id	sid	tid	token	lemma	pos
ap-1827	1	1	acta	acta	PROPN
ap-1827	1	2	polytechnica	polytechnica	PROPN
ap-1827	1	3	acta	acta	PROPN
ap-1827	1	4	polytechnica	polytechnica	PROPN
ap-1827	1	5	53(4):344–346	53(4):344–346	PROPN
ap-1827	1	6	,	,	PUNCT
ap-1827	1	7	2013	2013	NUM
ap-1827	1	8	©	©	PROPN
ap-1827	1	9	czech	czech	PROPN
ap-1827	1	10	technical	technical	PROPN
ap-1827	1	11	university	university	PROPN
ap-1827	1	12	in	in	ADP
ap-1827	1	13	prague	prague	PROPN
ap-1827	1	14	,	,	PUNCT
ap-1827	1	15	2013	2013	NUM
ap-1827	1	16	available	available	ADJ
ap-1827	1	17	online	online	ADV
ap-1827	1	18	at	at	ADP
ap-1827	1	19	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-1827	1	20	on	on	ADP
ap-1827	1	21	an	an	DET
ap-1827	1	22	algorithm	algorithm	NOUN
ap-1827	1	23	for	for	ADP
ap-1827	1	24	multiperiodic	multiperiodic	ADJ
ap-1827	1	25	words	word	NOUN
ap-1827	1	26	štěpán	štěpán	PROPN
ap-1827	1	27	holub∗	holub∗	PROPN
ap-1827	1	28	department	department	PROPN
ap-1827	1	29	of	of	ADP
ap-1827	1	30	algebra	algebra	PROPN
ap-1827	1	31	,	,	PUNCT
ap-1827	1	32	faculty	faculty	NOUN
ap-1827	1	33	of	of	ADP
ap-1827	1	34	mathematics	mathematic	NOUN
ap-1827	1	35	and	and	CCONJ
ap-1827	1	36	physics	physics	PROPN
ap-1827	1	37	,	,	PUNCT
ap-1827	1	38	charles	charles	PROPN
ap-1827	1	39	university	university	PROPN
ap-1827	1	40	,	,	PUNCT
ap-1827	1	41	sokolovská	sokolovská	NOUN
ap-1827	1	42	83	83	NUM
ap-1827	1	43	,	,	PUNCT
ap-1827	1	44	175	175	NUM
ap-1827	1	45	86	86	NUM
ap-1827	1	46	praha	praha	PROPN
ap-1827	1	47	∗	∗	NOUN
ap-1827	1	48	corresponding	correspond	VERB
ap-1827	1	49	author	author	NOUN
ap-1827	1	50	:	:	PUNCT
ap-1827	1	51	holub@karlin.mff.cuni.cz	holub@karlin.mff.cuni.cz	PROPN
ap-1827	1	52	abstract	abstract	ADJ
ap-1827	1	53	.	.	PUNCT
ap-1827	2	1	we	we	PRON
ap-1827	2	2	consider	consider	VERB
ap-1827	2	3	an	an	DET
ap-1827	2	4	algorithm	algorithm	NOUN
ap-1827	2	5	by	by	ADP
ap-1827	2	6	tijdeman	tijdeman	NOUN
ap-1827	2	7	and	and	CCONJ
ap-1827	2	8	zamboni	zamboni	NOUN
ap-1827	2	9	constructing	construct	VERB
ap-1827	2	10	a	a	DET
ap-1827	2	11	word	word	NOUN
ap-1827	2	12	of	of	ADP
ap-1827	2	13	length	length	NOUN
ap-1827	2	14	k	k	PROPN
ap-1827	3	1	that	that	PRON
ap-1827	3	2	has	have	VERB
ap-1827	3	3	periods	period	NOUN
ap-1827	3	4	p1	p1	NOUN
ap-1827	3	5	,	,	PUNCT
ap-1827	3	6	.	.	PUNCT
ap-1827	3	7	.	.	PUNCT
ap-1827	4	1	.	.	PUNCT
ap-1827	5	1	,	,	PUNCT
ap-1827	5	2	pr	pr	NOUN
ap-1827	5	3	,	,	PUNCT
ap-1827	5	4	and	and	CCONJ
ap-1827	5	5	the	the	DET
ap-1827	5	6	richest	rich	ADJ
ap-1827	5	7	possible	possible	ADJ
ap-1827	5	8	alphabet	alphabet	NOUN
ap-1827	5	9	.	.	PUNCT
ap-1827	6	1	we	we	PRON
ap-1827	6	2	show	show	VERB
ap-1827	6	3	that	that	SCONJ
ap-1827	6	4	this	this	DET
ap-1827	6	5	algorithm	algorithm	NOUN
ap-1827	6	6	can	can	AUX
ap-1827	6	7	be	be	AUX
ap-1827	6	8	easily	easily	ADV
ap-1827	6	9	stated	state	VERB
ap-1827	6	10	and	and	CCONJ
ap-1827	6	11	its	its	PRON
ap-1827	6	12	correctness	correctness	NOUN
ap-1827	6	13	briefly	briefly	ADV
ap-1827	6	14	proved	prove	VERB
ap-1827	6	15	using	use	VERB
ap-1827	6	16	the	the	DET
ap-1827	6	17	class	class	NOUN
ap-1827	6	18	equivalence	equivalence	NOUN
ap-1827	6	19	approach	approach	NOUN
ap-1827	6	20	.	.	PUNCT
ap-1827	7	1	keywords	keyword	NOUN
ap-1827	7	2	:	:	PUNCT
ap-1827	7	3	periodicity	periodicity	NOUN
ap-1827	7	4	,	,	PUNCT
ap-1827	7	5	combinatorics	combinatoric	NOUN
ap-1827	7	6	on	on	ADP
ap-1827	7	7	words	word	NOUN
ap-1827	7	8	.	.	PUNCT
ap-1827	8	1	1	1	X
ap-1827	8	2	.	.	X
ap-1827	8	3	a	a	DET
ap-1827	8	4	short	short	ADJ
ap-1827	8	5	(	(	PUNCT
ap-1827	8	6	personal	personal	ADJ
ap-1827	8	7	)	)	PUNCT
ap-1827	8	8	history	history	NOUN
ap-1827	8	9	non	non	ADJ
ap-1827	8	10	-	-	ADJ
ap-1827	8	11	trivial	trivial	ADJ
ap-1827	8	12	words	word	NOUN
ap-1827	8	13	with	with	ADP
ap-1827	8	14	a	a	DET
ap-1827	8	15	given	give	VERB
ap-1827	8	16	set	set	NOUN
ap-1827	8	17	of	of	ADP
ap-1827	8	18	periods	period	NOUN
ap-1827	8	19	p	p	NOUN
ap-1827	8	20	=	=	SYM
ap-1827	8	21	{	{	PUNCT
ap-1827	8	22	p1	p1	NOUN
ap-1827	8	23	,	,	PUNCT
ap-1827	8	24	p2	p2	NOUN
ap-1827	8	25	,	,	PUNCT
ap-1827	8	26	.	.	PUNCT
ap-1827	8	27	.	.	PUNCT
ap-1827	8	28	.	.	PUNCT
ap-1827	9	1	,	,	PUNCT
ap-1827	9	2	pr	pr	AUX
ap-1827	9	3	}	}	PUNCT
ap-1827	9	4	have	have	AUX
ap-1827	9	5	received	receive	VERB
ap-1827	9	6	a	a	DET
ap-1827	9	7	lot	lot	NOUN
ap-1827	9	8	of	of	ADP
ap-1827	9	9	attention	attention	NOUN
ap-1827	9	10	in	in	ADP
ap-1827	9	11	the	the	DET
ap-1827	9	12	past	past	ADJ
ap-1827	9	13	decade	decade	NOUN
ap-1827	9	14	.	.	PUNCT
ap-1827	10	1	the	the	DET
ap-1827	10	2	motivation	motivation	NOUN
ap-1827	10	3	was	be	AUX
ap-1827	10	4	to	to	PART
ap-1827	10	5	generalize	generalize	VERB
ap-1827	10	6	the	the	DET
ap-1827	10	7	result	result	NOUN
ap-1827	10	8	by	by	ADP
ap-1827	10	9	fine	fine	ADJ
ap-1827	10	10	and	and	CCONJ
ap-1827	10	11	wilf	wilf	NOUN
ap-1827	10	12	dealing	deal	VERB
ap-1827	10	13	with	with	ADP
ap-1827	10	14	two	two	NUM
ap-1827	10	15	periods	period	NOUN
ap-1827	10	16	,	,	PUNCT
ap-1827	10	17	which	which	PRON
ap-1827	10	18	has	have	AUX
ap-1827	10	19	become	become	VERB
ap-1827	10	20	part	part	NOUN
ap-1827	10	21	of	of	ADP
ap-1827	10	22	the	the	DET
ap-1827	10	23	folklore	folklore	NOUN
ap-1827	10	24	.	.	PUNCT
ap-1827	11	1	a	a	DET
ap-1827	11	2	word	word	NOUN
ap-1827	11	3	with	with	ADP
ap-1827	11	4	periods	period	NOUN
ap-1827	11	5	p	p	NOUN
ap-1827	11	6	is	be	AUX
ap-1827	11	7	called	call	VERB
ap-1827	11	8	trivial	trivial	ADJ
ap-1827	11	9	if	if	SCONJ
ap-1827	11	10	gcd(p	gcd(p	PROPN
ap-1827	11	11	)	)	PUNCT
ap-1827	11	12	is	be	AUX
ap-1827	11	13	its	its	PRON
ap-1827	11	14	period	period	NOUN
ap-1827	11	15	too	too	ADV
ap-1827	11	16	.	.	PUNCT
ap-1827	12	1	papers	paper	NOUN
ap-1827	13	1	[	[	X
ap-1827	13	2	1	1	X
ap-1827	13	3	]	]	PUNCT
ap-1827	13	4	and	and	CCONJ
ap-1827	13	5	[	[	X
ap-1827	13	6	2	2	NUM
ap-1827	13	7	]	]	PUNCT
ap-1827	13	8	are	be	AUX
ap-1827	13	9	two	two	NUM
ap-1827	13	10	(	(	PUNCT
ap-1827	13	11	independent	independent	ADJ
ap-1827	13	12	)	)	PUNCT
ap-1827	13	13	results	result	NOUN
ap-1827	13	14	considering	consider	VERB
ap-1827	13	15	non	non	ADJ
ap-1827	13	16	-	-	ADJ
ap-1827	13	17	trivial	trivial	ADJ
ap-1827	13	18	such	such	ADJ
ap-1827	13	19	words	word	NOUN
ap-1827	13	20	with	with	ADP
ap-1827	13	21	maximal	maximal	ADJ
ap-1827	13	22	length	length	NOUN
ap-1827	13	23	and	and	CCONJ
ap-1827	13	24	maximal	maximal	ADJ
ap-1827	13	25	cardinality	cardinality	NOUN
ap-1827	13	26	of	of	ADP
ap-1827	13	27	the	the	DET
ap-1827	13	28	alphabet	alphabet	NOUN
ap-1827	13	29	.	.	PUNCT
ap-1827	14	1	these	these	DET
ap-1827	14	2	papers	paper	NOUN
ap-1827	14	3	supplemented	supplement	VERB
ap-1827	14	4	some	some	DET
ap-1827	14	5	older	old	ADJ
ap-1827	14	6	research	research	NOUN
ap-1827	14	7	of	of	ADP
ap-1827	14	8	castelli	castelli	PROPN
ap-1827	14	9	,	,	PUNCT
ap-1827	14	10	mignosi	mignosi	NOUN
ap-1827	14	11	,	,	PUNCT
ap-1827	14	12	restivo	restivo	ADJ
ap-1827	14	13	and	and	CCONJ
ap-1827	14	14	justin	justin	PROPN
ap-1827	14	15	(	(	PUNCT
ap-1827	14	16	see	see	VERB
ap-1827	14	17	,	,	PUNCT
ap-1827	14	18	e.g.	e.g.	ADV
ap-1827	14	19	,	,	PUNCT
ap-1827	14	20	[	[	X
ap-1827	14	21	3	3	X
ap-1827	14	22	]	]	PUNCT
ap-1827	14	23	for	for	ADP
ap-1827	14	24	more	more	ADJ
ap-1827	14	25	details	detail	NOUN
ap-1827	14	26	and	and	CCONJ
ap-1827	14	27	references	reference	NOUN
ap-1827	14	28	)	)	PUNCT
ap-1827	14	29	.	.	PUNCT
ap-1827	15	1	already	already	ADV
ap-1827	15	2	in	in	ADP
ap-1827	15	3	1998	1998	NUM
ap-1827	15	4	,	,	PUNCT
ap-1827	15	5	i	i	PRON
ap-1827	15	6	wrote	write	VERB
ap-1827	15	7	a	a	DET
ap-1827	15	8	short	short	ADJ
ap-1827	15	9	manuscript	manuscript	NOUN
ap-1827	15	10	giving	give	VERB
ap-1827	15	11	an	an	DET
ap-1827	15	12	analogous	analogous	ADJ
ap-1827	15	13	result	result	NOUN
ap-1827	15	14	(	(	PUNCT
ap-1827	15	15	without	without	ADP
ap-1827	15	16	considering	consider	VERB
ap-1827	15	17	publishing	publish	VERB
ap-1827	15	18	it	it	PRON
ap-1827	15	19	)	)	PUNCT
ap-1827	15	20	,	,	PUNCT
ap-1827	15	21	which	which	PRON
ap-1827	15	22	i	i	PRON
ap-1827	15	23	showed	show	VERB
ap-1827	15	24	to	to	ADP
ap-1827	15	25	sorin	sorin	PROPN
ap-1827	15	26	constantinescu	constantinescu	PROPN
ap-1827	15	27	during	during	ADP
ap-1827	15	28	the	the	DET
ap-1827	15	29	words	word	NOUN
ap-1827	15	30	2003	2003	NUM
ap-1827	15	31	conference	conference	NOUN
ap-1827	15	32	in	in	ADP
ap-1827	15	33	turku	turku	PROPN
