id	sid	tid	token	lemma	pos
xd07gq7038v	1	1	in	in	ADP
xd07gq7038v	1	2	mathematics	mathematic	NOUN
xd07gq7038v	1	3	,	,	PUNCT
xd07gq7038v	1	4	one	one	NUM
xd07gq7038v	1	5	often	often	ADV
xd07gq7038v	1	6	tries	try	VERB
xd07gq7038v	1	7	to	to	PART
xd07gq7038v	1	8	classify	classify	VERB
xd07gq7038v	1	9	some	some	DET
xd07gq7038v	1	10	collection	collection	NOUN
xd07gq7038v	1	11	of	of	ADP
xd07gq7038v	1	12	objects	object	NOUN
xd07gq7038v	1	13	up	up	ADP
xd07gq7038v	1	14	to	to	ADP
xd07gq7038v	1	15	isomorphism	isomorphism	NOUN
xd07gq7038v	1	16	.	.	PUNCT
xd07gq7038v	2	1	in	in	ADP
xd07gq7038v	2	2	mathematical	mathematical	ADJ
xd07gq7038v	2	3	logic	logic	NOUN
xd07gq7038v	2	4	,	,	PUNCT
xd07gq7038v	2	5	we	we	PRON
xd07gq7038v	2	6	can	can	AUX
xd07gq7038v	2	7	explore	explore	VERB
xd07gq7038v	2	8	the	the	DET
xd07gq7038v	2	9	complexity	complexity	NOUN
xd07gq7038v	2	10	of	of	ADP
xd07gq7038v	2	11	that	that	DET
xd07gq7038v	2	12	classification	classification	NOUN
xd07gq7038v	2	13	.	.	PUNCT
xd07gq7038v	3	1	a	a	DET
xd07gq7038v	3	2	structure	structure	NOUN
xd07gq7038v	3	3	consists	consist	VERB
xd07gq7038v	3	4	of	of	ADP
xd07gq7038v	3	5	a	a	DET
xd07gq7038v	3	6	universe	universe	NOUN
xd07gq7038v	3	7	and	and	CCONJ
xd07gq7038v	3	8	an	an	DET
xd07gq7038v	3	9	interpretation	interpretation	NOUN
xd07gq7038v	3	10	of	of	ADP
xd07gq7038v	3	11	a	a	DET
xd07gq7038v	3	12	language	language	NOUN
xd07gq7038v	3	13	,	,	PUNCT
xd07gq7038v	3	14	where	where	SCONJ
xd07gq7038v	3	15	the	the	DET
xd07gq7038v	3	16	language	language	NOUN
xd07gq7038v	3	17	has	have	VERB
xd07gq7038v	3	18	symbols	symbol	NOUN
xd07gq7038v	3	19	representing	represent	VERB
xd07gq7038v	3	20	constants	constant	NOUN
xd07gq7038v	3	21	,	,	PUNCT
xd07gq7038v	3	22	operations	operation	NOUN
xd07gq7038v	3	23	,	,	PUNCT
xd07gq7038v	3	24	and	and	CCONJ
xd07gq7038v	3	25	relations	relation	NOUN
xd07gq7038v	3	26	.	.	PUNCT
xd07gq7038v	4	1	we	we	PRON
xd07gq7038v	4	2	consider	consider	VERB
xd07gq7038v	4	3	only	only	ADV
xd07gq7038v	4	4	structures	structure	NOUN
xd07gq7038v	4	5	whose	whose	DET
xd07gq7038v	4	6	universe	universe	NOUN
xd07gq7038v	4	7	is	be	AUX
xd07gq7038v	4	8	a	a	DET
xd07gq7038v	4	9	subset	subset	NOUN
xd07gq7038v	4	10	of	of	ADP
xd07gq7038v	4	11	$	$	SYM
xd07gq7038v	4	12	omega$	omega$	NOUN
xd07gq7038v	4	13	,	,	PUNCT
xd07gq7038v	4	14	and	and	CCONJ
