoever	WP
randomwalker-info-585	922	13	wins	win	VBZ
randomwalker-info-585	922	14	the	the	DT
randomwalker-info-585	922	15	race	race	NN
randomwalker-info-585	922	16	gets	get	VBZ
randomwalker-info-585	922	17	this	this	DT
randomwalker-info-585	922	18	transaction	transaction	NN
randomwalker-info-585	922	19	.	.	.
randomwalker-info-585	923	1	The	the	DT
randomwalker-info-585	923	2	race	race	NN
randomwalker-info-585	923	3	occurs	occur	VBZ
randomwalker-info-585	923	4	with	with	IN
randomwalker-info-585	923	5	probability	probability	NN
randomwalker-info-585	923	6	α(1	α(1	VB
randomwalker-info-585	923	7	−e−β+x)(1	−e−β+x)(1	IN
randomwalker-info-585	923	8	−α	−α	CD
randomwalker-info-585	923	9	)	)	-RRB-
randomwalker-info-585	923	10	,	,	,
randomwalker-info-585	923	11	and	and	CC
randomwalker-info-585	923	12	the	the	DT
randomwalker-info-585	923	13	selfish	selfish	JJ
randomwalker-info-585	923	14	miner	miner	NN
randomwalker-info-585	923	15	wins	win	VBZ
randomwalker-info-585	923	16	the	the	DT
randomwalker-info-585	923	17	race	race	NN
randomwalker-info-585	923	18	with	with	IN
randomwalker-info-585	923	19	probability	probability	NN
randomwalker-info-585	923	20	α	α	CD
randomwalker-info-585	923	21	+	+	CC
randomwalker-info-585	923	22	(	(	-LRB-
randomwalker-info-585	923	23	1	1	CD
randomwalker-info-585	923	24	−α)γ	−α)γ	NNP
randomwalker-info-585	923	25	.	.	.
randomwalker-info-585	924	1	So	so	RB
randomwalker-info-585	924	2	in	in	IN
randomwalker-info-585	924	3	total	total	NN
randomwalker-info-585	924	4	,	,	,
randomwalker-info-585	924	5	we	-PRON-	PRP
randomwalker-info-585	924	6	see	see	VBP
randomwalker-info-585	924	7	that	that	IN
randomwalker-info-585	924	8	f0(x	f0(x	NNP
randomwalker-info-585	924	9	)	)	-RRB-
randomwalker-info-585	924	10	=	=	NFP
randomwalker-info-585	924	11	α	α	XX
randomwalker-info-585	924	12	,	,	,
randomwalker-info-585	924	13	when	when	WRB
randomwalker-info-585	924	14	x	x	LS
randomwalker-info-585	924	15	≥	≥	UH
randomwalker-info-585	924	16	β	β	NN
randomwalker-info-585	924	17	,	,	,
randomwalker-info-585	924	18	and	and	CC
randomwalker-info-585	924	19	f0(x	f0(x	NNP
randomwalker-info-585	924	20	)	)	-RRB-
randomwalker-info-585	924	21	=	=	NFP
randomwalker-info-585	924	22	αe−β+x	αe−β+x	NN
randomwalker-info-585	924	23	+	+	XX
randomwalker-info-585	924	24	α2(1	α2(1	NNP
randomwalker-info-585	924	25	−e−β+x	−e−β+x	NNP
randomwalker-info-585	924	26	)	)	-RRB-
randomwalker-info-585	924	27	+	+	CC
randomwalker-info-585	924	28	α(1	α(1	NFP
randomwalker-info-585	924	29	−α)(1	−α)(1	XX
randomwalker-info-585	924	30	−e−β+x)(α	−e−β+x)(α	FW
randomwalker-info-585	924	31	+	+	NFP
randomwalker-info-585	924	32	(	(	-LRB-
randomwalker-info-585	924	33	1	1	CD
randomwalker-info-585	924	34	−α)γ	−α)γ	NNP
randomwalker-info-585	924	35	)	)	-RRB-
randomwalker-info-585	924	36	if	if	IN
randomwalker-info-585	924	37	x	x	NNP
randomwalker-info-585	924	38	≤	≤	NNP
randomwalker-info-585	924	39	β	β	NNP
randomwalker-info-585	924	40	.	.	.
randomwalker-info-585	924	41	Computing	computing	NN
randomwalker-info-585	924	42	f0′.	f0′.	NNS
randomwalker-info-585	925	1	If	if	IN
randomwalker-info-585	925	2	a	a	DT
randomwalker-info-585	925	3	new	new	JJ
randomwalker-info-585	925	4	transaction	transaction	NN
randomwalker-info-585	925	5	arrives	arrive	VBZ
randomwalker-info-585	925	6	when	when	WRB
randomwalker-info-585	925	7	there	there	EX
randomwalker-info-585	925	8	are	be	VBP
randomwalker-info-585	925	9	two	two	CD
randomwalker-info-585	925	10	chains	chain	NNS
randomwalker-info-585	925	11	competing	compete	VBG
randomwalker-info-585	925	12	of	of	IN
randomwalker-info-585	925	13	the	the	DT
randomwalker-info-585	925	14	same	same	JJ
randomwalker-info-585	925	15	length	length	NN
randomwalker-info-585	925	16	,	,	,
randomwalker-info-585	925	17	then	then	RB
randomwalker-info-585	925	18	the	the	DT
randomwalker-info-585	925	19	next	next	JJ
randomwalker-info-585	925	20	block	block	NN
randomwalker-info-585	925	21	found	find	VBN
randomwalker-info-585	925	22	is	be	VBZ
randomwalker-info-585	925	23	certainly	certainly	RB
randomwalker-info-585	925	24	contained	contain	VBN
randomwalker-info-585	925	25	in	in	IN
randomwalker-info-585	925	26	the	the	DT
randomwalker-info-585	925	27	eventual	eventual	JJ
randomwalker-info-585	925	28	longest	long	JJS
randomwalker-info-585	925	29	chain	chain	NN
randomwalker-info-585	925	30	(	(	-LRB-
randomwalker-info-585	925	31	because	because	IN
randomwalker-info-585	925	32	both	both	DT
randomwalker-info-585	925	33	miners	miner	NNS
randomwalker-info-585	925	34	choose	choose	VBP
randomwalker-info-585	925	35	to	to	TO
randomwalker-info-585	925	36	mine	-PRON-	PRP
randomwalker-info-585	925	37	on	on	IN
randomwalker-info-585	925	38	top	top	NN
randomwalker-info-585	925	39	of	of	IN
randomwalker-info-585	925	40	it	-PRON-	PRP
randomwalker-info-585	925	41	)	)	-RRB-
randomwalker-info-585	925	42	.	.	.
randomwalker-info-585	926	1	So	so	CC
randomwalker-info-585	926	2	if	if	IN
randomwalker-info-585	926	3	the	the	DT
randomwalker-info-585	926	4	next	next	JJ
randomwalker-info-585	926	5	block	block	NN
randomwalker-info-585	926	6	is	be	VBZ
randomwalker-info-585	926	7	found	find	VBN
randomwalker-info-585	926	8	by	by	IN
randomwalker-info-585	926	9	the	the	DT
randomwalker-info-585	926	10	selfish	selfish	JJ
randomwalker-info-585	926	11	miner	miner	NN
randomwalker-info-585	926	12	,	,	,
randomwalker-info-585	926	13	this	this	DT
randomwalker-info-585	926	14	transaction	transaction	NN
randomwalker-info-585	926	15	is	be	VBZ
randomwalker-info-585	926	16	won	win	VBN
randomwalker-info-585	926	17	by	by	IN
randomwalker-info-585	926	18	him	-PRON-	PRP
randomwalker-info-585	926	19	.	.	.