ap-1827	15	34	,	,	PUNCT
ap-1827	15	35	where	where	SCONJ
ap-1827	15	36	he	he	PRON
ap-1827	15	37	presented	present	VERB
ap-1827	15	38	their	their	PRON
ap-1827	15	39	results	result	NOUN
ap-1827	15	40	.	.	PUNCT
ap-1827	16	1	since	since	SCONJ
ap-1827	16	2	this	this	PRON
ap-1827	16	3	was	be	AUX
ap-1827	16	4	passed	pass	VERB
ap-1827	16	5	without	without	ADP
ap-1827	16	6	notice	notice	NOUN
ap-1827	16	7	in	in	ADP
ap-1827	16	8	the	the	DET
ap-1827	16	9	subsequent	subsequent	ADJ
ap-1827	16	10	publication	publication	NOUN
ap-1827	16	11	,	,	PUNCT
ap-1827	16	12	and	and	CCONJ
ap-1827	16	13	since	since	SCONJ
ap-1827	16	14	i	i	PRON
ap-1827	16	15	considered	consider	VERB
ap-1827	16	16	my	my	PRON
ap-1827	16	17	approach	approach	NOUN
ap-1827	16	18	simpler	simple	ADJ
ap-1827	16	19	and	and	CCONJ
ap-1827	16	20	more	more	ADV
ap-1827	16	21	natural	natural	ADJ
ap-1827	16	22	,	,	PUNCT
ap-1827	16	23	i	i	PRON
ap-1827	16	24	later	later	ADV
ap-1827	16	25	decided	decide	VERB
ap-1827	16	26	to	to	PART
ap-1827	16	27	publish	publish	VERB
ap-1827	16	28	it	it	PRON
ap-1827	16	29	in	in	ADP
ap-1827	16	30	[	[	X
ap-1827	16	31	4	4	NUM
ap-1827	16	32	]	]	PUNCT
ap-1827	16	33	.	.	PUNCT
ap-1827	17	1	there	there	PRON
ap-1827	17	2	was	be	VERB
ap-1827	17	3	a	a	DET
ap-1827	17	4	gap	gap	NOUN
ap-1827	17	5	in	in	ADP
ap-1827	17	6	my	my	PRON
ap-1827	17	7	paper	paper	NOUN
ap-1827	17	8	,	,	PUNCT
ap-1827	17	9	discovered	discover	VERB
ap-1827	17	10	by	by	ADP
ap-1827	17	11	gwénaël	gwénaël	ADJ
ap-1827	17	12	richomme	richomme	NOUN
ap-1827	17	13	,	,	PUNCT
ap-1827	17	14	which	which	PRON
ap-1827	17	15	is	be	AUX
ap-1827	17	16	fixed	fix	VERB
ap-1827	17	17	in	in	ADP
ap-1827	17	18	[	[	X
ap-1827	17	19	5	5	NUM
ap-1827	17	20	]	]	PUNCT
ap-1827	17	21	.	.	PUNCT
ap-1827	18	1	the	the	DET
ap-1827	18	2	present	present	ADJ
ap-1827	18	3	paper	paper	NOUN
ap-1827	18	4	extends	extend	VERB
ap-1827	18	5	the	the	DET
ap-1827	18	6	same	same	ADJ
ap-1827	18	7	approach	approach	NOUN
ap-1827	18	8	to	to	ADP
ap-1827	18	9	the	the	DET
ap-1827	18	10	construction	construction	NOUN
ap-1827	18	11	of	of	ADP
ap-1827	18	12	the	the	DET
ap-1827	18	13	richest	rich	ADJ
ap-1827	18	14	word	word	NOUN
ap-1827	18	15	with	with	ADP
ap-1827	18	16	a	a	DET
ap-1827	18	17	given	give	VERB
ap-1827	18	18	set	set	NOUN
ap-1827	18	19	of	of	ADP
ap-1827	18	20	periods	period	NOUN
ap-1827	18	21	and	and	CCONJ
ap-1827	18	22	a	a	DET
ap-1827	18	23	given	give	VERB
ap-1827	18	24	length	length	NOUN
ap-1827	18	25	.	.	PUNCT
ap-1827	19	1	the	the	DET
ap-1827	19	2	basic	basic	ADJ
ap-1827	19	3	idea	idea	NOUN
ap-1827	19	4	is	be	AUX
ap-1827	19	5	to	to	PART
ap-1827	19	6	consider	consider	VERB
ap-1827	19	7	relations	relation	NOUN
ap-1827	19	8	defined	define	VERB
ap-1827	19	9	by	by	ADP
ap-1827	19	10	the	the	DET
ap-1827	19	11	periods	period	NOUN
ap-1827	19	12	and	and	CCONJ
ap-1827	19	13	understand	understand	VERB
ap-1827	19	14	letters	letter	NOUN
ap-1827	19	15	as	as	ADP
ap-1827	19	16	(	(	PUNCT
ap-1827	19	17	names	name	NOUN
ap-1827	19	18	of	of	ADP
ap-1827	19	19	)	)	PUNCT
ap-1827	19	20	equivalence	equivalence	NOUN
ap-1827	19	21	classes	class	NOUN
ap-1827	19	22	generated	generate	VERB
ap-1827	19	23	by	by	ADP
ap-1827	19	24	those	those	DET
ap-1827	19	25	relations	relation	NOUN
ap-1827	19	26	.	.	PUNCT
ap-1827	20	1	the	the	DET
ap-1827	20	2	idea	idea	NOUN
ap-1827	20	3	is	be	AUX
ap-1827	20	4	obvious	obvious	ADJ
ap-1827	20	5	and	and	CCONJ
ap-1827	20	6	well	well	ADV
ap-1827	20	7	known	know	VERB
ap-1827	20	8	,	,	PUNCT
ap-1827	20	9	usually	usually	ADV
ap-1827	20	10	expressed	express	VERB
ap-1827	20	11	using	use	VERB
ap-1827	20	12	the	the	DET
ap-1827	20	13	graph	graph	NOUN
ap-1827	20	14	terminology	terminology	NOUN
ap-1827	20	15	(	(	PUNCT
ap-1827	20	16	edges	edge	NOUN
ap-1827	20	17	and	and	CCONJ
ap-1827	20	18	connected	connected	ADJ
ap-1827	20	19	components	component	NOUN
ap-1827	20	20	)	)	PUNCT
ap-1827	20	21	,	,	PUNCT
ap-1827	20	22	rather	rather	ADV
ap-1827	20	23	than	than	ADP
ap-1827	20	24	the	the	DET
ap-1827	20	25	algebraic	algebraic	ADJ
ap-1827	20	26	terminology	terminology	NOUN
ap-1827	20	27	(	(	PUNCT
ap-1827	20	28	relations	relation	NOUN
ap-1827	20	29	and	and	CCONJ
ap-1827	20	30	equivalence	equivalence	NOUN
ap-1827	20	31	classes	class	NOUN
ap-1827	20	32	)	)	PUNCT
ap-1827	20	33	.	.	PUNCT
ap-1827	21	1	tijdeman	tijdeman	NOUN
ap-1827	21	2	and	and	CCONJ
ap-1827	21	3	zamboni	zamboni	NOUN
ap-1827	22	1	[	[	X
ap-1827	22	2	3	3	NUM
ap-1827	22	3	]	]	PUNCT
ap-1827	22	4	point	point	NOUN
ap-1827	22	5	out	out	ADP
ap-1827	22	6	that	that	SCONJ
ap-1827	22	7	the	the	DET
ap-1827	22	8	straightforward	straightforward	ADJ
ap-1827	22	9	algorithm	algorithm	NOUN
ap-1827	22	10	based	base	VERB
ap-1827	22	11	on	on	ADP
ap-1827	22	12	the	the	DET
ap-1827	22	13	graph	graph	NOUN
ap-1827	22	14	approach	approach	NOUN
ap-1827	22	15	is	be	AUX
ap-1827	22	16	“	"	PUNCT
ap-1827	22	17	simple	simple	ADJ
ap-1827	22	18	but	but	CCONJ
ap-1827	22	19	inefficient	inefficient	ADJ
ap-1827	22	20	”	"	PUNCT
ap-1827	22	21	,	,	PUNCT
ap-1827	22	22	and	and	CCONJ
ap-1827	22	23	then	then	ADV
ap-1827	22	24	present	present	VERB
ap-1827	22	25	an	an	DET
ap-1827	22	26	algorithm	algorithm	NOUN
ap-1827	22	27	based	base	VERB
ap-1827	22	28	on	on	ADP
ap-1827	22	29	less	less	ADV
ap-1827	22	30	transparent	transparent	ADJ
ap-1827	22	31	combinatorial	combinatorial	ADJ
ap-1827	22	32	analysis	analysis	NOUN
ap-1827	22	33	.	.	PUNCT
ap-1827	23	1	the	the	DET
ap-1827	23	2	aim	aim	NOUN
ap-1827	23	3	of	of	ADP
ap-1827	23	4	this	this	DET
ap-1827	23	5	paper	paper	NOUN
ap-1827	23	6	is	be	AUX
ap-1827	23	7	to	to	PART
ap-1827	23	8	give	give	VERB
ap-1827	23	9	a	a	DET
ap-1827	23	10	short	short	ADJ
ap-1827	23	11	description	description	NOUN
ap-1827	23	12	of	of	ADP
ap-1827	23	13	their	their	PRON
ap-1827	23	14	algorithm	algorithm	NOUN
ap-1827	23	15	,	,	PUNCT
ap-1827	23	16	as	as	ADV
ap-1827	23	17	well	well	ADV
ap-1827	23	18	as	as	ADP
ap-1827	23	19	a	a	DET
ap-1827	23	20	short	short	ADJ
ap-1827	23	21	and	and	CCONJ
ap-1827	23	22	intuitive	intuitive	ADJ
ap-1827	23	23	proof	proof	NOUN
ap-1827	23	24	of	of	ADP
ap-1827	23	25	its	its	PRON
ap-1827	23	26	correctness	correctness	NOUN
ap-1827	23	27	,	,	PUNCT
ap-1827	23	28	using	use	VERB
ap-1827	23	29	consistently	consistently	ADV
ap-1827	23	30	the	the	DET
ap-1827	23	31	graph	graph	NOUN
ap-1827	23	32	/	/	SYM
ap-1827	23	33	equivalence	equivalence	NOUN
ap-1827	23	34	viewpoint	viewpoint	NOUN
ap-1827	23	35	.	.	PUNCT
ap-1827	24	1	2	2	X
ap-1827	24	2	.	.	X
ap-1827	24	3	notation	notation	NOUN
ap-1827	24	4	let	let	VERB
ap-1827	24	5	w	w	NOUN
ap-1827	24	6	be	be	AUX
ap-1827	24	7	a	a	DET
ap-1827	24	8	word	word	NOUN
ap-1827	24	9	of	of	ADP
ap-1827	24	10	length	length	NOUN
ap-1827	24	11	k	k	PROPN
ap-1827	24	12	over	over	ADP
ap-1827	24	13	an	an	DET
ap-1827	24	14	alphabet	alphabet	NOUN
ap-1827	24	15	a.	a.	NOUN
ap-1827	24	16	the	the	DET
ap-1827	24	17	set	set	NOUN
ap-1827	24	18	of	of	ADP
ap-1827	24	19	all	all	DET
ap-1827	24	20	letters	letter	NOUN
ap-1827	24	21	that	that	PRON
ap-1827	24	22	occur	occur	VERB
ap-1827	24	23	in	in	ADP
ap-1827	24	24	w	w	PROPN
ap-1827	24	25	is	be	AUX
ap-1827	24	26	denoted	denote	VERB
ap-1827	24	27	by	by	ADP
ap-1827	24	28	alph(w	alph(w	PROPN
ap-1827	24	29	)	)	PUNCT
ap-1827	24	30	.	.	PUNCT
ap-1827	25	1	the	the	DET
ap-1827	25	2	i	i	PROPN
ap-1827	25	3	-	-	PUNCT
ap-1827	25	4	th	th	X
ap-1827	25	5	letter	letter	NOUN
ap-1827	25	6	of	of	ADP
ap-1827	25	7	w	w	PROPN
ap-1827	25	8	is	be	AUX
ap-1827	25	9	denoted	denote	VERB
ap-1827	25	10	by	by	ADP
ap-1827	25	11	w[i	w[i	NOUN
ap-1827	25	12	−	−	PROPN
ap-1827	25	13	1	1	NUM
ap-1827	25	14	]	]	PUNCT
ap-1827	25	15	so	so	SCONJ
ap-1827	25	16	that	that	SCONJ
ap-1827	25	17	w	w	NOUN
ap-1827	25	18	=	=	SYM
ap-1827	25	19	w[0]w[1	w[0]w[1	NOUN
ap-1827	25	20	]	]	PUNCT
ap-1827	25	21	·	·	PUNCT
ap-1827	25	22	·	·	PUNCT
ap-1827	26	1	·	·	PUNCT
ap-1827	26	2	w[k	w[k	NOUN
ap-1827	26	3	−	−	NOUN
ap-1827	26	4	1	1	NUM
ap-1827	26	5	]	]	PUNCT
ap-1827	26	6	.	.	PUNCT
ap-1827	27	1	the	the	DET
ap-1827	27	2	prefix	prefix	NOUN
ap-1827	27	3	of	of	ADP
ap-1827	27	4	w	w	NOUN
ap-1827	27	5	of	of	ADP
ap-1827	27	6	length	length	NOUN
ap-1827	27	7	n	n	NUM
ap-1827	27	8	is	be	AUX
ap-1827	27	9	denoted	denote	VERB
ap-1827	27	10	by	by	ADP
ap-1827	27	11	prefn(w	prefn(w	ADV
ap-1827	27	12	)	)	PUNCT
ap-1827	27	13	.	.	PUNCT
ap-1827	28	1	we	we	PRON
ap-1827	28	2	say	say	VERB