xd07gq7038v	4	15	we	we	PRON
xd07gq7038v	4	16	define	define	VERB
xd07gq7038v	4	17	a	a	DET
xd07gq7038v	4	18	class	class	NOUN
xd07gq7038v	4	19	as	as	ADP
xd07gq7038v	4	20	a	a	DET
xd07gq7038v	4	21	collection	collection	NOUN
xd07gq7038v	4	22	of	of	ADP
xd07gq7038v	4	23	structures	structure	NOUN
xd07gq7038v	4	24	all	all	PRON
xd07gq7038v	4	25	with	with	ADP
xd07gq7038v	4	26	the	the	DET
xd07gq7038v	4	27	same	same	ADJ
xd07gq7038v	4	28	language	language	NOUN
xd07gq7038v	4	29	and	and	CCONJ
xd07gq7038v	4	30	closed	close	VERB
xd07gq7038v	4	31	under	under	ADP
xd07gq7038v	4	32	isomorphism	isomorphism	NOUN
xd07gq7038v	4	33	.	.	PUNCT
xd07gq7038v	5	1	one	one	NUM
xd07gq7038v	5	2	way	way	NOUN
xd07gq7038v	5	3	that	that	PRON
xd07gq7038v	5	4	the	the	DET
xd07gq7038v	5	5	complexity	complexity	NOUN
xd07gq7038v	5	6	of	of	ADP
xd07gq7038v	5	7	the	the	DET
xd07gq7038v	5	8	classification	classification	NOUN
xd07gq7038v	5	9	problem	problem	NOUN
xd07gq7038v	5	10	can	can	AUX
xd07gq7038v	5	11	be	be	AUX
xd07gq7038v	5	12	explored	explore	VERB
xd07gq7038v	5	13	is	be	AUX
xd07gq7038v	5	14	by	by	ADP
xd07gq7038v	5	15	looking	look	VERB
xd07gq7038v	5	16	at	at	ADP
xd07gq7038v	5	17	the	the	DET
xd07gq7038v	5	18	index	index	NOUN
xd07gq7038v	5	19	set	set	VERB
xd07gq7038v	5	20	for	for	ADP
xd07gq7038v	5	21	a	a	DET
xd07gq7038v	5	22	computable	computable	ADJ
xd07gq7038v	5	23	structure	structure	NOUN
xd07gq7038v	5	24	.	.	PUNCT
xd07gq7038v	6	1	we	we	PRON
xd07gq7038v	6	2	consider	consider	VERB
xd07gq7038v	6	3	indices	index	NOUN
xd07gq7038v	6	4	for	for	ADP
xd07gq7038v	6	5	computable	computable	ADJ
xd07gq7038v	6	6	structures	structure	NOUN
xd07gq7038v	6	7	,	,	PUNCT
xd07gq7038v	6	8	and	and	CCONJ
xd07gq7038v	6	9	write	write	VERB
xd07gq7038v	6	10	$	$	SYM
xd07gq7038v	6	11	mathcal{a}e$	mathcal{a}e$	NOUN
xd07gq7038v	6	12	where	where	SCONJ
xd07gq7038v	6	13	$	$	SYM
xd07gq7038v	6	14	varphi_e	varphi_e	NOUN
xd07gq7038v	6	15	=	=	SYM
xd07gq7038v	6	16	chi{d(mathcal{a})}$.	chi{d(mathcal{a})}$.	VERB
xd07gq7038v	6	17	the	the	DET
xd07gq7038v	6	18	index	index	NOUN
xd07gq7038v	6	19	set	set	VERB
xd07gq7038v	6	20	for	for	ADP
xd07gq7038v	6	21	$	$	SYM
xd07gq7038v	6	22	mathcal{a}$	mathcal{a}$	PROPN
xd07gq7038v	6	23	is	be	AUX
xd07gq7038v	6	24	the	the	DET
xd07gq7038v	6	25	set	set	NOUN
xd07gq7038v	6	26	of	of	ADP
xd07gq7038v	6	27	all	all	DET
xd07gq7038v	6	28	indices	index	NOUN