randomwalker-info-585	927	1	Otherwise	otherwise	RB
randomwalker-info-585	927	2	,	,	,
randomwalker-info-585	927	3	it	-PRON-	PRP
randomwalker-info-585	927	4	’s	’	VBZ
randomwalker-info-585	927	5	won	win	VBN
randomwalker-info-585	927	6	by	by	IN
randomwalker-info-585	927	7	the	the	DT
randomwalker-info-585	927	8	honest	honest	JJ
randomwalker-info-585	927	9	miner	miner	NN
randomwalker-info-585	927	10	.	.	.
randomwalker-info-585	928	1	So	so	RB
randomwalker-info-585	928	2	we	-PRON-	PRP
randomwalker-info-585	928	3	have	have	VBP
randomwalker-info-585	928	4	f0′	f0′	NN
randomwalker-info-585	928	5	=	=	SYM
randomwalker-info-585	928	6	α	α	XX
randomwalker-info-585	928	7	.	.	.
randomwalker-info-585	928	8	Computing	computing	NN
randomwalker-info-585	928	9	f0′′.	f0′′.	''
randomwalker-info-585	929	1	If	if	IN
randomwalker-info-585	929	2	a	a	DT
randomwalker-info-585	929	3	new	new	JJ
randomwalker-info-585	929	4	transaction	transaction	NN
randomwalker-info-585	929	5	arrives	arrive	VBZ
randomwalker-info-585	929	6	during	during	IN
randomwalker-info-585	929	7	the	the	DT
randomwalker-info-585	929	8	state	state	NN
randomwalker-info-585	929	9	0	0	CD
randomwalker-info-585	929	10	′′	′′	NN
randomwalker-info-585	929	11	,	,	,
randomwalker-info-585	929	12	the	the	DT
randomwalker-info-585	929	13	next	next	JJ
randomwalker-info-585	929	14	block	block	NN
randomwalker-info-585	929	15	found	find	VBN
randomwalker-info-585	929	16	is	be	VBZ
randomwalker-info-585	929	17	certainly	certainly	RB
randomwalker-info-585	929	18	contained	contain	VBN
randomwalker-info-585	929	19	in	in	IN
randomwalker-info-585	929	20	the	the	DT
randomwalker-info-585	929	21	eventual	eventual	JJ
randomwalker-info-585	929	22	longest	long	JJS
randomwalker-info-585	929	23	chain	chain	NN
randomwalker-info-585	929	24	again	again	RB
randomwalker-info-585	929	25	.	.	.
randomwalker-info-585	930	1	So	so	RB
randomwalker-info-585	930	2	we	-PRON-	PRP
randomwalker-info-585	930	3	again	again	RB
randomwalker-info-585	930	4	have	have	VBP
randomwalker-info-585	930	5	f0′′	f0′′	NNP
randomwalker-info-585	930	6	=	=	SYM
randomwalker-info-585	930	7	α	α	XX
randomwalker-info-585	930	8	.	.	.
randomwalker-info-585	930	9	Computing	Computing	NNP
randomwalker-info-585	930	10	f1	f1	NNP
randomwalker-info-585	930	11	.	.	.
randomwalker-info-585	931	1	If	if	IN
randomwalker-info-585	931	2	a	a	DT
randomwalker-info-585	931	3	new	new	JJ
randomwalker-info-585	931	4	transaction	transaction	NN
randomwalker-info-585	931	5	arrives	arrive	VBZ
randomwalker-info-585	931	6	when	when	WRB
randomwalker-info-585	931	7	the	the	DT
randomwalker-info-585	931	8	sefish	sefish	JJ
randomwalker-info-585	931	9	miner	miner	NN
randomwalker-info-585	931	10	has	have	VBZ
randomwalker-info-585	931	11	a	a	DT
randomwalker-info-585	931	12	private	private	JJ
randomwalker-info-585	931	13	chain	chain	NN
randomwalker-info-585	931	14	of	of	IN
randomwalker-info-585	931	15	length	length	NN
randomwalker-info-585	931	16	1	1	CD
randomwalker-info-585	931	17	,	,	,
randomwalker-info-585	931	18	let	let	VB
randomwalker-info-585	931	19	’s	-PRON-	PRP
randomwalker-info-585	931	20	consider	consider	VB
randomwalker-info-585	931	21	where	where	WRB
randomwalker-info-585	931	22	the	the	DT
randomwalker-info-585	931	23	transaction	transaction	NN
randomwalker-info-585	931	24	might	may	MD
randomwalker-info-585	931	25	wind	wind	VB
randomwalker-info-585	931	26	up	up	RP
randomwalker-info-585	931	27	:	:	:
randomwalker-info-585	931	28	•	•	VB
randomwalker-info-585	931	29	If	if	IN
randomwalker-info-585	931	30	the	the	DT
randomwalker-info-585	931	31	next	next	JJ
randomwalker-info-585	931	32	block	block	NN
randomwalker-info-585	931	33	is	be	VBZ
randomwalker-info-585	931	34	found	find	VBN
randomwalker-info-585	931	35	by	by	IN
randomwalker-info-585	931	36	the	the	DT
randomwalker-info-585	931	37	selfish	selfish	JJ
randomwalker-info-585	931	38	miner	miner	NN
randomwalker-info-585	931	39	,	,	,
randomwalker-info-585	931	40	then	then	RB
randomwalker-info-585	931	41	this	this	DT
randomwalker-info-585	931	42	transaction	transaction	NN
randomwalker-info-585	931	43	is	be	VBZ
randomwalker-info-585	931	44	contained	contain	VBN
randomwalker-info-585	931	45	in	in	IN
randomwalker-info-585	931	46	a	a	DT
randomwalker-info-585	931	47	block	block	NN
randomwalker-info-585	931	48	of	of	IN
randomwalker-info-585	931	49	the	the	DT
randomwalker-info-585	931	50	selfish	selfish	JJ
randomwalker-info-585	931	51	miner	miner	NN
randomwalker-info-585	931	52	that	that	WDT
randomwalker-info-585	931	53	will	will	MD
randomwalker-info-585	931	54	certainly	certainly	RB
randomwalker-info-585	931	55	be	be	VB
randomwalker-info-585	931	56	included	include	VBN
randomwalker-info-585	931	57	in	in	IN
randomwalker-info-585	931	58	the	the	DT
randomwalker-info-585	931	59	eventual	eventual	JJ
randomwalker-info-585	931	60	longest	long	JJS
randomwalker-info-585	931	61	chain	chain	NN
randomwalker-info-585	931	62	.	.	.
randomwalker-info-585	932	1	This	this	DT
randomwalker-info-585	932	2	happens	happen	VBZ
randomwalker-info-585	932	3	with	with	IN
randomwalker-info-585	932	4	probability	probability	NN
randomwalker-info-585	932	5	α	α	XX
randomwalker-info-585	932	6	.	.	.
randomwalker-info-585	933	1	•	•	VB
randomwalker-info-585	933	2	If	if	IN
randomwalker-info-585	933	3	the	the	DT
randomwalker-info-585	933	4	next	next	JJ
randomwalker-info-585	933	5	block	block	NN
randomwalker-info-585	933	6	is	be	VBZ
randomwalker-info-585	933	7	found	find	VBN
randomwalker-info-585	933	8	by	by	IN
randomwalker-info-585	933	9	the	the	DT
randomwalker-info-585	933	10	honest	honest	JJ
randomwalker-info-585	933	11	miner	miner	NN
randomwalker-info-585	933	12	,	,	,
randomwalker-info-585	933	13	then	then	RB
randomwalker-info-585	933	14	this	this	DT
randomwalker-info-585	933	15	triggers	trigger	VBZ
randomwalker-info-585	933	16	a	a	DT
randomwalker-info-585	933	17	release	release	NN
randomwalker-info-585	933	18	of	of	IN
randomwalker-info-585	933	19	the	the	DT
randomwalker-info-585	933	20	private	private	JJ
randomwalker-info-585	933	21	block	block	NN
randomwalker-info-585	933	22	and	and	CC
randomwalker-info-585	933	23	a	a	DT
randomwalker-info-585	933	24	race	race	NN
randomwalker-info-585	933	25	.	.	.