ap-1827	28	3	that	that	SCONJ
ap-1827	28	4	a	a	DET
ap-1827	28	5	positive	positive	ADJ
ap-1827	28	6	integer	integer	NOUN
ap-1827	28	7	p	p	NOUN
ap-1827	28	8	is	be	AUX
ap-1827	28	9	a	a	DET
ap-1827	28	10	period	period	NOUN
ap-1827	28	11	of	of	ADP
ap-1827	28	12	a	a	DET
ap-1827	28	13	word	word	NOUN
ap-1827	28	14	w	w	NOUN
ap-1827	28	15	if	if	SCONJ
ap-1827	28	16	w[i	w[i	NOUN
ap-1827	28	17	]	]	X
ap-1827	28	18	=	=	SYM
ap-1827	28	19	w[i	w[i	NOUN
ap-1827	29	1	+	+	CCONJ
ap-1827	29	2	p	p	X
ap-1827	29	3	]	]	X
ap-1827	29	4	for	for	ADP
ap-1827	29	5	all	all	PRON
ap-1827	29	6	0	0	NUM
ap-1827	29	7	≤	≤	NUM
ap-1827	29	8	i	i	PRON
ap-1827	29	9	≤	≤	NUM
ap-1827	29	10	|w|	|w|	VERB
ap-1827	29	11	−	−	PROPN
ap-1827	29	12	p	p	NOUN
ap-1827	29	13	−	−	PROPN
ap-1827	29	14	1	1	NUM
ap-1827	29	15	(	(	PUNCT
ap-1827	29	16	where	where	SCONJ
ap-1827	29	17	|w|	|w|	ADJ
ap-1827	29	18	denotes	denote	NOUN
ap-1827	29	19	the	the	DET
ap-1827	29	20	length	length	NOUN
ap-1827	29	21	of	of	ADP
ap-1827	29	22	the	the	DET
ap-1827	29	23	word	word	NOUN
ap-1827	29	24	)	)	PUNCT
ap-1827	29	25	.	.	PUNCT
ap-1827	30	1	note	note	VERB
ap-1827	30	2	that	that	SCONJ
ap-1827	30	3	any	any	DET
ap-1827	30	4	p	p	ADJ
ap-1827	30	5	≥	≥	NOUN
ap-1827	30	6	|w|	|w|	NOUN
ap-1827	30	7	is	be	AUX
ap-1827	30	8	a	a	DET
ap-1827	30	9	period	period	NOUN
ap-1827	30	10	of	of	ADP
ap-1827	30	11	u.	u.	NOUN
ap-1827	30	12	if	if	SCONJ
ap-1827	30	13	p	p	NOUN
ap-1827	30	14	is	be	AUX
ap-1827	30	15	a	a	DET
ap-1827	30	16	set	set	NOUN
ap-1827	30	17	of	of	ADP
ap-1827	30	18	positive	positive	ADJ
ap-1827	30	19	integers	integer	NOUN
ap-1827	30	20	such	such	ADJ
ap-1827	30	21	that	that	SCONJ
ap-1827	30	22	each	each	DET
ap-1827	30	23	p	p	PROPN
ap-1827	30	24	∈	∈	PROPN
ap-1827	30	25	p	p	NOUN
ap-1827	30	26	is	be	AUX
ap-1827	30	27	a	a	DET
ap-1827	30	28	period	period	NOUN
ap-1827	30	29	of	of	ADP
ap-1827	30	30	w	w	NOUN
ap-1827	30	31	,	,	PUNCT
ap-1827	30	32	we	we	PRON
ap-1827	30	33	say	say	VERB
ap-1827	30	34	that	that	SCONJ
ap-1827	30	35	w	w	NOUN
ap-1827	30	36	has	have	VERB
ap-1827	30	37	periods	period	NOUN
ap-1827	30	38	p	p	NOUN
ap-1827	30	39	.	.	PUNCT
ap-1827	31	1	the	the	DET
ap-1827	31	2	word	word	NOUN
ap-1827	31	3	of	of	ADP
ap-1827	31	4	length	length	NOUN
ap-1827	31	5	k	k	PROPN
ap-1827	31	6	having	have	VERB
ap-1827	31	7	periods	period	NOUN
ap-1827	31	8	p	p	NOUN
ap-1827	31	9	and	and	CCONJ
ap-1827	31	10	the	the	DET
ap-1827	31	11	maximal	maximal	ADJ
ap-1827	31	12	possible	possible	ADJ
ap-1827	31	13	cardinality	cardinality	NOUN
ap-1827	31	14	of	of	ADP
ap-1827	31	15	alph(w	alph(w	PROPN
ap-1827	31	16	)	)	PUNCT
ap-1827	31	17	is	be	AUX
ap-1827	31	18	called	call	VERB
ap-1827	31	19	an	an	DET
ap-1827	31	20	fw	fw	ADJ
ap-1827	31	21	-	-	PUNCT
ap-1827	31	22	word	word	NOUN
ap-1827	31	23	relative	relative	ADJ
ap-1827	31	24	to	to	ADP
ap-1827	31	25	p	p	NOUN
ap-1827	31	26	(	(	PUNCT
ap-1827	31	27	where	where	SCONJ
ap-1827	31	28	fw	fw	PROPN
ap-1827	31	29	stands	stand	VERB
ap-1827	31	30	for	for	ADP
ap-1827	31	31	“	"	PUNCT
ap-1827	31	32	fine	fine	ADJ
ap-1827	31	33	and	and	CCONJ
ap-1827	31	34	wilf	wilf	PROPN
ap-1827	31	35	”	"	PUNCT
ap-1827	31	36	for	for	ADP
ap-1827	31	37	historic	historic	ADJ
ap-1827	31	38	reasons	reason	NOUN
ap-1827	31	39	)	)	PUNCT
ap-1827	31	40	.	.	PUNCT
ap-1827	32	1	the	the	DET
ap-1827	32	2	word	word	NOUN
ap-1827	32	3	is	be	AUX
ap-1827	32	4	called	call	VERB
ap-1827	32	5	trivial	trivial	ADJ
ap-1827	32	6	with	with	ADP
ap-1827	32	7	respect	respect	NOUN
ap-1827	32	8	to	to	ADP
ap-1827	32	9	p	p	NOUN
ap-1827	32	10	if	if	SCONJ
ap-1827	32	11	gcd(p	gcd(p	PROPN
ap-1827	32	12	)	)	PUNCT
ap-1827	32	13	is	be	AUX
ap-1827	32	14	a	a	DET
ap-1827	32	15	period	period	NOUN
ap-1827	32	16	of	of	ADP
ap-1827	32	17	w.	w.	NOUN
ap-1827	32	18	the	the	DET
ap-1827	32	19	longest	long	ADJ
ap-1827	32	20	non	non	ADJ
ap-1827	32	21	-	-	ADJ
ap-1827	32	22	trivial	trivial	ADJ
ap-1827	32	23	fw	fw	ADJ
ap-1827	32	24	-	-	PUNCT
ap-1827	32	25	word	word	NOUN
ap-1827	32	26	relative	relative	ADJ
ap-1827	32	27	to	to	ADP
ap-1827	32	28	p	p	PROPN
ap-1827	32	29	is	be	AUX
ap-1827	32	30	called	call	VERB
ap-1827	32	31	an	an	DET
ap-1827	32	32	extremal	extremal	ADJ
ap-1827	32	33	fw	fw	ADJ
ap-1827	32	34	-	-	PUNCT
ap-1827	32	35	word	word	NOUN
ap-1827	32	36	relative	relative	ADJ
ap-1827	32	37	to	to	ADP
ap-1827	32	38	p	p	PROPN
ap-1827	32	39	.	.	PUNCT
ap-1827	33	1	we	we	PRON
ap-1827	33	2	denote	denote	VERB
ap-1827	33	3	its	its	PRON
ap-1827	33	4	length	length	NOUN
ap-1827	33	5	by	by	ADP
ap-1827	33	6	l(p	l(p	PROPN
ap-1827	33	7	)	)	PUNCT
ap-1827	33	8	(	(	PUNCT
ap-1827	33	9	note	note	VERB
ap-1827	33	10	that	that	SCONJ
ap-1827	33	11	l(p	l(p	NOUN
ap-1827	33	12	)	)	PUNCT
ap-1827	34	1	=	=	SYM
ap-1827	34	2	l(p	l(p	PROPN
ap-1827	34	3	)	)	PUNCT
ap-1827	34	4	−	−	PROPN
ap-1827	34	5	1	1	NUM
ap-1827	34	6	where	where	SCONJ
ap-1827	34	7	l(p	l(p	NOUN
ap-1827	34	8	)	)	PUNCT
ap-1827	34	9	is	be	AUX
ap-1827	34	10	the	the	DET
ap-1827	34	11	notation	notation	NOUN
ap-1827	34	12	adopted	adopt	VERB
ap-1827	34	13	in	in	ADP
ap-1827	34	14	[	[	X
ap-1827	34	15	3	3	NUM
ap-1827	34	16	]	]	NUM
ap-1827	34	17	)	)	PUNCT
ap-1827	34	18	.	.	PUNCT
ap-1827	35	1	3	3	X
ap-1827	35	2	.	.	X
ap-1827	35	3	classes	class	NOUN
ap-1827	35	4	of	of	ADP
ap-1827	35	5	equivalence	equivalence	NOUN
ap-1827	35	6	let	let	VERB
ap-1827	35	7	w	w	PART
ap-1827	35	8	be	be	AUX
ap-1827	35	9	a	a	DET
ap-1827	35	10	word	word	NOUN
ap-1827	35	11	which	which	PRON
ap-1827	35	12	has	have	VERB
ap-1827	35	13	periods	period	NOUN
ap-1827	35	14	p	p	PROPN
ap-1827	35	15	.	.	PUNCT
ap-1827	36	1	for	for	ADP
ap-1827	36	2	the	the	DET
ap-1827	36	3	rest	rest	NOUN
ap-1827	36	4	of	of	ADP
ap-1827	36	5	the	the	DET
ap-1827	36	6	paper	paper	NOUN
ap-1827	36	7	we	we	PRON
ap-1827	36	8	denote	denote	VERB
ap-1827	36	9	m	m	NOUN
ap-1827	36	10	=	=	SYM
ap-1827	36	11	min	min	PROPN
ap-1827	36	12	p	p	NOUN
ap-1827	36	13	.	.	PUNCT
ap-1827	37	1	obviously	obviously	ADV
ap-1827	37	2	,	,	PUNCT
ap-1827	37	3	if	if	SCONJ
ap-1827	37	4	i	i	PRON
ap-1827	37	5	≡	≡	PROPN
ap-1827	37	6	j	j	PROPN
ap-1827	37	7	mod	mod	PROPN
ap-1827	37	8	m	m	PROPN
ap-1827	37	9	or	or	CCONJ
ap-1827	37	10	|i	|i	VERB
ap-1827	37	11	−	−	PROPN
ap-1827	37	12	j|	j|	PROPN
ap-1827	37	13	∈	∈	PROPN
ap-1827	37	14	p	p	X
ap-1827	37	15	,	,	PUNCT
ap-1827	37	16	then	then	ADV
ap-1827	37	17	w[i	w[i	VERB
ap-1827	37	18	]	]	X
ap-1827	37	19	=	=	PUNCT
ap-1827	37	20	w[j	w[j	PROPN
ap-1827	37	21	]	]	PUNCT
ap-1827	37	22	.	.	PUNCT
ap-1827	38	1	these	these	DET
ap-1827	38	2	two	two	NUM
ap-1827	38	3	conditions	condition	NOUN
ap-1827	38	4	induce	induce	VERB
ap-1827	38	5	the	the	DET
ap-1827	38	6	relation	relation	NOUN
ap-1827	38	7	∼p	∼p	PROPN
ap-1827	38	8	,	,	PUNCT
ap-1827	38	9	k	k	PROPN
ap-1827	38	10	on	on	ADP
ap-1827	38	11	integers	integer	NOUN
ap-1827	38	12	{	{	PUNCT
ap-1827	38	13	0	0	NUM
ap-1827	38	14	,	,	PUNCT
ap-1827	38	15	.	.	PUNCT
ap-1827	38	16	.	.	PUNCT
ap-1827	38	17	.	.	PUNCT
ap-1827	39	1	,	,	PUNCT
ap-1827	40	1	k	k	PROPN
ap-1827	40	2	−	−	PROPN
ap-1827	40	3	1	1	NUM
ap-1827	40	4	}	}	PUNCT
ap-1827	40	5	defined	define	VERB
ap-1827	40	6	by	by	ADP
ap-1827	40	7	:	:	PUNCT
ap-1827	40	8	i	i	PROPN
ap-1827	40	9	∼p	∼p	PROPN
ap-1827	40	10	,	,	PUNCT
ap-1827	40	11	k	k	PROPN
ap-1827	40	12	j	j	PROPN
ap-1827	41	1	if	if	SCONJ
ap-1827	41	2	a	a	X
ap-1827	41	3	)	)	PUNCT
ap-1827	41	4	i	i	PROPN
ap-1827	41	5	≡	≡	PROPN
ap-1827	41	6	j	j	PROPN
ap-1827	41	7	mod	mod	PROPN
ap-1827	41	8	m	m	PROPN
ap-1827	41	9	,	,	PUNCT
ap-1827	41	10	or	or	CCONJ
ap-1827	41	11	b	b	X
ap-1827	41	12	)	)	PUNCT
ap-1827	41	13	there	there	PRON
ap-1827	41	14	are	be	VERB
ap-1827	41	15	integers	integer	NOUN
ap-1827	41	16	i′	i′	NOUN
ap-1827	41	17	,	,	PUNCT
ap-1827	41	18	j′	j′	PROPN
ap-1827	41	19	∈	∈	PROPN
ap-1827	41	20	{	{	PUNCT
ap-1827	41	21	0	0	NUM
ap-1827	41	22	,	,	PUNCT
ap-1827	41	23	.	.	PUNCT
ap-1827	41	24	.	.	PUNCT
ap-1827	42	1	.	.	PUNCT
ap-1827	43	1	,	,	PUNCT
ap-1827	44	1	k	k	PROPN
ap-1827	44	2	−	−	PROPN
ap-1827	45	1	1	1	NUM
ap-1827	45	2	}	}	PUNCT
ap-1827	45	3	such	such	ADJ
ap-1827	45	4	that	that	SCONJ
ap-1827	45	5	i	i	PRON
ap-1827	45	6	≡	≡	PROPN
ap-1827	45	7	i′	i′	VERB
ap-1827	45	8	mod	mod	PROPN
ap-1827	45	9	m	m	PROPN
ap-1827	45	10	,	,	PUNCT
ap-1827	45	11	j	j	PROPN
ap-1827	45	12	≡	≡	PROPN
ap-1827	45	13	j′	j′	PROPN
ap-1827	46	1	mod	mod	PROPN
ap-1827	47	1	m	m	PROPN
ap-1827	47	2	and	and	CCONJ
ap-1827	47	3	|i′	|i′	PROPN
ap-1827	47	4	−	−	NUM