xd07gq7038v	6	29	for	for	ADP
xd07gq7038v	6	30	computable	computable	ADJ
xd07gq7038v	6	31	isomorphic	isomorphic	ADJ
xd07gq7038v	6	32	copies	copy	NOUN
xd07gq7038v	6	33	of	of	ADP
xd07gq7038v	6	34	$	$	SYM
xd07gq7038v	6	35	mathcal{a}$.	mathcal{a}$.	VERB
xd07gq7038v	6	36	we	we	PRON
xd07gq7038v	6	37	write[i(mathcal{a	write[i(mathcal{a	X
xd07gq7038v	6	38	}	}	PUNCT
xd07gq7038v	6	39	)	)	PUNCT
xd07gq7038v	6	40	=	=	PUNCT
xd07gq7038v	6	41	{	{	PUNCT
xd07gq7038v	6	42	e	e	NOUN
xd07gq7038v	6	43	:	:	PUNCT
xd07gq7038v	6	44	mathcal{a}e	mathcal{a}e	PROPN
xd07gq7038v	6	45	cong	cong	PROPN
xd07gq7038v	6	46	mathcal{a}}.]in	mathcal{a}}.]in	PROPN
xd07gq7038v	6	47	the	the	DET
xd07gq7038v	6	48	present	present	ADJ
xd07gq7038v	6	49	work	work	NOUN
xd07gq7038v	6	50	,	,	PUNCT
xd07gq7038v	6	51	the	the	DET
xd07gq7038v	6	52	relationship	relationship	NOUN
xd07gq7038v	6	53	between	between	ADP
xd07gq7038v	6	54	the	the	DET
xd07gq7038v	6	55	complexity	complexity	NOUN
xd07gq7038v	6	56	of	of	ADP
xd07gq7038v	6	57	the	the	DET
xd07gq7038v	6	58	index	index	NOUN
xd07gq7038v	6	59	set	set	VERB
xd07gq7038v	6	60	for	for	ADP
xd07gq7038v	6	61	a	a	DET
xd07gq7038v	6	62	structure	structure	NOUN
xd07gq7038v	6	63	and	and	CCONJ
xd07gq7038v	6	64	the	the	DET
xd07gq7038v	6	65	complexity	complexity	NOUN
xd07gq7038v	6	66	of	of	ADP
xd07gq7038v	6	67	a	a	DET
xd07gq7038v	6	68	sentence	sentence	NOUN
xd07gq7038v	6	69	describing	describe	VERB
xd07gq7038v	6	70	the	the	DET
xd07gq7038v	6	71	structure	structure	NOUN
xd07gq7038v	6	72	(	(	PUNCT
xd07gq7038v	6	73	called	call	VERB
xd07gq7038v	6	74	a	a	DET
xd07gq7038v	6	75	scott	scott	PROPN
xd07gq7038v	6	76	sentence	sentence	NOUN
xd07gq7038v	6	77	)	)	PUNCT
xd07gq7038v	6	78	is	be	AUX
xd07gq7038v	6	79	explored	explore	VERB
xd07gq7038v	6	80	.	.	PUNCT
xd07gq7038v	7	1	we	we	PRON
xd07gq7038v	7	2	find	find	VERB
xd07gq7038v	7	3	an	an	DET
xd07gq7038v	7	4	example	example	NOUN
xd07gq7038v	7	5	of	of	ADP
xd07gq7038v	7	6	a	a	DET
xd07gq7038v	7	7	structure	structure	NOUN
xd07gq7038v	7	8	for	for	ADP
xd07gq7038v	7	9	which	which	PRON
xd07gq7038v	7	10	there	there	PRON
xd07gq7038v	7	11	is	be	VERB
xd07gq7038v	7	12	not	not	PART
xd07gq7038v	7	13	a	a	DET
xd07gq7038v	7	14	match	match	NOUN
xd07gq7038v	7	15	between	between	ADP
xd07gq7038v	7	16	the	the	DET
xd07gq7038v	7	17	complexity	complexity	NOUN