randomwalker-info-585	934	1	But	but	CC
randomwalker-info-585	934	2	,	,	,
randomwalker-info-585	934	3	the	the	DT
randomwalker-info-585	934	4	racing	race	VBG
randomwalker-info-585	934	5	selfish	selfish	JJ
randomwalker-info-585	934	6	block	block	NN
randomwalker-info-585	934	7	does	do	VBZ
randomwalker-info-585	934	8	not	not	RB
randomwalker-info-585	934	9	contain	contain	VB
randomwalker-info-585	934	10	this	this	DT
randomwalker-info-585	934	11	transaction	transaction	NN
randomwalker-info-585	934	12	,	,	,
randomwalker-info-585	934	13	whereas	whereas	IN
randomwalker-info-585	934	14	the	the	DT
randomwalker-info-585	934	15	racing	race	VBG
randomwalker-info-585	934	16	honest	honest	JJ
randomwalker-info-585	934	17	block	block	NN
randomwalker-info-585	934	18	does	do	VBZ
randomwalker-info-585	934	19	.	.	.
randomwalker-info-585	935	1	So	so	CC
randomwalker-info-585	935	2	if	if	IN
randomwalker-info-585	935	3	the	the	DT
randomwalker-info-585	935	4	racing	race	VBG
randomwalker-info-585	935	5	honest	honest	JJ
randomwalker-info-585	935	6	block	block	NN
randomwalker-info-585	935	7	wins	win	NNS
randomwalker-info-585	935	8	,	,	,
randomwalker-info-585	935	9	the	the	DT
randomwalker-info-585	935	10	honest	honest	JJ
randomwalker-info-585	935	11	miner	miner	NN
randomwalker-info-585	935	12	gets	get	VBZ
randomwalker-info-585	935	13	this	this	DT
randomwalker-info-585	935	14	transaction	transaction	NN
randomwalker-info-585	935	15	.	.	.
randomwalker-info-585	936	1	If	if	IN
randomwalker-info-585	936	2	the	the	DT
randomwalker-info-585	936	3	racing	race	VBG
randomwalker-info-585	936	4	selfish	selfish	JJ
randomwalker-info-585	936	5	block	block	NN
randomwalker-info-585	936	6	wins	win	NNS
randomwalker-info-585	936	7	,	,	,
randomwalker-info-585	936	8	whoever	whoever	WP
randomwalker-info-585	936	9	finds	find	VBZ
randomwalker-info-585	936	10	the	the	DT
randomwalker-info-585	936	11	block	block	NN
randomwalker-info-585	936	12	that	that	WDT
randomwalker-info-585	936	13	ends	end	VBZ
randomwalker-info-585	936	14	the	the	DT
randomwalker-info-585	936	15	race	race	NN
randomwalker-info-585	936	16	gets	get	VBZ
randomwalker-info-585	936	17	this	this	DT
randomwalker-info-585	936	18	transaction	transaction	NN
randomwalker-info-585	936	19	.	.	.
randomwalker-info-585	937	1	So	so	IN
randomwalker-info-585	937	2	the	the	DT
randomwalker-info-585	937	3	selfish	selfish	JJ
randomwalker-info-585	937	4	miner	miner	NN
randomwalker-info-585	937	5	gets	get	VBZ
randomwalker-info-585	937	6	the	the	DT
randomwalker-info-585	937	7	transaction	transaction	NN
randomwalker-info-585	937	8	in	in	IN
randomwalker-info-585	937	9	this	this	DT
randomwalker-info-585	937	10	case	case	NN
randomwalker-info-585	937	11	only	only	RB
randomwalker-info-585	937	12	if	if	IN
randomwalker-info-585	937	13	he	-PRON-	PRP
randomwalker-info-585	937	14	finds	find	VBZ
randomwalker-info-585	937	15	the	the	DT
randomwalker-info-585	937	16	block	block	NN
randomwalker-info-585	937	17	that	that	WDT
randomwalker-info-585	937	18	ends	end	VBZ
randomwalker-info-585	937	19	the	the	DT
randomwalker-info-585	937	20	race	race	NN
randomwalker-info-585	937	21	.	.	.
randomwalker-info-585	938	1	This	this	DT
randomwalker-info-585	938	2	happens	happen	VBZ
randomwalker-info-585	938	3	with	with	IN
randomwalker-info-585	938	4	probability	probability	NN
randomwalker-info-585	938	5	(	(	-LRB-
randomwalker-info-585	938	6	1	1	CD
randomwalker-info-585	938	7	−α)α	−α)α	NNS
randomwalker-info-585	938	8	.	.	.
randomwalker-info-585	939	1	So	so	RB
randomwalker-info-585	939	2	we	-PRON-	PRP
randomwalker-info-585	939	3	see	see	VBP
randomwalker-info-585	939	4	that	that	DT
randomwalker-info-585	939	5	f1	f1	NNP
randomwalker-info-585	939	6	=	=	SYM
randomwalker-info-585	939	7	α	α	NNP
randomwalker-info-585	939	8	+	+	SYM
randomwalker-info-585	939	9	(	(	-LRB-
randomwalker-info-585	939	10	1	1	CD
randomwalker-info-585	939	11	−α)α	−α)α	NNS
randomwalker-info-585	939	12	=	=	SYM
randomwalker-info-585	939	13	α(2	α(2	$
randomwalker-info-585	939	14	−α	−α	CD
randomwalker-info-585	939	15	)	)	-RRB-
randomwalker-info-585	939	16	.	.	.
randomwalker-info-585	940	1	Computing	computing	NN
randomwalker-info-585	940	2	fi	fi	RB
randomwalker-info-585	940	3	,	,	,
randomwalker-info-585	940	4	i	i	PRP
randomwalker-info-585	940	5	>	>	XX
randomwalker-info-585	940	6	1	1	CD
randomwalker-info-585	940	7	.	.	.