ap-1827	47	5	j′|	j′|	PROPN
ap-1827	47	6	∈	∈	PROPN
ap-1827	47	7	p.	p.	NOUN
ap-1827	47	8	let	let	VERB
ap-1827	47	9	≈p	≈p	PROPN
ap-1827	47	10	,	,	PUNCT
ap-1827	47	11	k	k	PROPN
ap-1827	47	12	be	be	AUX
ap-1827	47	13	the	the	DET
ap-1827	47	14	equivalence	equivalence	NOUN
ap-1827	47	15	closure	closure	NOUN
ap-1827	47	16	of	of	ADP
ap-1827	47	17	∼p	∼p	PROPN
ap-1827	47	18	,	,	PUNCT
ap-1827	47	19	k.	k.	NOUN
ap-1827	47	20	in	in	ADP
ap-1827	47	21	other	other	ADJ
ap-1827	47	22	words	word	NOUN
ap-1827	47	23	,	,	PUNCT
ap-1827	47	24	we	we	PRON
ap-1827	47	25	have	have	VERB
ap-1827	47	26	i	i	PRON
ap-1827	47	27	≈p	≈p	PROPN
ap-1827	47	28	,	,	PUNCT
ap-1827	47	29	k	k	PROPN
ap-1827	47	30	j	j	PROPN
ap-1827	48	1	if	if	SCONJ
ap-1827	48	2	and	and	CCONJ
ap-1827	48	3	only	only	ADV
ap-1827	48	4	if	if	SCONJ
ap-1827	48	5	i	i	PRON
ap-1827	48	6	and	and	CCONJ
ap-1827	48	7	j	j	PROPN
ap-1827	48	8	lie	lie	VERB
ap-1827	48	9	in	in	ADP
ap-1827	48	10	the	the	DET
ap-1827	48	11	same	same	ADJ
ap-1827	48	12	connected	connected	ADJ
ap-1827	48	13	component	component	NOUN
ap-1827	48	14	of	of	ADP
ap-1827	48	15	the	the	DET
ap-1827	48	16	graph	graph	NOUN
ap-1827	48	17	defined	define	VERB
ap-1827	48	18	by	by	ADP
ap-1827	48	19	edges	edge	NOUN
ap-1827	48	20	i	i	PROPN
ap-1827	48	21	∼p	∼p	PROPN
ap-1827	48	22	,	,	PUNCT
ap-1827	48	23	k	k	PROPN
ap-1827	48	24	j.	j.	PROPN
ap-1827	49	1	the	the	DET
ap-1827	49	2	class	class	NOUN
ap-1827	49	3	of	of	ADP
ap-1827	49	4	≈p	≈p	PROPN
ap-1827	49	5	,	,	PUNCT
ap-1827	49	6	k	k	PROPN
ap-1827	49	7	containing	contain	VERB
ap-1827	49	8	i	i	PRON
ap-1827	49	9	will	will	AUX
ap-1827	49	10	be	be	AUX
ap-1827	49	11	denoted	denote	VERB
ap-1827	49	12	by	by	ADP
ap-1827	49	13	[	[	X
ap-1827	49	14	i]p	i]p	PRON
ap-1827	49	15	,	,	PUNCT
ap-1827	49	16	k	k	PROPN
ap-1827	49	17	and	and	CCONJ
ap-1827	49	18	represented	represent	VERB
ap-1827	49	19	by	by	ADP
ap-1827	49	20	its	its	PRON
ap-1827	49	21	minimal	minimal	ADJ
ap-1827	49	22	element	element	NOUN
ap-1827	49	23	min[i]p	min[i]p	ADP
ap-1827	49	24	,	,	PUNCT
ap-1827	49	25	k.	k.	PROPN
ap-1827	50	1	then	then	ADV
ap-1827	50	2	we	we	PRON
ap-1827	50	3	define	define	VERB
ap-1827	50	4	a	a	DET
ap-1827	50	5	word	word	NOUN
ap-1827	50	6	fw(p	fw(p	NOUN
ap-1827	50	7	,	,	PUNCT
ap-1827	50	8	k	k	NOUN
ap-1827	50	9	)	)	PUNCT
ap-1827	50	10	of	of	ADP
ap-1827	50	11	length	length	NOUN
ap-1827	50	12	k	k	PROPN
ap-1827	50	13	over	over	ADP
ap-1827	50	14	the	the	DET
ap-1827	50	15	alphabet	alphabet	NOUN
ap-1827	50	16	n	n	X
ap-1827	50	17	by	by	ADP
ap-1827	50	18	fw(p	fw(p	NOUN
ap-1827	50	19	,	,	PUNCT
ap-1827	50	20	k)[i	k)[i	PROPN
ap-1827	50	21	]	]	X
ap-1827	50	22	=	=	PUNCT
ap-1827	50	23	min[i]p	min[i]p	NOUN
ap-1827	50	24	,	,	PUNCT
ap-1827	50	25	k.	k.	PROPN
ap-1827	50	26	344	344	NUM
ap-1827	50	27	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-1827	50	28	vol	vol	NOUN
ap-1827	50	29	.	.	PUNCT
ap-1827	51	1	53	53	NUM
ap-1827	51	2	no	no	NOUN
ap-1827	51	3	.	.	PUNCT
ap-1827	52	1	4/2013	4/2013	NOUN
ap-1827	52	2	on	on	ADP
ap-1827	52	3	an	an	DET
ap-1827	52	4	algorithm	algorithm	NOUN
ap-1827	52	5	for	for	ADP
ap-1827	52	6	multiperiodic	multiperiodic	ADJ
ap-1827	52	7	words	word	NOUN
ap-1827	52	8	the	the	DET
ap-1827	52	9	construction	construction	NOUN
ap-1827	52	10	immediately	immediately	ADV
ap-1827	52	11	yields	yield	VERB
ap-1827	52	12	that	that	PRON
ap-1827	52	13	fw(p	fw(p	NOUN
ap-1827	52	14	,	,	PUNCT
ap-1827	52	15	k	k	NOUN
ap-1827	52	16	)	)	PUNCT
ap-1827	52	17	is	be	AUX
ap-1827	52	18	the	the	DET
ap-1827	52	19	unique	unique	ADJ
ap-1827	52	20	(	(	PUNCT
ap-1827	52	21	up	up	ADP
ap-1827	52	22	to	to	ADP
ap-1827	52	23	renaming	rename	VERB
ap-1827	52	24	of	of	ADP
ap-1827	52	25	letters	letter	NOUN
ap-1827	52	26	)	)	PUNCT
ap-1827	52	27	fw	fw	ADJ
ap-1827	52	28	-	-	PUNCT
ap-1827	52	29	word	word	NOUN
ap-1827	52	30	of	of	ADP
ap-1827	52	31	length	length	NOUN
ap-1827	52	32	k	k	PROPN
ap-1827	52	33	relative	relative	ADJ
ap-1827	52	34	to	to	ADP
ap-1827	52	35	p	p	PROPN
ap-1827	52	36	.	.	PUNCT
ap-1827	53	1	the	the	DET
ap-1827	53	2	alphabet	alphabet	NOUN
ap-1827	53	3	eventually	eventually	ADV
ap-1827	53	4	used	use	VERB
ap-1827	53	5	in	in	ADP
ap-1827	53	6	fw(p	fw(p	NOUN
ap-1827	53	7	,	,	PUNCT
ap-1827	53	8	k	k	NOUN
ap-1827	53	9	)	)	PUNCT
ap-1827	53	10	depends	depend	VERB
ap-1827	53	11	on	on	ADP
ap-1827	53	12	the	the	DET
ap-1827	53	13	number	number	NOUN
ap-1827	53	14	of	of	ADP
ap-1827	53	15	equivalence	equivalence	NOUN
ap-1827	53	16	classes	class	NOUN
ap-1827	53	17	.	.	PUNCT
ap-1827	54	1	in	in	ADP
ap-1827	54	2	fact	fact	NOUN
ap-1827	54	3	,	,	PUNCT
ap-1827	54	4	its	its	PRON
ap-1827	54	5	cardinality	cardinality	NOUN
ap-1827	54	6	is	be	AUX
ap-1827	54	7	part	part	NOUN
ap-1827	54	8	of	of	ADP
ap-1827	54	9	the	the	DET
ap-1827	54	10	information	information	NOUN
ap-1827	54	11	yielded	yield	VERB
ap-1827	54	12	by	by	ADP
ap-1827	54	13	the	the	DET
ap-1827	54	14	algorithm	algorithm	NOUN
ap-1827	54	15	.	.	PUNCT
ap-1827	55	1	example	example	NOUN
ap-1827	56	1	1	1	NUM
ap-1827	56	2	.	.	PUNCT
ap-1827	56	3	let	let	VERB
ap-1827	56	4	p	p	NOUN
ap-1827	56	5	=	=	X
ap-1827	56	6	{	{	PUNCT
ap-1827	56	7	5	5	NUM
ap-1827	56	8	,	,	PUNCT
ap-1827	56	9	7	7	NUM
ap-1827	56	10	}	}	PUNCT
ap-1827	56	11	.	.	PUNCT
ap-1827	57	1	the	the	DET
ap-1827	57	2	following	follow	VERB
ap-1827	57	3	picture	picture	NOUN
ap-1827	57	4	illustrates	illustrate	VERB
ap-1827	57	5	the	the	DET
ap-1827	57	6	construction	construction	NOUN
ap-1827	57	7	of	of	ADP
ap-1827	57	8	the	the	DET
ap-1827	57	9	word	word	NOUN
ap-1827	57	10	fw(p	fw(p	NOUN
ap-1827	57	11	,	,	PUNCT
ap-1827	57	12	8)	8)	NUM
ap-1827	57	13	=	=	SYM
ap-1827	57	14	01034010	01034010	NUM
ap-1827	57	15	.	.	PUNCT
ap-1827	58	1	the	the	DET
ap-1827	58	2	upper	upper	ADJ
ap-1827	58	3	edges	edge	NOUN
ap-1827	58	4	correspond	correspond	VERB
ap-1827	58	5	to	to	ADP
ap-1827	58	6	i	i	PROPN
ap-1827	58	7	≡	≡	PROPN
ap-1827	58	8	j	j	PROPN
ap-1827	58	9	mod	mod	PROPN
ap-1827	58	10	5	5	NUM
ap-1827	58	11	,	,	PUNCT
ap-1827	58	12	and	and	CCONJ
ap-1827	58	13	the	the	DET
ap-1827	58	14	lower	low	ADJ
ap-1827	58	15	edge	edge	NOUN
ap-1827	58	16	corresponds	correspond	NOUN
ap-1827	58	17	to	to	ADP
ap-1827	58	18	|i−	|i−	NOUN
ap-1827	58	19	j|	j|	PROPN
ap-1827	58	20	=	=	PUNCT
ap-1827	58	21	7	7	X
ap-1827	58	22	.	.	NOUN
ap-1827	58	23	0	0	NUM
ap-1827	58	24	1	1	NUM
ap-1827	58	25	2	2	NUM
ap-1827	58	26	3	3	NUM
ap-1827	58	27	4	4	NUM
ap-1827	58	28	5	5	NUM
ap-1827	58	29	6	6	NUM
ap-1827	58	30	7	7	NUM
ap-1827	58	31	note	note	NOUN
ap-1827	58	32	that	that	SCONJ
ap-1827	58	33	the	the	DET
ap-1827	58	34	condition	condition	NOUN
ap-1827	58	35	•	•	VERB
ap-1827	58	36	i	i	PRON
ap-1827	58	37	∼p	∼p	PROPN
ap-1827	58	38	,	,	PUNCT
ap-1827	58	39	k	k	PROPN
ap-1827	58	40	j	j	PROPN
ap-1827	58	41	if	if	SCONJ
ap-1827	58	42	|i−	|i−	NOUN
ap-1827	58	43	j|	j|	PROPN
ap-1827	58	44	∈	∈	PROPN
ap-1827	58	45	p	p	PROPN
ap-1827	58	46	would	would	AUX
ap-1827	58	47	alone	alone	ADV
ap-1827	58	48	be	be	AUX
ap-1827	58	49	enough	enough	ADJ
ap-1827	58	50	in	in	ADP
ap-1827	58	51	order	order	NOUN
ap-1827	58	52	to	to	PART
ap-1827	58	53	generate	generate	VERB
ap-1827	58	54	the	the	DET
ap-1827	58	55	equivalence	equivalence	NOUN
ap-1827	58	56	≈p	≈p	PROPN
ap-1827	58	57	,	,	PUNCT
ap-1827	58	58	k.	k.	PROPN
ap-1827	58	59	however	however	ADV
ap-1827	58	60	,	,	PUNCT
ap-1827	58	61	conditions	condition	NOUN
ap-1827	58	62	a	a	PRON
ap-1827	58	63	)	)	PUNCT
ap-1827	58	64	and	and	CCONJ
ap-1827	58	65	b	b	X
ap-1827	58	66	)	)	PUNCT
ap-1827	58	67	,	,	PUNCT
ap-1827	58	68	though	though	SCONJ
ap-1827	58	69	more	more	ADV
ap-1827	58	70	complicated	complicated	ADJ
ap-1827	58	71	,	,	PUNCT
ap-1827	58	72	are	be	AUX
ap-1827	58	73	convenient	convenient	ADJ
ap-1827	58	74	since	since	SCONJ
ap-1827	58	75	they	they	PRON
ap-1827	58	76	allow	allow	VERB
ap-1827	58	77	to	to	PART
ap-1827	58	78	limit	limit	VERB
ap-1827	58	79	the	the	DET
ap-1827	58	80	number	number	NOUN
ap-1827	58	81	of	of	ADP
ap-1827	58	82	equivalence	equivalence	NOUN
ap-1827	58	83	classes	class	NOUN
ap-1827	58	84	to	to	ADP
ap-1827	58	85	m	m	PROPN
ap-1827	58	86	(	(	PUNCT
ap-1827	58	87	and	and	CCONJ
ap-1827	58	88	the	the	DET
ap-1827	58	89	alphabet	alphabet	NOUN
ap-1827	58	90	to	to	ADP
ap-1827	58	91	{	{	PUNCT
ap-1827	58	92	0	0	NUM
ap-1827	58	93	,	,	PUNCT
ap-1827	58	94	1	1	NUM
ap-1827	58	95	,	,	PUNCT
ap-1827	58	96	.	.	PUNCT
ap-1827	58	97	.	.	PUNCT
ap-1827	59	1	.	.	PUNCT