xd07gq7038v	7	18	of	of	ADP
xd07gq7038v	7	19	the	the	DET
xd07gq7038v	7	20	index	index	NOUN
xd07gq7038v	7	21	set	set	NOUN
xd07gq7038v	7	22	and	and	CCONJ
xd07gq7038v	7	23	the	the	DET
xd07gq7038v	7	24	complexity	complexity	NOUN
xd07gq7038v	7	25	of	of	ADP
xd07gq7038v	7	26	a	a	DET
xd07gq7038v	7	27	scott	scott	PROPN
xd07gq7038v	7	28	sentence	sentence	NOUN
xd07gq7038v	7	29	.	.	PUNCT
xd07gq7038v	8	1	we	we	PRON
xd07gq7038v	8	2	also	also	ADV
xd07gq7038v	8	3	examine	examine	VERB
xd07gq7038v	8	4	the	the	DET
xd07gq7038v	8	5	possible	possible	ADJ
xd07gq7038v	8	6	complexities	complexity	NOUN
xd07gq7038v	8	7	of	of	ADP
xd07gq7038v	8	8	an	an	DET
xd07gq7038v	8	9	index	index	NOUN
xd07gq7038v	8	10	set	set	NOUN
xd07gq7038v	8	11	,	,	PUNCT
xd07gq7038v	8	12	and	and	CCONJ
xd07gq7038v	8	13	give	give	VERB
xd07gq7038v	8	14	results	result	NOUN
xd07gq7038v	8	15	characterizing	characterize	VERB
xd07gq7038v	8	16	when	when	SCONJ
xd07gq7038v	8	17	a	a	DET
xd07gq7038v	8	18	particular	particular	ADJ
xd07gq7038v	8	19	class	class	NOUN
xd07gq7038v	8	20	will	will	AUX
xd07gq7038v	8	21	have	have	VERB
xd07gq7038v	8	22	an	an	DET
xd07gq7038v	8	23	index	index	NOUN
xd07gq7038v	8	24	set	set	NOUN
xd07gq7038v	8	25	that	that	PRON
xd07gq7038v	8	26	is	be	AUX
xd07gq7038v	8	27	$	$	SYM
xd07gq7038v	8	28	m$-complete	m$-complete	ADJ
xd07gq7038v	8	29	at	at	ADP
xd07gq7038v	8	30	a	a	DET
xd07gq7038v	8	31	certain	certain	ADJ
xd07gq7038v	8	32	complexity	complexity	NOUN
xd07gq7038v	8	33	level.another	level.another	ADJ
xd07gq7038v	8	34	idea	idea	NOUN
xd07gq7038v	8	35	explored	explore	VERB
xd07gq7038v	8	36	in	in	ADP
xd07gq7038v	8	37	the	the	DET
xd07gq7038v	8	38	present	present	ADJ
xd07gq7038v	8	39	work	work	NOUN
xd07gq7038v	8	40	is	be	AUX
xd07gq7038v	8	41	that	that	PRON
xd07gq7038v	8	42	of	of	ADP
xd07gq7038v	8	43	comparing	compare	VERB
xd07gq7038v	8	44	the	the	DET
xd07gq7038v	8	45	complexity	complexity	NOUN
xd07gq7038v	8	46	of	of	ADP
xd07gq7038v	8	47	the	the	DET
xd07gq7038v	8	48	classification	classification	NOUN
xd07gq7038v	8	49	problem	problem	NOUN
xd07gq7038v	8	50	for	for	ADP
xd07gq7038v	8	51	various	various	ADJ
xd07gq7038v	8	52	classes	class	NOUN
xd07gq7038v	8	53	of	of	ADP
xd07gq7038v	8	54	structures	structure	NOUN
xd07gq7038v	8	55	,	,	PUNCT
xd07gq7038v	8	56	using	use	VERB
xd07gq7038v	8	57	the	the	DET
xd07gq7038v	8	58	notion	notion	NOUN