randomwalker-info-585	941	1	If	if	IN
randomwalker-info-585	941	2	a	a	DT
randomwalker-info-585	941	3	new	new	JJ
randomwalker-info-585	941	4	transaction	transaction	NN
randomwalker-info-585	941	5	arrives	arrive	VBZ
randomwalker-info-585	941	6	when	when	WRB
randomwalker-info-585	941	7	the	the	DT
randomwalker-info-585	941	8	selfish	selfish	JJ
randomwalker-info-585	941	9	miner	miner	NN
randomwalker-info-585	941	10	has	have	VBZ
randomwalker-info-585	941	11	a	a	DT
randomwalker-info-585	941	12	private	private	JJ
randomwalker-info-585	941	13	chain	chain	NN
randomwalker-info-585	941	14	of	of	IN
randomwalker-info-585	941	15	length	length	NN
randomwalker-info-585	941	16	i	i	PRP
randomwalker-info-585	941	17	>	>	VBP
randomwalker-info-585	941	18	1	1	CD
randomwalker-info-585	941	19	,	,	,
randomwalker-info-585	941	20	let	let	VB
randomwalker-info-585	941	21	’s	-PRON-	PRP
randomwalker-info-585	941	22	again	again	RB
randomwalker-info-585	941	23	consider	consider	VB
randomwalker-info-585	941	24	where	where	WRB
randomwalker-info-585	941	25	this	this	DT
randomwalker-info-585	941	26	transaction	transaction	NN
randomwalker-info-585	941	27	might	may	MD
randomwalker-info-585	941	28	wind	wind	VB
randomwalker-info-585	941	29	up	up	RP
randomwalker-info-585	941	30	:	:	:
randomwalker-info-585	941	31	•	•	VB
randomwalker-info-585	941	32	If	if	IN
randomwalker-info-585	941	33	the	the	DT
randomwalker-info-585	941	34	next	next	JJ
randomwalker-info-585	941	35	block	block	NN
randomwalker-info-585	941	36	is	be	VBZ
randomwalker-info-585	941	37	found	find	VBN
randomwalker-info-585	941	38	by	by	IN
randomwalker-info-585	941	39	the	the	DT
randomwalker-info-585	941	40	selfish	selfish	JJ
randomwalker-info-585	941	41	miner	miner	NN
randomwalker-info-585	941	42	,	,	,
randomwalker-info-585	941	43	then	then	RB
randomwalker-info-585	941	44	this	this	DT
randomwalker-info-585	941	45	transaction	transaction	NN
randomwalker-info-585	941	46	is	be	VBZ
randomwalker-info-585	941	47	contained	contain	VBN
randomwalker-info-585	941	48	in	in	IN
randomwalker-info-585	941	49	a	a	DT
randomwalker-info-585	941	50	block	block	NN
randomwalker-info-585	941	51	of	of	IN
randomwalker-info-585	941	52	the	the	DT
randomwalker-info-585	941	53	selfish	selfish	JJ
randomwalker-info-585	941	54	miner	miner	NN
randomwalker-info-585	941	55	that	that	WDT
randomwalker-info-585	941	56	will	will	MD
randomwalker-info-585	941	57	certainly	certainly	RB
randomwalker-info-585	941	58	be	be	VB
randomwalker-info-585	941	59	included	include	VBN
randomwalker-info-585	941	60	in	in	IN
randomwalker-info-585	941	61	the	the	DT
randomwalker-info-585	941	62	eventual	eventual	JJ
randomwalker-info-585	941	63	longest	long	JJS
randomwalker-info-585	941	64	chain	chain	NN
randomwalker-info-585	941	65	.	.	.
randomwalker-info-585	942	1	This	this	DT
randomwalker-info-585	942	2	happens	happen	VBZ
randomwalker-info-585	942	3	with	with	IN
randomwalker-info-585	942	4	probability	probability	NN
randomwalker-info-585	942	5	α	α	XX
randomwalker-info-585	942	6	.	.	.
randomwalker-info-585	943	1	•	•	VB
randomwalker-info-585	943	2	If	if	IN
randomwalker-info-585	943	3	the	the	DT
randomwalker-info-585	943	4	next	next	JJ
randomwalker-info-585	943	5	i−	i−	NNP
randomwalker-info-585	943	6	1	1	CD
randomwalker-info-585	943	7	blocks	block	NNS
randomwalker-info-585	943	8	are	be	VBP
randomwalker-info-585	943	9	all	all	DT
randomwalker-info-585	943	10	found	find	VBN
randomwalker-info-585	943	11	by	by	IN
randomwalker-info-585	943	12	the	the	DT
randomwalker-info-585	943	13	honest	honest	JJ
randomwalker-info-585	943	14	miner	miner	NN
randomwalker-info-585	943	15	,	,	,
randomwalker-info-585	943	16	then	then	RB
randomwalker-info-585	943	17	this	this	DT
randomwalker-info-585	943	18	triggers	trigger	VBZ
randomwalker-info-585	943	19	a	a	DT
randomwalker-info-585	943	20	release	release	NN
randomwalker-info-585	943	21	of	of	IN
randomwalker-info-585	943	22	the	the	DT
randomwalker-info-585	943	23	private	private	JJ
randomwalker-info-585	943	24	chain	chain	NN
randomwalker-info-585	943	25	,	,	,
randomwalker-info-585	943	26	and	and	CC
randomwalker-info-585	943	27	all	all	PDT
randomwalker-info-585	943	28	those	those	DT
randomwalker-info-585	943	29	blocks	block	NNS
randomwalker-info-585	943	30	found	find	VBN
randomwalker-info-585	943	31	by	by	IN
randomwalker-info-585	943	32	the	the	DT
randomwalker-info-585	943	33	honest	honest	JJ
randomwalker-info-585	943	34	miner	miner	NN
randomwalker-info-585	943	35	are	be	VBP
randomwalker-info-585	943	36	immediately	immediately	RB
randomwalker-info-585	943	37	ignored	ignore	VBN
randomwalker-info-585	943	38	.	.	.
randomwalker-info-585	944	1	At	at	IN
randomwalker-info-585	944	2	this	this	DT
randomwalker-info-585	944	3	point	point	NN
randomwalker-info-585	944	4	,	,	,
randomwalker-info-585	944	5	the	the	DT
randomwalker-info-585	944	6	transaction	transaction	NN
randomwalker-info-585	944	7	has	have	VBZ
randomwalker-info-585	944	8	still	still	RB
randomwalker-info-585	944	9	not	not	RB
randomwalker-info-585	944	10	been	be	VBN
randomwalker-info-585	944	11	included	include	VBN
randomwalker-info-585	944	12	in	in	IN
randomwalker-info-585	944	13	any	any	DT
randomwalker-info-585	944	14	block	block	NN
randomwalker-info-585	944	15	,	,	,
randomwalker-info-585	944	16	so	so	CC
randomwalker-info-585	944	17	it	-PRON-	PRP
randomwalker-info-585	944	18	is	be	VBZ
randomwalker-info-585	944	19	as	as	IN
randomwalker-info-585	944	20	if	if	IN
randomwalker-info-585	944	21	the	the	DT
randomwalker-info-585	944	22	transaction	transaction	NN
randomwalker-info-585	944	23	arrived	arrive	VBD
randomwalker-info-585	944	24	in	in	IN
randomwalker-info-585	944	25	state	state	NN
randomwalker-info-585	944	26	0′′.	0′′.	.
randomwalker-info-585	945	1	So	so	IN
randomwalker-info-585	945	2	the	the	DT
randomwalker-info-585	945	3	selfish	selfish	JJ
randomwalker-info-585	945	4	miner	miner	NN
randomwalker-info-585	945	5	gets	get	VBZ
randomwalker-info-585	945	6	this	this	DT
randomwalker-info-585	945	7	transaction	transaction	NN
randomwalker-info-585	945	8	with	with	IN
randomwalker-info-585	945	9	probability	probability	NN
randomwalker-info-585	945	10	f0′′	f0′′	NNS
randomwalker-info-585	945	11	in	in	IN
randomwalker-info-585	945	12	this	this	DT
randomwalker-info-585	945	13	case	case	NN
randomwalker-info-585	945	14	.	.	.