ap-1827	60	1	,	,	PUNCT
ap-1827	60	2	m−	m−	PROPN
ap-1827	60	3	1	1	NUM
ap-1827	60	4	}	}	PUNCT
ap-1827	60	5	)	)	PUNCT
ap-1827	60	6	from	from	ADP
ap-1827	60	7	the	the	DET
ap-1827	60	8	very	very	ADJ
ap-1827	60	9	beginning	beginning	NOUN
ap-1827	60	10	.	.	PUNCT
ap-1827	61	1	consider	consider	VERB
ap-1827	61	2	,	,	PUNCT
ap-1827	61	3	for	for	ADP
ap-1827	61	4	example	example	NOUN
ap-1827	61	5	,	,	PUNCT
ap-1827	61	6	how	how	SCONJ
ap-1827	61	7	0	0	NUM
ap-1827	61	8	≈p,8	≈p,8	ADJ
ap-1827	61	9	2	2	NUM
ap-1827	61	10	is	be	AUX
ap-1827	61	11	immediately	immediately	ADV
ap-1827	61	12	seen	see	VERB
ap-1827	61	13	in	in	ADP
ap-1827	61	14	the	the	DET
ap-1827	61	15	following	following	ADJ
ap-1827	61	16	adjusted	adjusted	ADJ
ap-1827	61	17	picture	picture	NOUN
ap-1827	61	18	.	.	PUNCT
ap-1827	62	1	0	0	NUM
ap-1827	62	2	1	1	NUM
ap-1827	62	3	2	2	NUM
ap-1827	62	4	3	3	NUM
ap-1827	62	5	4	4	NUM
ap-1827	62	6	0	0	NUM
ap-1827	62	7	1	1	NUM
ap-1827	62	8	2	2	NUM
ap-1827	62	9	4	4	NUM
ap-1827	62	10	.	.	PUNCT
ap-1827	63	1	the	the	DET
ap-1827	63	2	algorithm	algorithm	NOUN
ap-1827	63	3	the	the	DET
ap-1827	63	4	basic	basic	ADJ
ap-1827	63	5	step	step	NOUN
ap-1827	63	6	of	of	ADP
ap-1827	63	7	the	the	DET
ap-1827	63	8	algorithm	algorithm	NOUN
ap-1827	63	9	is	be	AUX
ap-1827	63	10	the	the	DET
ap-1827	63	11	reduction	reduction	NOUN
ap-1827	63	12	of	of	ADP
ap-1827	63	13	p	p	NOUN
ap-1827	63	14	to	to	ADP
ap-1827	63	15	a	a	DET
ap-1827	63	16	new	new	ADJ
ap-1827	63	17	set	set	NOUN
ap-1827	63	18	of	of	ADP
ap-1827	63	19	periods	period	NOUN
ap-1827	63	20	q	q	AUX
ap-1827	63	21	defined	define	VERB
ap-1827	63	22	by	by	ADP
ap-1827	63	23	q	q	PROPN
ap-1827	63	24	=	=	X
ap-1827	63	25	{	{	PUNCT
ap-1827	63	26	p−m	p−m	NOUN
ap-1827	63	27	|	|	ADV
ap-1827	63	28	p	p	NOUN
ap-1827	63	29	∈	∈	PROPN
ap-1827	63	30	p	p	X
ap-1827	63	31	,	,	PUNCT
ap-1827	63	32	p	p	NOUN
ap-1827	63	33	6=	6=	PROPN
ap-1827	63	34	m	m	PRON
ap-1827	63	35	}	}	PUNCT
ap-1827	63	36	∪	∪	ADJ
ap-1827	63	37	{	{	PUNCT
ap-1827	63	38	m	m	NOUN
ap-1827	63	39	}	}	PUNCT
ap-1827	63	40	(	(	PUNCT
ap-1827	63	41	1	1	X
ap-1827	63	42	)	)	PUNCT
ap-1827	63	43	(	(	PUNCT
ap-1827	63	44	where	where	SCONJ
ap-1827	63	45	m	m	VERB
ap-1827	63	46	=	=	SYM
ap-1827	63	47	min	min	PROPN
ap-1827	63	48	p	p	NOUN
ap-1827	63	49	according	accord	VERB
ap-1827	63	50	to	to	ADP
ap-1827	63	51	our	our	PRON
ap-1827	63	52	convention	convention	NOUN
ap-1827	63	53	)	)	PUNCT
ap-1827	63	54	.	.	PUNCT
ap-1827	64	1	this	this	DET
ap-1827	64	2	reduction	reduction	NOUN
ap-1827	64	3	is	be	AUX
ap-1827	64	4	,	,	PUNCT
ap-1827	64	5	in	in	ADP
ap-1827	64	6	fact	fact	NOUN
ap-1827	64	7	,	,	PUNCT
ap-1827	64	8	one	one	NUM
ap-1827	64	9	step	step	NOUN
ap-1827	64	10	in	in	ADP
ap-1827	64	11	the	the	DET
ap-1827	64	12	eucledean	eucledean	ADJ
ap-1827	64	13	algorithm	algorithm	NOUN
ap-1827	64	14	,	,	PUNCT
ap-1827	64	15	and	and	CCONJ
ap-1827	64	16	is	be	AUX
ap-1827	64	17	well	well	ADV
ap-1827	64	18	known	know	VERB
ap-1827	64	19	in	in	ADP
ap-1827	64	20	the	the	DET
ap-1827	64	21	literature	literature	NOUN
ap-1827	64	22	on	on	ADP
ap-1827	64	23	multiperiodic	multiperiodic	ADJ
ap-1827	64	24	words	word	NOUN
ap-1827	64	25	.	.	PUNCT
ap-1827	65	1	the	the	DET
ap-1827	65	2	key	key	ADJ
ap-1827	65	3	fact	fact	NOUN
ap-1827	65	4	about	about	ADP
ap-1827	65	5	p	p	NOUN
ap-1827	65	6	and	and	CCONJ
ap-1827	65	7	q	q	NOUN
ap-1827	65	8	is	be	AUX
ap-1827	65	9	expressed	express	VERB
ap-1827	65	10	in	in	ADP
ap-1827	65	11	the	the	DET
ap-1827	65	12	following	follow	VERB
ap-1827	65	13	lemma	lemma	PROPN
ap-1827	65	14	,	,	PUNCT
ap-1827	65	15	which	which	PRON
ap-1827	65	16	is	be	AUX
ap-1827	65	17	an	an	DET
ap-1827	65	18	improved	improved	ADJ
ap-1827	65	19	version	version	NOUN
ap-1827	65	20	of	of	ADP
ap-1827	65	21	lemma	lemma	PROPN
ap-1827	65	22	2	2	NUM
ap-1827	65	23	from	from	ADP
ap-1827	65	24	[	[	X
ap-1827	65	25	4	4	NUM
ap-1827	65	26	]	]	PUNCT
ap-1827	65	27	.	.	PUNCT
ap-1827	66	1	lemma	lemma	PROPN
ap-1827	66	2	1	1	X
ap-1827	66	3	.	.	PUNCT
ap-1827	67	1	let	let	VERB
ap-1827	67	2	k	k	PROPN
ap-1827	67	3	≥	≥	PROPN
ap-1827	67	4	0	0	NUM
ap-1827	67	5	.	.	PUNCT
ap-1827	68	1	then	then	ADV
ap-1827	68	2	for	for	ADP
ap-1827	68	3	all	all	DET
ap-1827	68	4	i	i	PRON
ap-1827	68	5	,	,	PUNCT
ap-1827	68	6	j	j	PROPN
ap-1827	68	7	∈	∈	PROPN
ap-1827	68	8	{	{	PUNCT
ap-1827	68	9	0	0	NUM
ap-1827	68	10	,	,	PUNCT
ap-1827	68	11	1	1	NUM
ap-1827	68	12	,	,	PUNCT
ap-1827	68	13	.	.	PUNCT
ap-1827	68	14	.	.	PUNCT
ap-1827	68	15	.	.	PUNCT
ap-1827	69	1	,	,	PUNCT
ap-1827	69	2	k	k	X
ap-1827	69	3	}	}	PUNCT
ap-1827	70	1	[	[	X
ap-1827	70	2	i]q	i]q	X
ap-1827	70	3	,	,	PUNCT
ap-1827	70	4	k	k	NOUN
ap-1827	71	1	=	=	PUNCT
ap-1827	72	1	[	[	X
ap-1827	72	2	j]q	j]q	PROPN
ap-1827	72	3	,	,	PUNCT
ap-1827	72	4	k	k	PROPN
ap-1827	72	5	if	if	SCONJ
ap-1827	72	6	and	and	CCONJ
ap-1827	72	7	only	only	ADV
ap-1827	72	8	if	if	SCONJ
ap-1827	72	9	[	[	X
ap-1827	72	10	i]p	i]p	NOUN
ap-1827	72	11	,	,	PUNCT
ap-1827	72	12	k+m	k+m	X
ap-1827	72	13	=	=	PUNCT
ap-1827	73	1	[	[	X
ap-1827	73	2	j]p	j]p	NOUN
ap-1827	73	3	,	,	PUNCT
ap-1827	73	4	k+m	k+m	X
ap-1827	73	5	.	.	PUNCT
ap-1827	74	1	proof	proof	NOUN
ap-1827	74	2	.	.	PUNCT
ap-1827	75	1	“	"	PUNCT
ap-1827	75	2	⇒	⇒	NOUN
ap-1827	75	3	”	"	PUNCT
ap-1827	75	4	:	:	PUNCT
ap-1827	75	5	if	if	SCONJ
ap-1827	75	6	[	[	X
ap-1827	75	7	i]q	i]q	X
ap-1827	75	8	,	,	PUNCT
ap-1827	75	9	k	k	NOUN
ap-1827	76	1	=	=	PUNCT
ap-1827	77	1	[	[	X
ap-1827	77	2	j]q	j]q	PROPN
ap-1827	77	3	,	,	PUNCT
ap-1827	77	4	k	k	PROPN
ap-1827	77	5	,	,	PUNCT
ap-1827	77	6	then	then	ADV
ap-1827	77	7	there	there	PRON
ap-1827	77	8	is	be	VERB
ap-1827	77	9	a	a	DET
ap-1827	77	10	sequence	sequence	NOUN
ap-1827	77	11	i	i	PRON
ap-1827	77	12	=	=	SYM
ap-1827	77	13	i0	i0	PROPN
ap-1827	77	14	,	,	PUNCT
ap-1827	77	15	.	.	PUNCT
ap-1827	77	16	.	.	PUNCT
ap-1827	78	1	.	.	PUNCT
ap-1827	79	1	,	,	PUNCT
ap-1827	79	2	i	i	PRON
ap-1827	79	3	`	`	PUNCT
ap-1827	79	4	=	=	SYM
ap-1827	79	5	j	j	PROPN
ap-1827	79	6	,	,	PUNCT
ap-1827	79	7	of	of	ADP
ap-1827	79	8	numbers	number	NOUN
ap-1827	79	9	from	from	ADP
ap-1827	79	10	{	{	PUNCT
ap-1827	79	11	0	0	NUM
ap-1827	79	12	,	,	PUNCT
ap-1827	79	13	1	1	NUM
ap-1827	79	14	,	,	PUNCT
ap-1827	79	15	.	.	PUNCT
ap-1827	79	16	.	.	PUNCT
ap-1827	79	17	.	.	PUNCT
ap-1827	80	1	,	,	PUNCT
ap-1827	81	1	k	k	PROPN
ap-1827	81	2	−	−	PROPN
ap-1827	82	1	1	1	NUM
ap-1827	82	2	}	}	PUNCT
ap-1827	82	3	such	such	ADJ
ap-1827	82	4	that	that	PRON
ap-1827	82	5	is	be	AUX
ap-1827	82	6	∼q	∼q	PROPN
ap-1827	82	7	,	,	PUNCT
ap-1827	82	8	k	k	PROPN
ap-1827	82	9	is+1	is+1	PROPN
ap-1827	82	10	for	for	ADP
ap-1827	82	11	each	each	DET
ap-1827	82	12	s	s	PART
ap-1827	82	13	=	=	NOUN
ap-1827	82	14	0	0	NUM
ap-1827	82	15	,	,	PUNCT
ap-1827	82	16	.	.	PUNCT
ap-1827	82	17	.	.	PUNCT
ap-1827	82	18	.	.	PUNCT
ap-1827	83	1	,	,	PUNCT
ap-1827	83	2	`	`	PUNCT
ap-1827	83	3	−	−	NOUN
ap-1827	83	4	1	1	X
ap-1827	83	5	.	.	PUNCT
ap-1827	84	1	the	the	DET
ap-1827	84	2	relation	relation	NOUN
ap-1827	84	3	is	be	AUX
ap-1827	84	4	∼q	∼q	PROPN
ap-1827	84	5	,	,	PUNCT
ap-1827	84	6	k	k	PROPN
ap-1827	84	7	is+1	is+1	PROPN
ap-1827	84	8	implies	imply	VERB
ap-1827	84	9	is	be	AUX
ap-1827	84	10	∼p	∼p	PROPN
ap-1827	84	11	,	,	PUNCT
ap-1827	84	12	k+m	k+m	PROPN
ap-1827	84	13	is+1	is+1	NOUN
ap-1827	84	14	,	,	PUNCT
ap-1827	84	15	since	since	SCONJ
ap-1827	84	16	either	either	CCONJ
ap-1827	84	17	•	•	NOUN
ap-1827	84	18	is	be	AUX
ap-1827	84	19	≡	≡	PROPN
ap-1827	84	20	is+1	is+1	PROPN
ap-1827	84	21	mod	mod	PROPN
ap-1827	84	22	m	m	PROPN
ap-1827	84	23	,	,	PUNCT
ap-1827	84	24	or	or	CCONJ
ap-1827	84	25	•	•	NUM
ap-1827	84	26	max{is	max{is	NOUN
ap-1827	84	27	,	,	PUNCT
ap-1827	84	28	is+1}+	is+1}+	ADJ
ap-1827	84	29	m−min{is	m−min{is	NOUN
ap-1827	84	30	,	,	PUNCT
ap-1827	84	31	is+1	is+1	PROPN
ap-1827	84	32	}	}	PUNCT
ap-1827	84	33	∈	∈	PROPN
ap-1827	84	34	p	p	NOUN
ap-1827	84	35	.	.	PUNCT
ap-1827	85	1	therefore	therefore	ADV
ap-1827	85	2	[	[	X
ap-1827	85	3	i]p	i]p	ADP
ap-1827	85	4	,	,	PUNCT
ap-1827	85	5	k+m	k+m	X
ap-1827	85	6	=	=	PUNCT
ap-1827	86	1	[	[	X
ap-1827	86	2	j]p	j]p	NOUN
ap-1827	86	3	,	,	PUNCT
ap-1827	86	4	k+m	k+m	NUM
ap-1827	86	5	.	.	PUNCT
ap-1827	87	1	“	"	PUNCT
ap-1827	87	2	⇐	⇐	NOUN
ap-1827	87	3	”	"	PUNCT
ap-1827	87	4	:	:	PUNCT
ap-1827	87	5	on	on	ADP
ap-1827	87	6	the	the	DET
ap-1827	87	7	other	other	ADJ
ap-1827	87	8	hand	hand	NOUN
ap-1827	87	9	,	,	PUNCT
ap-1827	87	10	let	let	VERB
ap-1827	87	11	i	i	PRON
ap-1827	87	12	=	=	SYM
ap-1827	87	13	i0	i0	PROPN