xd07gq7038v	8	59	of	of	ADP
xd07gq7038v	8	60	a	a	DET
xd07gq7038v	8	61	turing	ture	VERB
xd07gq7038v	8	62	computable	computable	NOUN
xd07gq7038v	8	63	embedding.oindent	embedding.oindent	ADJ
xd07gq7038v	8	64	extbf{definition}.a	extbf{definition}.a	ADJ
xd07gq7038v	8	65	turing	ture	VERB
xd07gq7038v	8	66	computable	computable	NOUN
xd07gq7038v	8	67	embedding	embedding	NOUN
xd07gq7038v	8	68	of	of	ADP
xd07gq7038v	8	69	$	$	SYM
xd07gq7038v	8	70	k$	k$	VERB
xd07gq7038v	8	71	into	into	ADP
xd07gq7038v	8	72	$	$	SYM
xd07gq7038v	8	73	k'$	k'$	PROPN
xd07gq7038v	8	74	is	be	AUX
xd07gq7038v	8	75	an	an	DET
xd07gq7038v	8	76	operator	operator	NOUN
xd07gq7038v	8	77	$	$	SYM
xd07gq7038v	8	78	phi	phi	NOUN
xd07gq7038v	8	79	=	=	PUNCT
xd07gq7038v	8	80	varphi_e$	varphi_e$	X
xd07gq7038v	8	81	such	such	ADJ
xd07gq7038v	8	82	that	that	SCONJ
xd07gq7038v	8	83	egin{enumerate}item	egin{enumerate}item	PROPN
xd07gq7038v	8	84	for	for	ADP
xd07gq7038v	8	85	each	each	DET
xd07gq7038v	8	86	$	$	SYM
xd07gq7038v	8	87	mathcal{a}in	mathcal{a}in	PROPN
xd07gq7038v	8	88	k$	k$	NOUN
xd07gq7038v	8	89	,	,	PUNCT
xd07gq7038v	8	90	there	there	PRON
xd07gq7038v	8	91	exists	exist	VERB
xd07gq7038v	8	92	$	$	SYM
xd07gq7038v	8	93	mathcal{b}in	mathcal{b}in	ADJ
xd07gq7038v	8	94	k'$	k'$	PROPN
xd07gq7038v	8	95	such	such	ADJ
xd07gq7038v	8	96	that	that	SCONJ
xd07gq7038v	8	97	$	$	SYM
xd07gq7038v	8	98	varphi_e^{d(mathcal{a	varphi_e^{d(mathcal{a	X
xd07gq7038v	8	99	}	}	PUNCT
xd07gq7038v	8	100	)	)	PUNCT
xd07gq7038v	8	101	}	}	PUNCT
xd07gq7038v	8	102	=	=	X
xd07gq7038v	8	103	chi{d(mathcal{b})}$	chi{d(mathcal{b})}$	PROPN
xd07gq7038v	8	104	,	,	PUNCT
xd07gq7038v	8	105	anditem	anditem	PROPN
xd07gq7038v	8	106	if	if	SCONJ
xd07gq7038v	8	107	$	$	SYM
xd07gq7038v	8	108	mathcal{a},mathcal{a}'in	mathcal{a},mathcal{a}'in	NOUN
xd07gq7038v	8	109	k$	k$	X
xd07gq7038v	8	110	correspond	correspond	VERB
xd07gq7038v	8	111	,	,	PUNCT
xd07gq7038v	8	112	respectively	respectively	ADV
xd07gq7038v	8	113	,	,	PUNCT
xd07gq7038v	8	114	to	to	ADP
xd07gq7038v	8	115	$	$	SYM
xd07gq7038v	8	116	mathcal{b},mathcal{b}'in	mathcal{b},mathcal{b}'in	NOUN
xd07gq7038v	8	117	k'$	k'$	PROPN
xd07gq7038v	8	118	,	,	PUNCT
xd07gq7038v	8	119	then	then	ADV
xd07gq7038v	8	120	$	$	SYM
xd07gq7038v	8	121	mathcal{a}congmathcal{a}'$	mathcal{a}congmathcal{a}'$	NUM
xd07gq7038v	8	122	if	if	SCONJ