randomwalker-info-585	946	1	•	•	VB
randomwalker-info-585	946	2	If	if	IN
randomwalker-info-585	946	3	any	any	DT
randomwalker-info-585	946	4	of	of	IN
randomwalker-info-585	946	5	the	the	DT
randomwalker-info-585	946	6	next	next	JJ
randomwalker-info-585	946	7	i−1	i−1	NN
randomwalker-info-585	946	8	blocks	block	NNS
randomwalker-info-585	946	9	are	be	VBP
randomwalker-info-585	946	10	found	find	VBN
randomwalker-info-585	946	11	by	by	IN
randomwalker-info-585	946	12	the	the	DT
randomwalker-info-585	946	13	selfish	selfish	JJ
randomwalker-info-585	946	14	miner	miner	NN
randomwalker-info-585	946	15	,	,	,
randomwalker-info-585	946	16	then	then	RB
randomwalker-info-585	946	17	this	this	DT
randomwalker-info-585	946	18	block	block	NN
randomwalker-info-585	946	19	is	be	VBZ
randomwalker-info-585	946	20	certainly	certainly	RB
randomwalker-info-585	946	21	included	include	VBN
randomwalker-info-585	946	22	in	in	IN
randomwalker-info-585	946	23	the	the	DT
randomwalker-info-585	946	24	eventual	eventual	JJ
randomwalker-info-585	946	25	longest	long	JJS
randomwalker-info-585	946	26	chain	chain	NN
randomwalker-info-585	946	27	,	,	,
randomwalker-info-585	946	28	because	because	IN
randomwalker-info-585	946	29	it	-PRON-	PRP
randomwalker-info-585	946	30	is	be	VBZ
randomwalker-info-585	946	31	found	find	VBN
randomwalker-info-585	946	32	when	when	WRB
randomwalker-info-585	946	33	the	the	DT
randomwalker-info-585	946	34	selfish	selfish	JJ
randomwalker-info-585	946	35	miner	miner	NN
randomwalker-info-585	946	36	has	have	VBZ
randomwalker-info-585	946	37	a	a	DT
randomwalker-info-585	946	38	lead	lead	NN
randomwalker-info-585	946	39	of	of	IN
randomwalker-info-585	946	40	at	at	RB
randomwalker-info-585	946	41	least	least	RBS
randomwalker-info-585	946	42	two	two	CD
randomwalker-info-585	946	43	.	.	.
randomwalker-info-585	947	1	So	so	RB
randomwalker-info-585	947	2	we	-PRON-	PRP
randomwalker-info-585	947	3	see	see	VBP
randomwalker-info-585	947	4	that	that	IN
randomwalker-info-585	947	5	the	the	DT
randomwalker-info-585	947	6	only	only	JJ
randomwalker-info-585	947	7	way	way	NN
randomwalker-info-585	947	8	the	the	DT
randomwalker-info-585	947	9	selfish	selfish	JJ
randomwalker-info-585	947	10	miner	miner	NN
randomwalker-info-585	947	11	might	may	MD
randomwalker-info-585	947	12	possibly	possibly	RB
randomwalker-info-585	947	13	lose	lose	VB
randomwalker-info-585	947	14	the	the	DT
randomwalker-info-585	947	15	transaction	transaction	NN
randomwalker-info-585	947	16	is	be	VBZ
randomwalker-info-585	947	17	if	if	IN
randomwalker-info-585	947	18	each	each	DT
randomwalker-info-585	947	19	of	of	IN
randomwalker-info-585	947	20	the	the	DT
randomwalker-info-585	947	21	next	next	JJ
randomwalker-info-585	947	22	i−	i−	NNP
randomwalker-info-585	947	23	1	1	CD
randomwalker-info-585	947	24	blocks	block	NNS
randomwalker-info-585	947	25	are	be	VBP
randomwalker-info-585	947	26	found	find	VBN
randomwalker-info-585	947	27	by	by	IN
randomwalker-info-585	947	28	the	the	DT
randomwalker-info-585	947	29	honest	honest	JJ
randomwalker-info-585	947	30	miner	miner	NN
randomwalker-info-585	947	31	,	,	,
randomwalker-info-585	947	32	and	and	CC
randomwalker-info-585	947	33	even	even	RB
randomwalker-info-585	947	34	in	in	IN
randomwalker-info-585	947	35	this	this	DT
randomwalker-info-585	947	36	case	case	NN
randomwalker-info-585	947	37	the	the	DT
randomwalker-info-585	947	38	selfish	selfish	JJ
randomwalker-info-585	947	39	miner	miner	NN
randomwalker-info-585	947	40	still	still	RB
randomwalker-info-585	947	41	wins	win	VBZ
randomwalker-info-585	947	42	the	the	DT
randomwalker-info-585	947	43	transaction	transaction	NN
randomwalker-info-585	947	44	with	with	IN
randomwalker-info-585	947	45	probability	probability	NN
randomwalker-info-585	947	46	f0′′	f0′′	NNP
randomwalker-info-585	947	47	=	=	SYM
randomwalker-info-585	947	48	α	α	XX
randomwalker-info-585	947	49	.	.	.
randomwalker-info-585	948	1	So	so	RB
randomwalker-info-585	948	2	the	the	DT
randomwalker-info-585	948	3	honest	honest	JJ
randomwalker-info-585	948	4	miner	miner	NN
randomwalker-info-585	948	5	only	only	RB
randomwalker-info-585	948	6	wins	win	VBZ
randomwalker-info-585	948	7	this	this	DT
randomwalker-info-585	948	8	transaction	transaction	NN
randomwalker-info-585	948	9	with	with	IN
randomwalker-info-585	948	10	probability	probability	NN
randomwalker-info-585	948	11	(	(	-LRB-
randomwalker-info-585	948	12	1	1	CD
randomwalker-info-585	948	13	−α)i−1(1	−α)i−1(1	NNP
randomwalker-info-585	948	14	−α	−α	CD
randomwalker-info-585	948	15	)	)	-RRB-
randomwalker-info-585	948	16	,	,	,
randomwalker-info-585	948	17	and	and	CC
randomwalker-info-585	948	18	we	-PRON-	PRP
randomwalker-info-585	948	19	have	have	VBP
randomwalker-info-585	948	20	fi	fi	IN
randomwalker-info-585	948	21	=	=	SYM
randomwalker-info-585	948	22	1	1	CD
randomwalker-info-585	948	23	−	−	NNP
randomwalker-info-585	948	24	(	(	-LRB-
randomwalker-info-585	948	25	1	1	CD
randomwalker-info-585	948	26	−α)i	−α)i	NNP
randomwalker-info-585	948	27	.	.	.
randomwalker-info-585	949	1	Now	now	RB
randomwalker-info-585	949	2	,	,	,
randomwalker-info-585	949	3	we	-PRON-	PRP
randomwalker-info-585	949	4	just	just	RB
randomwalker-info-585	949	5	have	have	VBP
randomwalker-info-585	949	6	to	to	TO
randomwalker-info-585	949	7	sum	sum	VB
randomwalker-info-585	949	8	/	/	SYM
randomwalker-info-585	949	9	integrate	integrate	VB
randomwalker-info-585	949	10	over	over	IN
randomwalker-info-585	949	11	all	all	DT
randomwalker-info-585	949	12	states	state	NNS
randomwalker-info-585	949	13	and	and	CC
randomwalker-info-585	949	14	success	success	NN
randomwalker-info-585	949	15	probabilities	probability	NNS
randomwalker-info-585	949	16	to	to	TO
randomwalker-info-585	949	17	compute	compute	VB
randomwalker-info-585	949	18	the	the	DT
randomwalker-info-585	949	19	fraction	fraction	NN
randomwalker-info-585	949	20	of	of	IN
randomwalker-info-585	949	21	transactions	transaction	NNS
randomwalker-info-585	949	22	that	that	WDT
randomwalker-info-585	949	23	go	go	VBP
randomwalker-info-585	949	24	to	to	IN
randomwalker-info-585	949	25	the	the	DT
randomwalker-info-585	949	26	selfish	selfish	JJ
randomwalker-info-585	949	27	miner	miner	NN
randomwalker-info-585	949	28	.	.	.