ap-1827	87	14	,	,	PUNCT
ap-1827	87	15	.	.	PUNCT
ap-1827	87	16	.	.	PUNCT
ap-1827	88	1	.	.	PUNCT
ap-1827	89	1	,	,	PUNCT
ap-1827	89	2	i	i	PRON
ap-1827	89	3	`	`	PUNCT
ap-1827	89	4	=	=	SYM
ap-1827	89	5	j	j	NOUN
ap-1827	89	6	,	,	PUNCT
ap-1827	89	7	be	be	AUX
ap-1827	89	8	a	a	DET
ap-1827	89	9	sequence	sequence	NOUN
ap-1827	89	10	of	of	ADP
ap-1827	89	11	numbers	number	NOUN
ap-1827	89	12	from	from	ADP
ap-1827	89	13	{	{	PUNCT
ap-1827	89	14	0	0	NUM
ap-1827	89	15	,	,	PUNCT
ap-1827	89	16	.	.	PUNCT
ap-1827	89	17	.	.	PUNCT
ap-1827	90	1	.	.	PUNCT
ap-1827	91	1	,	,	PUNCT
ap-1827	91	2	k	k	PROPN
ap-1827	91	3	+	+	CCONJ
ap-1827	91	4	m−	m−	PROPN
ap-1827	91	5	1	1	NUM
ap-1827	91	6	}	}	PUNCT
ap-1827	91	7	,	,	PUNCT
ap-1827	91	8	with	with	ADP
ap-1827	91	9	i	i	PRON
ap-1827	91	10	,	,	PUNCT
ap-1827	91	11	j	j	PROPN
ap-1827	91	12	∈	∈	PROPN
ap-1827	91	13	{	{	PUNCT
ap-1827	91	14	0	0	NUM
ap-1827	91	15	,	,	PUNCT
ap-1827	91	16	.	.	PUNCT
ap-1827	91	17	.	.	PUNCT
ap-1827	92	1	.	.	PUNCT
ap-1827	93	1	,	,	PUNCT
ap-1827	94	1	k	k	PROPN
ap-1827	95	1	−	−	NOUN
ap-1827	96	1	1	1	NUM
ap-1827	96	2	}	}	PUNCT
ap-1827	96	3	,	,	PUNCT
ap-1827	96	4	such	such	ADJ
ap-1827	96	5	that	that	PRON
ap-1827	96	6	is	be	AUX
ap-1827	96	7	∼p	∼p	PROPN
ap-1827	96	8	,	,	PUNCT
ap-1827	96	9	k+m	k+m	X
ap-1827	96	10	is+1	is+1	NOUN
ap-1827	96	11	for	for	ADP
ap-1827	96	12	each	each	DET
ap-1827	96	13	s	s	PART
ap-1827	96	14	=	=	NOUN
ap-1827	96	15	0	0	NUM
ap-1827	96	16	,	,	PUNCT
ap-1827	96	17	.	.	PUNCT
ap-1827	96	18	.	.	PUNCT
ap-1827	96	19	.	.	PUNCT
ap-1827	97	1	,	,	PUNCT
ap-1827	97	2	`	`	PUNCT
ap-1827	97	3	−	−	NOUN
ap-1827	97	4	1	1	X
ap-1827	97	5	.	.	PUNCT
ap-1827	98	1	certainly	certainly	ADV
ap-1827	98	2	,	,	PUNCT
ap-1827	98	3	we	we	PRON
ap-1827	98	4	can	can	AUX
ap-1827	98	5	suppose	suppose	VERB
ap-1827	98	6	that	that	SCONJ
ap-1827	98	7	the	the	DET
ap-1827	98	8	numbers	number	NOUN
ap-1827	98	9	in	in	ADP
ap-1827	98	10	the	the	DET
ap-1827	98	11	sequence	sequence	NOUN
ap-1827	98	12	are	be	AUX
ap-1827	98	13	pairwise	pairwise	NOUN
ap-1827	98	14	distinct	distinct	ADJ
ap-1827	98	15	,	,	PUNCT
ap-1827	98	16	whence	whence	ADP
ap-1827	98	17	|is	|is	PRON
ap-1827	98	18	−	−	PROPN
ap-1827	98	19	is+1|	is+1|	PROPN
ap-1827	98	20	≥	≥	NOUN
ap-1827	98	21	m	m	ADJ
ap-1827	98	22	and	and	CCONJ
ap-1827	98	23	both	both	PRON
ap-1827	98	24	min{is	min{is	NOUN
ap-1827	98	25	,	,	PUNCT
ap-1827	98	26	is+1	is+1	NOUN
ap-1827	98	27	}	}	PUNCT
ap-1827	98	28	and	and	CCONJ
ap-1827	98	29	max{is	max{is	NOUN
ap-1827	98	30	,	,	PUNCT
ap-1827	98	31	is+1	is+1	PROPN
ap-1827	98	32	}	}	PUNCT
ap-1827	98	33	−	−	PROPN
ap-1827	98	34	m	m	NOUN
ap-1827	98	35	are	be	AUX
ap-1827	98	36	in	in	ADP
ap-1827	98	37	{	{	PUNCT
ap-1827	98	38	0	0	NUM
ap-1827	98	39	,	,	PUNCT
ap-1827	98	40	1	1	NUM
ap-1827	98	41	,	,	PUNCT
ap-1827	98	42	.	.	PUNCT
ap-1827	98	43	.	.	PUNCT
ap-1827	98	44	.	.	PUNCT
ap-1827	99	1	,	,	PUNCT
ap-1827	100	1	k	k	PROPN
ap-1827	101	1	−	−	PROPN
ap-1827	102	1	1	1	NUM
ap-1827	102	2	}	}	PUNCT
ap-1827	102	3	.	.	PUNCT
ap-1827	103	1	we	we	PRON
ap-1827	103	2	now	now	ADV
ap-1827	103	3	see	see	VERB
ap-1827	103	4	that	that	DET
ap-1827	103	5	max{is	max{is	NOUN
ap-1827	103	6	,	,	PUNCT
ap-1827	103	7	is+1	is+1	PROPN
ap-1827	103	8	}	}	PUNCT
ap-1827	103	9	−m	−m	PROPN
ap-1827	103	10	∼q	∼q	PROPN
ap-1827	103	11	,	,	PUNCT
ap-1827	103	12	k	k	PROPN
ap-1827	103	13	min{is	min{is	X
ap-1827	103	14	,	,	PUNCT
ap-1827	103	15	is+1	is+1	PROPN
ap-1827	103	16	}	}	PUNCT
ap-1827	103	17	.	.	PUNCT
ap-1827	104	1	therefore	therefore	ADV
ap-1827	104	2	the	the	DET
ap-1827	104	3	sequence	sequence	NOUN
ap-1827	104	4	i	i	PRON
ap-1827	104	5	=	=	SYM
ap-1827	104	6	i0	i0	PROPN
ap-1827	104	7	,	,	PUNCT
ap-1827	104	8	(	(	PUNCT
ap-1827	104	9	i0	i0	PROPN
ap-1827	104	10	mod	mod	PROPN
ap-1827	104	11	m	m	PROPN
ap-1827	104	12	)	)	PUNCT
ap-1827	104	13	,	,	PUNCT
ap-1827	104	14	.	.	PUNCT
ap-1827	104	15	.	.	PUNCT
ap-1827	104	16	.	.	PUNCT
ap-1827	105	1	,	,	PUNCT
ap-1827	105	2	(	(	PUNCT
ap-1827	105	3	i	i	PRON
ap-1827	105	4	`	`	PUNCT
ap-1827	105	5	mod	mod	PROPN
ap-1827	105	6	m	m	PROPN
ap-1827	105	7	)	)	PUNCT
ap-1827	105	8	,	,	PUNCT
ap-1827	105	9	i	i	PRON
ap-1827	105	10	`	`	PUNCT
ap-1827	105	11	=	=	PUNCT
ap-1827	105	12	j	j	PROPN
ap-1827	105	13	proves	prove	VERB
ap-1827	105	14	[	[	X
ap-1827	105	15	i]q	i]q	X
ap-1827	105	16	,	,	PUNCT
ap-1827	105	17	k	k	NOUN
ap-1827	106	1	=	=	PUNCT
ap-1827	107	1	[	[	X
ap-1827	107	2	j]q	j]q	PROPN
ap-1827	107	3	,	,	PUNCT
ap-1827	107	4	k.	k.	PROPN
ap-1827	108	1	we	we	PRON
ap-1827	108	2	have	have	VERB
ap-1827	108	3	an	an	DET
ap-1827	108	4	immediate	immediate	ADJ
ap-1827	108	5	corollary	corollary	NOUN
ap-1827	108	6	.	.	PUNCT
ap-1827	109	1	corollary	corollary	ADJ
ap-1827	109	2	1	1	NUM
ap-1827	109	3	.	.	PUNCT
ap-1827	110	1	for	for	ADP
ap-1827	110	2	any	any	DET
ap-1827	110	3	k	k	PROPN
ap-1827	110	4	≥	≥	NOUN
ap-1827	110	5	0	0	NUM
ap-1827	110	6	,	,	PUNCT
ap-1827	110	7	the	the	DET
ap-1827	110	8	word	word	NOUN
ap-1827	110	9	fw(q	fw(q	NOUN
ap-1827	110	10	,	,	PUNCT
ap-1827	110	11	k	k	NOUN
ap-1827	110	12	)	)	PUNCT
ap-1827	110	13	is	be	AUX
ap-1827	110	14	a	a	DET
ap-1827	110	15	prefix	prefix	NOUN
ap-1827	110	16	of	of	ADP
ap-1827	110	17	fw(p	fw(p	NOUN
ap-1827	110	18	,	,	PUNCT
ap-1827	110	19	k	k	PROPN
ap-1827	110	20	+	+	PROPN
ap-1827	110	21	m	m	PROPN
ap-1827	110	22	)	)	PUNCT
ap-1827	110	23	.	.	PUNCT
ap-1827	111	1	the	the	DET
ap-1827	111	2	following	follow	VERB
ap-1827	111	3	lemma	lemma	PROPN
ap-1827	111	4	is	be	AUX
ap-1827	111	5	an	an	DET
ap-1827	111	6	easy	easy	ADJ
ap-1827	111	7	observation	observation	NOUN
ap-1827	111	8	.	.	PUNCT
ap-1827	112	1	lemma	lemma	PROPN
ap-1827	112	2	2	2	X
ap-1827	112	3	.	.	PUNCT
ap-1827	113	1	let	let	VERB
ap-1827	113	2	k−m	k−m	PROPN
ap-1827	113	3	≤	≤	NUM
ap-1827	113	4	i	i	PRON
ap-1827	113	5	≤	≤	PUNCT
ap-1827	114	1	m−1	m−1	PROPN
ap-1827	114	2	.	.	PUNCT
ap-1827	115	1	then	then	ADV
ap-1827	115	2	[	[	X
ap-1827	115	3	i]p	i]p	ADP
ap-1827	115	4	,	,	PUNCT
ap-1827	115	5	k	k	NOUN
ap-1827	115	6	=	=	PUNCT
ap-1827	115	7	{	{	PUNCT
ap-1827	115	8	i	i	NOUN
ap-1827	115	9	}	}	PUNCT
ap-1827	115	10	.	.	PUNCT
ap-1827	116	1	proof	proof	NOUN
ap-1827	116	2	.	.	PUNCT
ap-1827	117	1	both	both	PRON
ap-1827	117	2	i	i	PRON
ap-1827	117	3	−	−	VERB
ap-1827	118	1	p	p	NOUN
ap-1827	119	1	and	and	CCONJ
ap-1827	119	2	i	i	PRON
ap-1827	120	1	+	+	CCONJ
ap-1827	120	2	p	p	NOUN
ap-1827	120	3	are	be	AUX
ap-1827	120	4	out	out	ADP
ap-1827	120	5	of	of	ADP
ap-1827	120	6	range	range	NOUN
ap-1827	120	7	{	{	PUNCT
ap-1827	120	8	0	0	NUM
ap-1827	120	9	,	,	PUNCT
ap-1827	120	10	1	1	NUM
ap-1827	120	11	,	,	PUNCT
ap-1827	120	12	.	.	PUNCT
ap-1827	120	13	.	.	PUNCT
ap-1827	121	1	.	.	PUNCT
ap-1827	122	1	,	,	PUNCT
ap-1827	123	1	k	k	PROPN
ap-1827	123	2	−	−	PROPN
ap-1827	124	1	1	1	NUM
ap-1827	124	2	}	}	PUNCT
ap-1827	124	3	for	for	ADP
ap-1827	124	4	any	any	DET
ap-1827	124	5	p	p	NOUN
ap-1827	124	6	∈	∈	PROPN
ap-1827	124	7	p	p	NOUN
ap-1827	124	8	(	(	PUNCT
ap-1827	124	9	including	include	VERB
ap-1827	124	10	m	m	PROPN
ap-1827	124	11	)	)	PUNCT
ap-1827	124	12	.	.	PUNCT
ap-1827	125	1	therefore	therefore	ADV
ap-1827	125	2	i	i	PRON
ap-1827	125	3	is	be	AUX
ap-1827	125	4	not	not	PART
ap-1827	125	5	related	relate	VERB
ap-1827	125	6	by	by	ADP
ap-1827	125	7	∼p	∼p	PROPN
ap-1827	125	8	,	,	PUNCT
ap-1827	125	9	k	k	PROPN
ap-1827	125	10	to	to	ADP
ap-1827	125	11	any	any	DET
ap-1827	125	12	other	other	ADJ
ap-1827	125	13	element	element	NOUN
ap-1827	125	14	.	.	PUNCT
ap-1827	126	1	from	from	ADP
ap-1827	126	2	corollary	corollary	ADJ
ap-1827	126	3	1	1	NUM
ap-1827	126	4	and	and	CCONJ
ap-1827	126	5	lemma	lemma	PROPN
ap-1827	126	6	2	2	NUM
ap-1827	126	7	,	,	PUNCT
ap-1827	126	8	the	the	DET
ap-1827	126	9	formula	formula	NOUN
ap-1827	126	10	lp	lp	NOUN
ap-1827	126	11	=	=	NOUN
ap-1827	126	12	m	m	PROPN
ap-1827	126	13	+	+	X
ap-1827	126	14	max{lq	max{lq	PROPN
ap-1827	126	15	,	,	PUNCT
ap-1827	126	16	m−	m−	PROPN
ap-1827	126	17	1	1	NUM
ap-1827	126	18	}	}	PUNCT
ap-1827	126	19	can	can	AUX
ap-1827	126	20	be	be	AUX
ap-1827	126	21	readily	readily	ADV
ap-1827	126	22	derived	derive	VERB
ap-1827	126	23	(	(	PUNCT
ap-1827	126	24	see	see	VERB
ap-1827	126	25	[	[	X
ap-1827	126	26	4	4	NUM
ap-1827	126	27	,	,	PUNCT
ap-1827	126	28	5	5	NUM
ap-1827	126	29	]	]	PUNCT
ap-1827	126	30	)	)	PUNCT
ap-1827	126	31	.	.	PUNCT
ap-1827	127	1	in	in	ADP
ap-1827	127	2	addition	addition	NOUN
ap-1827	127	3	,	,	PUNCT
ap-1827	127	4	it	it	PRON