xd07gq7038v	8	123	and	and	CCONJ
xd07gq7038v	8	124	only	only	ADV
xd07gq7038v	8	125	if	if	SCONJ
xd07gq7038v	8	126	$	$	SYM
xd07gq7038v	8	127	mathcal{b}congmathcal{b}'$.	mathcal{b}congmathcal{b}'$.	VERB
xd07gq7038v	8	128	end{enumerate}oindentthe	end{enumerate}oindentthe	PRON
xd07gq7038v	8	129	ordering	ordering	NOUN
xd07gq7038v	8	130	of	of	ADP
xd07gq7038v	8	131	classes	class	NOUN
xd07gq7038v	8	132	of	of	ADP
xd07gq7038v	8	133	structures	structure	NOUN
xd07gq7038v	8	134	that	that	PRON
xd07gq7038v	8	135	arises	arise	VERB
xd07gq7038v	8	136	from	from	ADP
xd07gq7038v	8	137	this	this	DET
xd07gq7038v	8	138	embedding	embedding	NOUN
xd07gq7038v	8	139	allows	allow	VERB
xd07gq7038v	8	140	us	we	PRON
xd07gq7038v	8	141	to	to	PART
xd07gq7038v	8	142	compare	compare	VERB
xd07gq7038v	8	143	the	the	DET
xd07gq7038v	8	144	complexity	complexity	NOUN
xd07gq7038v	8	145	of	of	ADP
xd07gq7038v	8	146	the	the	DET
xd07gq7038v	8	147	classification	classification	NOUN
xd07gq7038v	8	148	problem	problem	NOUN
xd07gq7038v	8	149	for	for	ADP
xd07gq7038v	8	150	those	those	PRON
xd07gq7038v	8	151	classes.in	classes.in	NUM
xd07gq7038v	8	152	the	the	DET
xd07gq7038v	8	153	present	present	ADJ
xd07gq7038v	8	154	work	work	NOUN
xd07gq7038v	8	155	,	,	PUNCT
xd07gq7038v	8	156	we	we	PRON
xd07gq7038v	8	157	give	give	VERB
xd07gq7038v	8	158	characterizations	characterization	NOUN
xd07gq7038v	8	159	for	for	ADP
xd07gq7038v	8	160	the	the	DET
xd07gq7038v	8	161	classes	class	NOUN
xd07gq7038v	8	162	of	of	ADP
xd07gq7038v	8	163	structures	structure	NOUN
xd07gq7038v	8	164	that	that	PRON
xd07gq7038v	8	165	embed	embe	VERB
xd07gq7038v	8	166	into	into	ADP
xd07gq7038v	8	167	the	the	DET
xd07gq7038v	8	168	class	class	NOUN
xd07gq7038v	8	169	of	of	ADP
xd07gq7038v	8	170	equivalence	equivalence	NOUN
xd07gq7038v	8	171	structures	structure	NOUN
xd07gq7038v	8	172	,	,	PUNCT
xd07gq7038v	8	173	as	as	ADV
xd07gq7038v	8	174	well	well	ADV
xd07gq7038v	8	175	as	as	ADP
xd07gq7038v	8	176	into	into	ADP
xd07gq7038v	8	177	the	the	DET
xd07gq7038v	8	178	class	class	NOUN
xd07gq7038v	8	179	of	of	ADP
xd07gq7038v	8	180	reduced	reduce	VERB
xd07gq7038v	8	181	abelian	abelian	NOUN
xd07gq7038v	8	182	$	$	SYM
xd07gq7038v	8	183	p$-groups	p$-group	NOUN
xd07gq7038v	8	184	of	of	ADP
xd07gq7038v	8	185	various	various	ADJ
xd07gq7038v	8	186	lengths	length	NOUN
xd07gq7038v	8	187	.	.	PUNCT