randomwalker-info-585	950	1	f0′p0′	f0′p0′	NFP
randomwalker-info-585	950	2	=	=	SYM
randomwalker-info-585	950	3	α(1	α(1	ADD
randomwalker-info-585	950	4	−α)p1	−α)p1	NNP
randomwalker-info-585	950	5	.	.	.
randomwalker-info-585	951	1	f0′′p0′′	f0′′p0′′	NNP
randomwalker-info-585	951	2	=	=	SYM
randomwalker-info-585	951	3	α	α	NNP
randomwalker-info-585	951	4	2	2	CD
randomwalker-info-585	951	5	p1	p1	NN
randomwalker-info-585	951	6	.	.	.
randomwalker-info-585	952	1	f1p1	f1p1	NN
randomwalker-info-585	952	2	=	=	SYM
randomwalker-info-585	952	3	α(2	α(2	$
randomwalker-info-585	952	4	−α)p1	−α)p1	NN
randomwalker-info-585	952	5	.	.	.
randomwalker-info-585	953	1	fipi	fipi	NNP
randomwalker-info-585	953	2	=	=	SYM
randomwalker-info-585	953	3	(	(	-LRB-
randomwalker-info-585	953	4	1	1	CD
randomwalker-info-585	953	5	−	−	NNP
randomwalker-info-585	953	6	(	(	-LRB-
randomwalker-info-585	953	7	1	1	CD
randomwalker-info-585	953	8	−α)i)αi−1p1	−α)i)αi−1p1	CD
randomwalker-info-585	953	9	(	(	-LRB-
randomwalker-info-585	953	10	1	1	CD
randomwalker-info-585	953	11	−α)i−1	−α)i−1	NNP
randomwalker-info-585	953	12	,	,	,
randomwalker-info-585	953	13	i	i	PRP
randomwalker-info-585	953	14	>	>	VBP
randomwalker-info-585	953	15	1	1	CD
randomwalker-info-585	953	16	.	.	.
randomwalker-info-585	953	17	f0(x)p0(x	f0(x)p0(x	NNP
randomwalker-info-585	953	18	)	)	-RRB-
randomwalker-info-585	953	19	=	=	NFP
randomwalker-info-585	953	20	p1e	p1e	NNP
randomwalker-info-585	953	21	−xdx	−xdx	NN
randomwalker-info-585	953	22	1	1	CD
randomwalker-info-585	953	23	−e−β	−e−β	NN
randomwalker-info-585	953	24	,	,	,
randomwalker-info-585	953	25	x	x	LS
randomwalker-info-585	953	26	≥	≥	UH
randomwalker-info-585	953	27	β	β	NN
randomwalker-info-585	953	28	.	.	.
randomwalker-info-585	953	29	f0(x)p0(x	f0(x)p0(x	NNP
randomwalker-info-585	953	30	)	)	-RRB-
randomwalker-info-585	953	31	=	=	NFP
randomwalker-info-585	953	32	p1e	p1e	NNP
randomwalker-info-585	953	33	−xdx(e−β+x	−xdx(e−β+x	JJ
randomwalker-info-585	953	34	+	+	SYM
randomwalker-info-585	953	35	α(1	α(1	NFP
randomwalker-info-585	953	36	−e−β+x	−e−β+x	NN
randomwalker-info-585	953	37	)	)	-RRB-
randomwalker-info-585	953	38	+	+	CC
randomwalker-info-585	953	39	(	(	-LRB-
randomwalker-info-585	953	40	1	1	CD
randomwalker-info-585	953	41	−α)(1	−α)(1	CD
randomwalker-info-585	953	42	−e−β+x)(α	−e−β+x)(α	NNP
randomwalker-info-585	953	43	+	+	NFP
randomwalker-info-585	953	44	(	(	-LRB-
randomwalker-info-585	953	45	1	1	CD
randomwalker-info-585	953	46	−α)γ	−α)γ	NNP
randomwalker-info-585	953	47	)	)	-RRB-
randomwalker-info-585	953	48	)	)	-RRB-
randomwalker-info-585	953	49	1	1	CD
randomwalker-info-585	953	50	−e−β	−e−β	NN
randomwalker-info-585	953	51	,	,	,
randomwalker-info-585	953	52	x	x	NNP
randomwalker-info-585	953	53	≤	≤	NNP
randomwalker-info-585	953	54	β	β	NNP
randomwalker-info-585	953	55	.	.	.
randomwalker-info-585	954	1	∑	∑	NFP
randomwalker-info-585	954	2	i>1	i>1	NN
randomwalker-info-585	954	3	αi−1	αi−1	.
randomwalker-info-585	954	4	(	(	-LRB-
randomwalker-info-585	954	5	1	1	CD
randomwalker-info-585	954	6	−α)i−1	−α)i−1	NNPS
randomwalker-info-585	954	7	=	=	SYM
randomwalker-info-585	954	8	α	α	NNP
randomwalker-info-585	954	9	1	1	CD
randomwalker-info-585	954	10	−	−	NNP
randomwalker-info-585	954	11	2α	2α	CD
randomwalker-info-585	954	12	.	.	.
randomwalker-info-585	955	1	∑	∑	NFP
randomwalker-info-585	955	2	i>1	i>1	NN
randomwalker-info-585	955	3	α	α	NNP
randomwalker-info-585	955	4	i−1	i−1	NNP
randomwalker-info-585	955	5	=	=	SYM
randomwalker-info-585	955	6	α	α	NNP
randomwalker-info-585	955	7	1	1	CD
randomwalker-info-585	955	8	−α	−α	CD
randomwalker-info-585	955	9	.	.	.
randomwalker-info-585	956	1	⇒	⇒	NNP
randomwalker-info-585	956	2	∑	∑	.
randomwalker-info-585	956	3	i>1	i>1	NN
randomwalker-info-585	956	4	fipi	fipi	NN
randomwalker-info-585	956	5	=	=	SYM
randomwalker-info-585	956	6	p1	p1	NN
randomwalker-info-585	956	7	(	(	-LRB-
randomwalker-info-585	956	8	∑	∑	.
randomwalker-info-585	956	9	i>1	i>1	NN
randomwalker-info-585	956	10	αi−1	αi−1	.
randomwalker-info-585	956	11	(	(	-LRB-
randomwalker-info-585	956	12	1	1	CD
randomwalker-info-585	956	13	−α)i−1	−α)i−1	NNP
randomwalker-info-585	956	14	−	−	NNP
randomwalker-info-585	956	15	(	(	-LRB-
randomwalker-info-585	956	16	1	1	CD
randomwalker-info-585	956	17	−α	−α	CD
randomwalker-info-585	956	18	)	)	-RRB-
randomwalker-info-585	956	19	∑	∑	.
randomwalker-info-585	956	20	i>1	i>1	NN
randomwalker-info-585	956	21	α	α	NNP
randomwalker-info-585	956	22	i−1	i−1	NN
randomwalker-info-585	956	23	)	)	-RRB-
randomwalker-info-585	956	24	=	=	NFP
randomwalker-info-585	956	25	(	(	-LRB-
randomwalker-info-585	956	26	α	α	DT
randomwalker-info-585	956	27	1	1	CD
randomwalker-info-585	956	28	−	−	NNP
randomwalker-info-585	956	29	2α	2α	CD
randomwalker-info-585	956	30	−α	−α	CD
randomwalker-info-585	956	31	)	)	-RRB-
randomwalker-info-585	956	32	p1	p1	NN
randomwalker-info-585	956	33	=	=	NFP
randomwalker-info-585	956	34	2α2p1	2α2p1	CD
randomwalker-info-585	956	35	1	1	CD
randomwalker-info-585	956	36	−	−	NNP
randomwalker-info-585	956	37	2α	2α	CD
randomwalker-info-585	956	38	.	.	.