ap-1827	127	5	yields	yield	VERB
ap-1827	127	6	the	the	DET
ap-1827	127	7	following	follow	VERB
ap-1827	127	8	construction	construction	NOUN
ap-1827	127	9	of	of	ADP
ap-1827	127	10	fw(p	fw(p	NOUN
ap-1827	127	11	,	,	PUNCT
ap-1827	127	12	k	k	NOUN
ap-1827	127	13	)	)	PUNCT
ap-1827	127	14	,	,	PUNCT
ap-1827	127	15	equivalent	equivalent	ADJ
ap-1827	127	16	to	to	ADP
ap-1827	127	17	algorithm	algorithm	PROPN
ap-1827	127	18	b	b	NOUN
ap-1827	127	19	described	describe	VERB
ap-1827	127	20	in	in	ADP
ap-1827	127	21	[	[	X
ap-1827	127	22	3	3	NUM
ap-1827	127	23	]	]	PUNCT
ap-1827	127	24	.	.	PUNCT
ap-1827	128	1	fw	fw	ADJ
ap-1827	128	2	-	-	PUNCT
ap-1827	128	3	construction	construction	NOUN
ap-1827	128	4	(	(	PUNCT
ap-1827	128	5	algorithm	algorithm	NOUN
ap-1827	128	6	b	b	NOUN
ap-1827	128	7	)	)	PUNCT
ap-1827	128	8	.	.	PUNCT
ap-1827	129	1	(	(	PUNCT
ap-1827	129	2	1	1	NUM
ap-1827	129	3	.	.	PUNCT
ap-1827	129	4	)	)	PUNCT
ap-1827	130	1	if	if	SCONJ
ap-1827	130	2	k	k	PROPN
ap-1827	130	3	≤	≤	PROPN
ap-1827	130	4	m	m	PROPN
ap-1827	130	5	,	,	PUNCT
ap-1827	130	6	then	then	ADV
ap-1827	130	7	lemma	lemma	PROPN
ap-1827	130	8	2	2	NUM
ap-1827	130	9	gives	give	VERB
ap-1827	130	10	fw(p	fw(p	NOUN
ap-1827	130	11	,	,	PUNCT
ap-1827	130	12	k	k	NOUN
ap-1827	130	13	)	)	PUNCT
ap-1827	130	14	=	=	SYM
ap-1827	131	1	0	0	X
ap-1827	131	2	·	·	SYM
ap-1827	131	3	1	1	NUM
ap-1827	131	4	·	·	PUNCT
ap-1827	131	5	·	·	PUNCT
ap-1827	131	6	·	·	PUNCT
ap-1827	131	7	(	(	PUNCT
ap-1827	131	8	k−	k−	PROPN
ap-1827	131	9	1	1	NUM
ap-1827	131	10	)	)	PUNCT
ap-1827	131	11	.	.	PUNCT
ap-1827	132	1	(	(	PUNCT
ap-1827	132	2	recall	recall	VERB
ap-1827	132	3	that	that	SCONJ
ap-1827	132	4	we	we	PRON
ap-1827	132	5	consider	consider	VERB
ap-1827	132	6	integers	integer	NOUN
ap-1827	132	7	as	as	ADP
ap-1827	132	8	letters	letter	NOUN
ap-1827	132	9	.	.	PUNCT
ap-1827	133	1	to	to	PART
ap-1827	133	2	stress	stress	VERB
ap-1827	133	3	this	this	PRON
ap-1827	133	4	,	,	PUNCT
ap-1827	133	5	we	we	PRON
ap-1827	133	6	use	use	VERB
ap-1827	133	7	the	the	DET
ap-1827	133	8	typewriter	typewriter	NOUN
ap-1827	133	9	font	font	NOUN
ap-1827	133	10	for	for	ADP
ap-1827	133	11	them	they	PRON
ap-1827	133	12	.	.	PUNCT
ap-1827	134	1	the	the	DET
ap-1827	134	2	multiplication	multiplication	NOUN
ap-1827	134	3	sign	sign	NOUN
ap-1827	134	4	means	mean	VERB
ap-1827	134	5	concatenation	concatenation	NOUN
ap-1827	134	6	)	)	PUNCT
ap-1827	134	7	.	.	PUNCT
ap-1827	135	1	(	(	PUNCT
ap-1827	135	2	2	2	NUM
ap-1827	135	3	.	.	PUNCT
ap-1827	135	4	)	)	PUNCT
ap-1827	135	5	let	let	VERB
ap-1827	135	6	k	k	PRON
ap-1827	135	7	>	>	X
ap-1827	135	8	m.	m.	NOUN
ap-1827	135	9	since	since	SCONJ
ap-1827	135	10	the	the	DET
ap-1827	135	11	word	word	NOUN
ap-1827	135	12	fw(p	fw(p	NOUN
ap-1827	135	13	,	,	PUNCT
ap-1827	135	14	k	k	NOUN
ap-1827	135	15	)	)	PUNCT
ap-1827	135	16	has	have	VERB
ap-1827	135	17	a	a	DET
ap-1827	135	18	period	period	NOUN
ap-1827	135	19	m	m	NOUN
ap-1827	135	20	,	,	PUNCT
ap-1827	135	21	it	it	PRON
ap-1827	135	22	is	be	AUX
ap-1827	135	23	determined	determine	VERB
ap-1827	135	24	by	by	ADP
ap-1827	135	25	its	its	PRON
ap-1827	135	26	prefix	prefix	NOUN
ap-1827	135	27	w	w	NOUN
ap-1827	135	28	of	of	ADP
ap-1827	135	29	length	length	NOUN
ap-1827	135	30	m.	m.	NOUN
ap-1827	135	31	denote	denote	VERB
ap-1827	135	32	u	u	NOUN
ap-1827	135	33	=	=	NOUN
ap-1827	135	34	fw(q	fw(q	NOUN
ap-1827	135	35	,	,	PUNCT
ap-1827	135	36	k−m	k−m	NOUN
ap-1827	135	37	)	)	PUNCT
ap-1827	135	38	.	.	PUNCT
ap-1827	136	1	corollary	corollary	ADJ
ap-1827	136	2	1	1	NUM
ap-1827	136	3	and	and	CCONJ
ap-1827	136	4	lemma	lemma	PROPN
ap-1827	136	5	2	2	NUM
ap-1827	136	6	imply	imply	VERB
ap-1827	136	7	that	that	PRON
ap-1827	136	8	•	•	NUM
ap-1827	136	9	w	w	NOUN
ap-1827	136	10	=	=	SYM
ap-1827	136	11	prefm(u	prefm(u	NOUN
ap-1827	136	12	)	)	PUNCT
ap-1827	136	13	if	if	SCONJ
ap-1827	136	14	m	m	VERB
ap-1827	136	15	≤	≤	X
ap-1827	136	16	k	k	NOUN
ap-1827	136	17	−m	−m	NOUN
ap-1827	136	18	,	,	PUNCT
ap-1827	136	19	and	and	CCONJ
ap-1827	136	20	•	•	NUM
ap-1827	136	21	w	w	NOUN
ap-1827	136	22	=	=	SYM
ap-1827	136	23	u	u	X
ap-1827	136	24	·	·	PUNCT
ap-1827	136	25	|u|	|u|	X
ap-1827	136	26	·	·	PUNCT
ap-1827	136	27	(	(	PUNCT
ap-1827	136	28	|u|+	|u|+	NOUN
ap-1827	136	29	1	1	NUM
ap-1827	136	30	)	)	PUNCT
ap-1827	136	31	·	·	PUNCT
ap-1827	136	32	·	·	PUNCT
ap-1827	136	33	·	·	PUNCT
ap-1827	137	1	(	(	PUNCT
ap-1827	137	2	m−	m−	PROPN
ap-1827	137	3	1	1	NUM
ap-1827	137	4	)	)	PUNCT
ap-1827	137	5	otherwise	otherwise	ADV
ap-1827	137	6	.	.	PUNCT
ap-1827	138	1	this	this	PRON
ap-1827	138	2	can	can	AUX
ap-1827	138	3	be	be	AUX
ap-1827	138	4	succinctly	succinctly	ADV
ap-1827	138	5	stated	state	VERB
ap-1827	138	6	as	as	ADP
ap-1827	138	7	:	:	PUNCT
ap-1827	138	8	fw(p	fw(p	NOUN
ap-1827	138	9	,	,	PUNCT
ap-1827	138	10	k)[i	k)[i	PROPN
ap-1827	138	11	]	]	X
ap-1827	138	12	=	=	SYM
ap-1827	138	13			PROPN
ap-1827	138	14	fw(q	fw(q	NOUN
ap-1827	138	15	,	,	PUNCT
ap-1827	138	16	k	k	PROPN
ap-1827	138	17	−m)[i	−m)[i	NOUN
ap-1827	138	18	mod	mod	PROPN
ap-1827	139	1	m	m	X
ap-1827	139	2	]	]	X
ap-1827	139	3	if	if	SCONJ
ap-1827	139	4	(	(	PUNCT
ap-1827	139	5	i	i	PRON
ap-1827	139	6	mod	mod	PROPN
ap-1827	139	7	m	m	PROPN
ap-1827	139	8	)	)	PUNCT
ap-1827	139	9	<	<	X
ap-1827	139	10	k	k	PROPN
ap-1827	139	11	−m	−m	NOUN
ap-1827	139	12	;	;	PUNCT
ap-1827	139	13	i	i	PRON
ap-1827	139	14	mod	mod	PROPN
ap-1827	139	15	m	m	VERB
ap-1827	139	16	otherwise	otherwise	ADV
ap-1827	139	17	.	.	PUNCT
ap-1827	140	1	345	345	NUM
ap-1827	140	2	štěpán	štěpán	PROPN
ap-1827	140	3	holub	holub	PROPN
ap-1827	140	4	acta	acta	PROPN
ap-1827	140	5	polytechnica	polytechnica	PROPN
ap-1827	140	6	example	example	NOUN
ap-1827	140	7	2	2	X
ap-1827	140	8	.	.	PUNCT
ap-1827	141	1	let	let	VERB
ap-1827	141	2	p	p	NOUN
ap-1827	141	3	=	=	X
ap-1827	141	4	{	{	PUNCT
ap-1827	141	5	5	5	NUM
ap-1827	141	6	,	,	PUNCT
ap-1827	141	7	7	7	NUM
ap-1827	141	8	}	}	PUNCT
ap-1827	141	9	and	and	CCONJ
ap-1827	141	10	k	k	X
ap-1827	141	11	=	=	NOUN
ap-1827	141	12	8	8	NUM
ap-1827	141	13	as	as	ADP
ap-1827	141	14	in	in	ADP
ap-1827	141	15	example	example	NOUN
ap-1827	141	16	1	1	NUM
ap-1827	141	17	.	.	PUNCT
ap-1827	141	18	recursive	recursive	ADJ
ap-1827	141	19	definition	definition	NOUN
ap-1827	141	20	of	of	ADP
ap-1827	141	21	fw(p	fw(p	NOUN
ap-1827	141	22	,	,	PUNCT
ap-1827	141	23	8)	8)	NUM
ap-1827	141	24	leads	lead	VERB
ap-1827	141	25	to	to	ADP
ap-1827	141	26	p	p	NOUN
ap-1827	141	27	=	=	NOUN
ap-1827	141	28	q0	q0	NOUN
ap-1827	141	29	=	=	PUNCT
ap-1827	141	30	{	{	PUNCT
ap-1827	141	31	5	5	NUM
ap-1827	141	32	,	,	PUNCT
ap-1827	141	33	7	7	NUM
ap-1827	141	34	}	}	PUNCT
ap-1827	141	35	k	k	PROPN
ap-1827	141	36	=	=	PUNCT
ap-1827	141	37	k0	k0	PROPN
ap-1827	141	38	=	=	SYM
ap-1827	141	39	8	8	NUM
ap-1827	141	40	q1	q1	NOUN
ap-1827	141	41	=	=	SYM
ap-1827	141	42	{	{	PUNCT
ap-1827	141	43	2	2	NUM
ap-1827	141	44	,	,	PUNCT
ap-1827	141	45	5	5	NUM
ap-1827	141	46	}	}	PUNCT
ap-1827	141	47	k1	k1	NOUN
ap-1827	141	48	=	=	SYM
ap-1827	141	49	3	3	NUM
ap-1827	141	50	q2	q2	NOUN
ap-1827	141	51	=	=	SYM
ap-1827	141	52	{	{	PUNCT
ap-1827	141	53	2	2	NUM
ap-1827	141	54	,	,	PUNCT
ap-1827	141	55	3	3	NUM
ap-1827	141	56	}	}	PUNCT
ap-1827	141	57	k2	k2	NOUN
ap-1827	141	58	=	=	NOUN
ap-1827	141	59	1	1	NUM
ap-1827	141	60	in	in	ADP
ap-1827	141	61	order	order	NOUN
ap-1827	141	62	to	to	PART
ap-1827	141	63	obtain	obtain	VERB
ap-1827	141	64	the	the	DET
ap-1827	141	65	word	word	NOUN
ap-1827	141	66	u0	u0	ADJ
ap-1827	141	67	=	=	NOUN
ap-1827	141	68	fw(q0	fw(q0	PROPN
ap-1827	141	69	,	,	PUNCT
ap-1827	141	70	k0	k0	PROPN
ap-1827	141	71	)	)	PUNCT
ap-1827	141	72	=	=	SYM
ap-1827	141	73	fw(p	fw(p	NOUN
ap-1827	141	74	,	,	PUNCT
ap-1827	141	75	8)	8)	NUM
ap-1827	141	76	we	we	PRON
ap-1827	141	77	will	will	AUX
ap-1827	141	78	need	need	VERB
ap-1827	141	79	words	word	NOUN
ap-1827	141	80	u1	u1	NOUN
ap-1827	141	81	=	=	SYM
ap-1827	141	82	fw(q1	fw(q1	NOUN
ap-1827	141	83	,	,	PUNCT
ap-1827	141	84	k1	k1	NOUN
ap-1827	141	85	)	)	PUNCT
ap-1827	141	86	and	and	CCONJ
ap-1827	141	87	u2	u2	NOUN
ap-1827	141	88	=	=	SYM
ap-1827	141	89	fw(q2	fw(q2	NOUN
ap-1827	141	90	,	,	PUNCT
ap-1827	141	91	k2	k2	NOUN
ap-1827	141	92	)	)	PUNCT
ap-1827	141	93	.	.	PUNCT
ap-1827	142	1	since	since	SCONJ
ap-1827	142	2	k2	k2	PROPN
ap-1827	142	3	=	=	SYM
ap-1827	142	4	1	1	NUM
ap-1827	142	5	,	,	PUNCT
ap-1827	142	6	we	we	PRON
ap-1827	142	7	have	have	VERB
ap-1827	142	8	u2	u2	NOUN
ap-1827	142	9	=	=	NOUN
ap-1827	142	10	0	0	NUM