randomwalker-info-585	957	1	∫	∫	NFP
randomwalker-info-585	957	2	x≥β	x≥β	NNP
randomwalker-info-585	957	3	f0(x)p0(x	f0(x)p0(x	NNP
randomwalker-info-585	957	4	)	)	-RRB-
randomwalker-info-585	957	5	=	=	NFP
randomwalker-info-585	957	6	p1	p1	NN
randomwalker-info-585	957	7	1	1	CD
randomwalker-info-585	957	8	−e−β	−e−β	NNP
randomwalker-info-585	957	9	∫	∫	XX
randomwalker-info-585	957	10	x≥β	x≥β	NNP
randomwalker-info-585	957	11	e	e	NNP
randomwalker-info-585	957	12	−x	−x	CD
randomwalker-info-585	957	13	dx	dx	NNP
randomwalker-info-585	957	14	=	=	FW
randomwalker-info-585	957	15	e−βp1	e−βp1	NNP
randomwalker-info-585	957	16	1	1	CD
randomwalker-info-585	957	17	−e−β	−e−β	NN
randomwalker-info-585	957	18	.	.	.
randomwalker-info-585	958	1	∫	∫	NFP
randomwalker-info-585	958	2	x=0	x=0	NNP
randomwalker-info-585	958	3	β	β	NNP
randomwalker-info-585	958	4	f0(x)p0(x	f0(x)p0(x	NNP
randomwalker-info-585	958	5	)	)	-RRB-
randomwalker-info-585	958	6	=	=	NFP
randomwalker-info-585	958	7	∫	∫	NFP
randomwalker-info-585	958	8	β	β	NNP
randomwalker-info-585	958	9	x=0	x=0	NNP
randomwalker-info-585	958	10	p1	p1	NNP
randomwalker-info-585	958	11	1	1	CD
randomwalker-info-585	958	12	−e−β	−e−β	NN
randomwalker-info-585	958	13	(	(	-LRB-
randomwalker-info-585	958	14	(	(	-LRB-
randomwalker-info-585	958	15	e	e	NNP
randomwalker-info-585	958	16	−β	−β	NNP
randomwalker-info-585	958	17	−αe−β	−αe−β	NNP
randomwalker-info-585	958	18	−	−	NNP
randomwalker-info-585	958	19	(	(	-LRB-
randomwalker-info-585	958	20	1	1	CD
randomwalker-info-585	958	21	−α)(α	−α)(α	NNP
randomwalker-info-585	958	22	+	+	NFP
randomwalker-info-585	958	23	(	(	-LRB-
randomwalker-info-585	958	24	1	1	CD
randomwalker-info-585	958	25	−α)γ)e−β	−α)γ)e−β	NN
randomwalker-info-585	958	26	)	)	-RRB-
randomwalker-info-585	958	27	+	+	CC
randomwalker-info-585	958	28	(	(	-LRB-
randomwalker-info-585	958	29	αe	αe	UH
randomwalker-info-585	958	30	−x	−x	CD
randomwalker-info-585	958	31	+	+	SYM
randomwalker-info-585	958	32	(	(	-LRB-
randomwalker-info-585	958	33	1	1	CD
randomwalker-info-585	958	34	−α)(α	−α)(α	NNP
randomwalker-info-585	958	35	+	+	NFP
randomwalker-info-585	958	36	(	(	-LRB-
randomwalker-info-585	958	37	1	1	CD
randomwalker-info-585	958	38	−α)γ)e−x	−α)γ)e−x	NNP
randomwalker-info-585	958	39	)	)	-RRB-
randomwalker-info-585	958	40	)	)	-RRB-
randomwalker-info-585	958	41	dx	dx	NNP
randomwalker-info-585	958	42	.	.	.
randomwalker-info-585	959	1	=	=	NFP
randomwalker-info-585	959	2	p1βe	p1βe	NNP
randomwalker-info-585	959	3	−β(1	−β(1	NNP
randomwalker-info-585	959	4	−α−	−α−	NN
randomwalker-info-585	959	5	(	(	-LRB-
randomwalker-info-585	959	6	1	1	CD
randomwalker-info-585	959	7	−α)(α	−α)(α	NNP
randomwalker-info-585	959	8	+	+	NFP
randomwalker-info-585	959	9	(	(	-LRB-
randomwalker-info-585	959	10	1	1	CD
randomwalker-info-585	959	11	−α)γ	−α)γ	NNP
randomwalker-info-585	959	12	)	)	-RRB-
randomwalker-info-585	959	13	)	)	-RRB-
randomwalker-info-585	959	14	1	1	CD
randomwalker-info-585	959	15	−e−β	−e−β	NN
randomwalker-info-585	959	16	+	+	CC
randomwalker-info-585	959	17	p1(1	p1(1	.
randomwalker-info-585	959	18	−e−β)(α	−e−β)(α	NNP
randomwalker-info-585	959	19	+	+	NFP
randomwalker-info-585	959	20	(	(	-LRB-
randomwalker-info-585	959	21	1	1	CD
randomwalker-info-585	959	22	−α)(α	−α)(α	NNS
randomwalker-info-585	959	23	+	+	NFP
randomwalker-info-585	959	24	(	(	-LRB-
randomwalker-info-585	959	25	1	1	CD
randomwalker-info-585	959	26	−α)γ	−α)γ	NNP
randomwalker-info-585	959	27	)	)	-RRB-
randomwalker-info-585	959	28	)	)	-RRB-
randomwalker-info-585	959	29	1	1	CD
randomwalker-info-585	959	30	−e−β	−e−β	NN
randomwalker-info-585	959	31	=	=	SYM
randomwalker-info-585	959	32	p1	p1	NN
randomwalker-info-585	959	33	(	(	-LRB-
randomwalker-info-585	959	34	βe−β(1	βe−β(1	CD
randomwalker-info-585	959	35	−α)(1	−α)(1	VBN
randomwalker-info-585	959	36	−α−	−α−	NNP
randomwalker-info-585	959	37	(	(	-LRB-
randomwalker-info-585	959	38	1	1	CD
randomwalker-info-585	959	39	−α)γ	−α)γ	NNP
randomwalker-info-585	959	40	)	)	-RRB-
randomwalker-info-585	959	41	+	+	CC
randomwalker-info-585	959	42	(	(	-LRB-
randomwalker-info-585	959	43	1	1	CD
randomwalker-info-585	959	44	−e−β)(α	−e−β)(α	NNP
randomwalker-info-585	959	45	+	+	NFP
randomwalker-info-585	959	46	(	(	-LRB-
randomwalker-info-585	959	47	1	1	CD
randomwalker-info-585	959	48	−α)(α	−α)(α	NNS
randomwalker-info-585	959	49	+	+	NFP
randomwalker-info-585	959	50	(	(	-LRB-
randomwalker-info-585	959	51	1	1	CD
randomwalker-info-585	959	52	−α)γ	−α)γ	NNP
randomwalker-info-585	959	53	)	)	-RRB-
randomwalker-info-585	959	54	)	)	-RRB-
randomwalker-info-585	959	55	)	)	-RRB-
randomwalker-info-585	959	56	1	1	CD
randomwalker-info-585	959	57	−e−β	−e−β	NN
randomwalker-info-585	959	58	.	.	.
randomwalker-info-585	960	1	Summing	sum	VBG
randomwalker-info-585	960	2	everything	everything	NN
randomwalker-info-585	960	3	together	together	RB
randomwalker-info-585	960	4	,	,	,
randomwalker-info-585	960	5	we	-PRON-	PRP
randomwalker-info-585	960	6	then	then	RB
randomwalker-info-585	960	7	get:∫	get:∫	NNP
randomwalker-info-585	960	8	∞	∞	NNP
randomwalker-info-585	960	9	0	0	NFP
randomwalker-info-585	960	10	p0(x)f0(x	p0(x)f0(x	NN
randomwalker-info-585	960	11	)	)	-RRB-
randomwalker-info-585	960	12	+	+	CC
randomwalker-info-585	960	13	∑	∑	.
randomwalker-info-585	960	14	i>1	i>1	NN
randomwalker-info-585	960	15	pifi	pifi	NN
randomwalker-info-585	960	16	+	+	CC
randomwalker-info-585	960	17	p0′f0′	p0′f0′	XX
randomwalker-info-585	960	18	+	+	SYM
randomwalker-info-585	960	19	p0′′f0′′	p0′′f0′′	NNP
randomwalker-info-585	960	20	+	+	SYM
randomwalker-info-585	960	21	p1f1	p1f1	NNS
randomwalker-info-585	960	22	=	=	FW
randomwalker-info-585	960	23	(	(	-LRB-
randomwalker-info-585	960	24	βe−β(1	βe−β(1	CD
randomwalker-info-585	960	25	−α)(1	−α)(1	VBN
randomwalker-info-585	960	26	−α−	−α−	NNP
randomwalker-info-585	960	27	(	(	-LRB-
randomwalker-info-585	960	28	1	1	CD
randomwalker-info-585	960	29	−α)γ	−α)γ	NNP
randomwalker-info-585	960	30	)	)	-RRB-
randomwalker-info-585	960	31	1	1	CD
randomwalker-info-585	960	32	−e−β	−e−β	NN
randomwalker-info-585	960	33	+	+	SYM
randomwalker-info-585	960	34	α	α	NN
randomwalker-info-585	960	35	+	+	SYM
randomwalker-info-585	960	36	(	(	-LRB-
randomwalker-info-585	960	37	1	1	CD
randomwalker-info-585	960	38	−α)(α	−α)(α	NNS
randomwalker-info-585	960	39	+	+	NFP
randomwalker-info-585	960	40	(	(	-LRB-
randomwalker-info-585	960	41	1	1	CD
randomwalker-info-585	960	42	−α)γ	−α)γ	NNP
randomwalker-info-585	960	43	)	)	-RRB-
randomwalker-info-585	960	44	+	+	CC
randomwalker-info-585	960	45	e−β	e−β	NN
randomwalker-info-585	960	46	1	1	CD
randomwalker-info-585	960	47	−e−β	−e−β	NN
randomwalker-info-585	960	48	+	+	CC
randomwalker-info-585	960	49	2α2	2α2	CD
randomwalker-info-585	960	50	1	1	CD
randomwalker-info-585	960	51	−	−	NNP
randomwalker-info-585	960	52	2α	2α	CD
randomwalker-info-585	960	53	+	+	SYM
randomwalker-info-585	960	54	3α−α2	3α−α2	CD
randomwalker-info-585	960	55	)	)	-RRB-
randomwalker-info-585	960	56	p1	p1	NN
randomwalker-info-585	960	57	.	.	.
randomwalker-info-585	961	1	This	this	DT
randomwalker-info-585	961	2	can	can	MD
randomwalker-info-585	961	3	be	be	VB
randomwalker-info-585	961	4	further	further	RB
randomwalker-info-585	961	5	simplified	simplify	VBN
randomwalker-info-585	961	6	to	to	TO
randomwalker-info-585	961	7	yield	yield	VB
randomwalker-info-585	961	8	the	the	DT
randomwalker-info-585	961	9	bound	bound	NN
randomwalker-info-585	961	10	provided	provide	VBN
randomwalker-info-585	961	11	in	in	IN
randomwalker-info-585	961	12	the	the	DT
randomwalker-info-585	961	13	paper	paper	NN
randomwalker-info-585	961	14	.	.	.
randomwalker-info-585	962	1	(	(	-LRB-
randomwalker-info-585	962	2	βe−β(1	βe−β(1	CD
randomwalker-info-585	962	3	−α)(1	−α)(1	VBN
randomwalker-info-585	962	4	−α−	−α−	NNP
randomwalker-info-585	962	5	(	(	-LRB-
randomwalker-info-585	962	6	1	1	CD
randomwalker-info-585	962	7	−α)γ	−α)γ	NNP
randomwalker-info-585	962	8	)	)	-RRB-
randomwalker-info-585	962	9	1	1	CD
randomwalker-info-585	962	10	−e−β	−e−β	NN
randomwalker-info-585	962	11	+	+	SYM
randomwalker-info-585	962	12	α	α	NN
randomwalker-info-585	962	13	+	+	SYM
randomwalker-info-585	962	14	(	(	-LRB-
randomwalker-info-585	962	15	1	1	CD
randomwalker-info-585	962	16	−α)(α	−α)(α	NNS
randomwalker-info-585	962	17	+	+	NFP
randomwalker-info-585	962	18	(	(	-LRB-
randomwalker-info-585	962	19	1	1	CD
randomwalker-info-585	962	20	−α)γ	−α)γ	NNP
randomwalker-info-585	962	21	)	)	-RRB-
randomwalker-info-585	962	22	+	+	CC
randomwalker-info-585	962	23	e−β	e−β	NN
randomwalker-info-585	962	24	1	1	CD
randomwalker-info-585	962	25	−e−β	−e−β	NN
randomwalker-info-585	962	26	+	+	CC
randomwalker-info-585	962	27	2α2	2α2	CD
randomwalker-info-585	962	28	1	1	CD
randomwalker-info-585	962	29	−	−	NNP
randomwalker-info-585	962	30	2α	2α	CD
randomwalker-info-585	962	31	+	+	SYM
randomwalker-info-585	962	32	3α−α2	3α−α2	CD
randomwalker-info-585	962	33	)	)	-RRB-
randomwalker-info-585	962	34	p1	p1	NN
randomwalker-info-585	962	35	.	.	.
randomwalker-info-585	963	1	=	=	SYM
randomwalker-info-585	963	2	1	1	CD
randomwalker-info-585	963	3	+	+	SYM
randomwalker-info-585	963	4	β(1	β(1	NNS
randomwalker-info-585	963	5	−α)2(1	−α)2(1	NNP
randomwalker-info-585	963	6	−γ	−γ	NNP
randomwalker-info-585	963	7	)	)	-RRB-
randomwalker-info-585	963	8	eβ	eβ	NNP
randomwalker-info-585	963	9	−	−	NNP
randomwalker-info-585	963	10	1	1	CD
randomwalker-info-585	963	11	+	+	CC
randomwalker-info-585	963	12	4α	4α	CD
randomwalker-info-585	963	13	+	+	SYM
randomwalker-info-585	963	14	(	(	-LRB-
randomwalker-info-585	963	15	1	1	CD
randomwalker-info-585	963	16	−α)(α	−α)(α	NNS
randomwalker-info-585	963	17	+	+	NFP
randomwalker-info-585	963	18	(	(	-LRB-
randomwalker-info-585	963	19	1	1	CD
randomwalker-info-585	963	20	−α)γ	−α)γ	NNP
randomwalker-info-585	963	21	)	)	-RRB-
randomwalker-info-585	963	22	+	+	CC
randomwalker-info-585	963	23	2α2	2α2	CD
randomwalker-info-585	963	24	1	1	CD
randomwalker-info-585	963	25	−	−	NNP
randomwalker-info-585	963	26	2α	2α	CD
randomwalker-info-585	963	27	−α2	−α2	NNP
randomwalker-info-585	963	28	.	.	.