ap-1827	142	11	.	.	PUNCT
ap-1827	143	1	from	from	ADP
ap-1827	143	2	the	the	DET
ap-1827	143	3	point	point	NOUN
ap-1827	143	4	(	(	PUNCT
ap-1827	143	5	2	2	NUM
ap-1827	143	6	.	.	PUNCT
ap-1827	143	7	)	)	PUNCT
ap-1827	143	8	above	above	ADP
ap-1827	143	9	we	we	PRON
ap-1827	143	10	have	have	VERB
ap-1827	143	11	u1	u1	NOUN
ap-1827	143	12	=	=	SYM
ap-1827	143	13	pref3(wω	pref3(wω	NOUN
ap-1827	143	14	1	1	X
ap-1827	143	15	)	)	PUNCT
ap-1827	143	16	where	where	SCONJ
ap-1827	143	17	w1	w1	NOUN
ap-1827	143	18	=	=	SYM
ap-1827	143	19	01	01	PROPN
ap-1827	143	20	.	.	PUNCT
ap-1827	144	1	therefore	therefore	ADV
ap-1827	144	2	u1	u1	PROPN
ap-1827	144	3	=	=	SYM
ap-1827	144	4	010	010	NUM
ap-1827	144	5	.	.	PUNCT
ap-1827	145	1	similarly	similarly	ADV
ap-1827	145	2	,	,	PUNCT
ap-1827	145	3	we	we	PRON
ap-1827	145	4	get	get	VERB
ap-1827	145	5	u0	u0	ADJ
ap-1827	145	6	=	=	NOUN
ap-1827	145	7	pref8(wω	pref8(wω	NOUN
ap-1827	145	8	0	0	NUM
ap-1827	145	9	)	)	PUNCT
ap-1827	145	10	where	where	SCONJ
ap-1827	145	11	w0	w0	PROPN
ap-1827	145	12	=	=	SYM
ap-1827	145	13	01034	01034	NUM
ap-1827	145	14	,	,	PUNCT
ap-1827	145	15	whence	whence	NOUN
ap-1827	145	16	fw(p	fw(p	NOUN
ap-1827	145	17	,	,	PUNCT
ap-1827	145	18	8)	8)	NUM
ap-1827	145	19	=	=	SYM
ap-1827	145	20	01034010	01034010	NUM
ap-1827	145	21	.	.	PUNCT
ap-1827	146	1	schematically	schematically	NOUN
ap-1827	146	2	:	:	PUNCT
ap-1827	146	3	q0	q0	PROPN
ap-1827	146	4	=	=	PUNCT
ap-1827	146	5	{	{	PUNCT
ap-1827	146	6	5	5	NUM
ap-1827	146	7	,	,	PUNCT
ap-1827	146	8	7	7	NUM
ap-1827	146	9	}	}	PUNCT
ap-1827	146	10	q1	q1	NOUN
ap-1827	146	11	=	=	SYM
ap-1827	146	12	{	{	PUNCT
ap-1827	146	13	2	2	NUM
ap-1827	146	14	,	,	PUNCT
ap-1827	146	15	5	5	NUM
ap-1827	146	16	}	}	PUNCT
ap-1827	146	17	q2	q2	NOUN
ap-1827	146	18	=	=	SYM
ap-1827	146	19	{	{	PUNCT
ap-1827	146	20	2	2	NUM
ap-1827	146	21	,	,	PUNCT
ap-1827	146	22	3	3	NUM
ap-1827	146	23	}	}	PUNCT
ap-1827	146	24	k0	k0	PROPN
ap-1827	146	25	=	=	SYM
ap-1827	146	26	8	8	NUM
ap-1827	146	27	k1	k1	NOUN
ap-1827	146	28	=	=	SYM
ap-1827	146	29	3	3	NUM
ap-1827	146	30	k2	k2	NOUN
ap-1827	146	31	=	=	SYM
ap-1827	146	32	1	1	NUM
ap-1827	146	33	u0	u0	ADJ
ap-1827	146	34	=	=	PUNCT
ap-1827	146	35	01034010	01034010	NUM
ap-1827	146	36	u1	u1	NOUN
ap-1827	146	37	=	=	SYM
ap-1827	146	38	010	010	NUM
ap-1827	147	1	u2	u2	NOUN
ap-1827	147	2	=	=	SYM
ap-1827	147	3	0	0	NUM
ap-1827	147	4	w0	w0	PROPN
ap-1827	147	5	=	=	SYM
ap-1827	147	6	01034	01034	NUM
ap-1827	147	7	w1	w1	NOUN
ap-1827	147	8	=	=	SYM
ap-1827	147	9	01	01	NUM
ap-1827	147	10	from	from	ADP
ap-1827	147	11	the	the	DET
ap-1827	147	12	above	above	ADJ
ap-1827	147	13	example	example	NOUN
ap-1827	147	14	we	we	PRON
ap-1827	147	15	see	see	VERB
ap-1827	147	16	that	that	SCONJ
ap-1827	147	17	the	the	DET
ap-1827	147	18	procedure	procedure	NOUN
ap-1827	147	19	has	have	VERB
ap-1827	147	20	two	two	NUM
ap-1827	147	21	parts	part	NOUN
ap-1827	147	22	:	:	PUNCT
ap-1827	147	23	“	"	PUNCT
ap-1827	147	24	descending	descend	VERB
ap-1827	147	25	”	"	PUNCT
ap-1827	147	26	and	and	CCONJ
ap-1827	147	27	“	"	PUNCT
ap-1827	147	28	ascending	ascend	VERB
ap-1827	147	29	”	"	PUNCT
ap-1827	147	30	,	,	PUNCT
ap-1827	147	31	which	which	PRON
ap-1827	147	32	are	be	AUX
ap-1827	147	33	called	call	VERB
ap-1827	147	34	“	"	PUNCT
ap-1827	147	35	reduction	reduction	NOUN
ap-1827	147	36	”	"	PUNCT
ap-1827	147	37	and	and	CCONJ
ap-1827	147	38	“	"	PUNCT
ap-1827	147	39	extension	extension	NOUN
ap-1827	147	40	”	"	PUNCT
ap-1827	147	41	in	in	ADP
ap-1827	147	42	[	[	X
ap-1827	147	43	3	3	NUM
ap-1827	147	44	]	]	PUNCT
ap-1827	147	45	.	.	PUNCT
ap-1827	148	1	the	the	DET
ap-1827	148	2	end	end	NOUN
ap-1827	148	3	of	of	ADP
ap-1827	148	4	reduction	reduction	NOUN
ap-1827	148	5	can	can	AUX
ap-1827	148	6	be	be	AUX
ap-1827	148	7	defined	define	VERB
ap-1827	148	8	in	in	ADP
ap-1827	148	9	several	several	ADJ
ap-1827	148	10	ways	way	NOUN
ap-1827	148	11	.	.	PUNCT
ap-1827	149	1	we	we	PRON
ap-1827	149	2	have	have	AUX
ap-1827	149	3	seen	see	VERB
ap-1827	149	4	that	that	SCONJ
ap-1827	149	5	we	we	PRON
ap-1827	149	6	can	can	AUX
ap-1827	149	7	turn	turn	VERB
ap-1827	149	8	to	to	ADP
ap-1827	149	9	extension	extension	NOUN
ap-1827	149	10	as	as	ADV
ap-1827	149	11	soon	soon	ADV
ap-1827	149	12	as	as	SCONJ
ap-1827	149	13	we	we	PRON
ap-1827	149	14	know	know	VERB
ap-1827	149	15	fw(qi	fw(qi	PROPN
ap-1827	149	16	,	,	PUNCT
ap-1827	149	17	ki	ki	PROPN
ap-1827	149	18	)	)	PUNCT
ap-1827	149	19	.	.	PUNCT
ap-1827	150	1	this	this	PRON
ap-1827	150	2	typically	typically	ADV
ap-1827	150	3	happens	happen	VERB
ap-1827	150	4	if	if	SCONJ
ap-1827	150	5	ki	ki	PROPN
ap-1827	150	6	≤	≤	NUM
ap-1827	150	7	min	min	PROPN
ap-1827	150	8	qi	qi	PROPN
ap-1827	150	9	,	,	PUNCT
ap-1827	150	10	or	or	CCONJ
ap-1827	150	11	if	if	SCONJ
ap-1827	150	12	min	min	PROPN
ap-1827	150	13	qi	qi	PROPN
ap-1827	150	14	=	=	SYM
ap-1827	150	15	gcd(qi	gcd(qi	X
ap-1827	150	16	)	)	PUNCT
ap-1827	150	17	.	.	PUNCT
ap-1827	151	1	5	5	X
ap-1827	151	2	.	.	X
ap-1827	151	3	concluding	conclude	VERB
ap-1827	151	4	remarks	remark	NOUN
ap-1827	151	5	as	as	SCONJ
ap-1827	151	6	already	already	ADV
ap-1827	151	7	remarked	remark	VERB
ap-1827	151	8	,	,	PUNCT
ap-1827	151	9	the	the	DET
ap-1827	151	10	above	above	ADJ
ap-1827	151	11	algorithm	algorithm	NOUN
ap-1827	151	12	is	be	AUX
ap-1827	151	13	identical	identical	ADJ
ap-1827	151	14	with	with	ADP
ap-1827	151	15	algorithm	algorithm	PROPN
ap-1827	151	16	b	b	PROPN
ap-1827	151	17	from	from	ADP
ap-1827	151	18	[	[	X
ap-1827	151	19	3	3	NUM
ap-1827	151	20	]	]	PUNCT
ap-1827	151	21	.	.	PUNCT
ap-1827	152	1	even	even	ADV
ap-1827	152	2	all	all	DET
ap-1827	152	3	arguments	argument	NOUN
ap-1827	152	4	we	we	PRON
ap-1827	152	5	use	use	VERB
ap-1827	152	6	can	can	AUX
ap-1827	152	7	be	be	AUX
ap-1827	152	8	in	in	ADP
ap-1827	152	9	some	some	DET
ap-1827	152	10	way	way	NOUN
ap-1827	152	11	traced	trace	VERB
ap-1827	152	12	back	back	ADV
ap-1827	152	13	to	to	ADP
ap-1827	152	14	similar	similar	ADJ
ap-1827	152	15	arguments	argument	NOUN
ap-1827	152	16	in	in	ADP
ap-1827	152	17	the	the	DET
ap-1827	152	18	literature	literature	NOUN
ap-1827	152	19	.	.	PUNCT
ap-1827	153	1	nevertheless	nevertheless	ADV
ap-1827	153	2	,	,	PUNCT
ap-1827	153	3	i	i	PRON
ap-1827	153	4	believe	believe	VERB
ap-1827	153	5	that	that	SCONJ
ap-1827	153	6	the	the	DET
ap-1827	153	7	description	description	NOUN
ap-1827	153	8	presented	present	VERB
ap-1827	153	9	here	here	ADV
ap-1827	153	10	provides	provide	VERB
ap-1827	153	11	further	further	ADJ
ap-1827	153	12	evidence	evidence	NOUN
ap-1827	153	13	that	that	SCONJ
ap-1827	153	14	the	the	DET
ap-1827	153	15	equivalence	equivalence	NOUN
ap-1827	153	16	class	class	NOUN
ap-1827	153	17	approach	approach	NOUN
ap-1827	153	18	is	be	AUX
ap-1827	153	19	not	not	PART
ap-1827	153	20	only	only	ADV
ap-1827	153	21	simple	simple	ADJ
ap-1827	153	22	but	but	CCONJ
ap-1827	153	23	it	it	PRON
ap-1827	153	24	also	also	ADV
ap-1827	153	25	yields	yield	VERB
ap-1827	153	26	an	an	DET
ap-1827	153	27	intuition	intuition	NOUN
ap-1827	153	28	sufficient	sufficient	ADJ
ap-1827	153	29	to	to	PART
ap-1827	153	30	formulate	formulate	VERB
ap-1827	153	31	and	and	CCONJ
ap-1827	153	32	understand	understand	VERB
ap-1827	153	33	the	the	DET
ap-1827	153	34	construction	construction	NOUN
ap-1827	153	35	.	.	PUNCT
ap-1827	154	1	(	(	PUNCT
ap-1827	154	2	another	another	DET
ap-1827	154	3	elegant	elegant	ADJ
ap-1827	154	4	example	example	NOUN
ap-1827	154	5	,	,	PUNCT
ap-1827	154	6	in	in	ADP
ap-1827	154	7	my	my	PRON
ap-1827	154	8	opinion	opinion	NOUN
ap-1827	154	9	,	,	PUNCT
ap-1827	154	10	is	be	AUX
ap-1827	154	11	the	the	DET
ap-1827	154	12	proof	proof	NOUN
ap-1827	154	13	of	of	ADP
ap-1827	154	14	the	the	DET
ap-1827	154	15	fact	fact	NOUN
ap-1827	154	16	that	that	SCONJ
ap-1827	154	17	the	the	DET
ap-1827	154	18	extremal	extremal	ADJ
ap-1827	154	19	fw	fw	ADJ
ap-1827	154	20	-	-	PUNCT
ap-1827	154	21	word	word	NOUN
ap-1827	154	22	is	be	AUX
ap-1827	154	23	a	a	DET
ap-1827	154	24	palindrome	palindrome	NOUN
ap-1827	154	25	,	,	PUNCT
ap-1827	154	26	given	give	VERB
ap-1827	154	27	in	in	ADP
ap-1827	154	28	[	[	X
ap-1827	154	29	4	4	NUM
ap-1827	154	30	]	]	NUM
ap-1827	154	31	.	.	PUNCT
ap-1827	154	32	)	)	PUNCT
ap-1827	155	1	that	that	PRON
ap-1827	155	2	said	say	VERB
ap-1827	155	3	,	,	PUNCT
ap-1827	155	4	one	one	PRON
ap-1827	155	5	should	should	AUX
ap-1827	155	6	stress	stress	VERB
ap-1827	155	7	that	that	SCONJ
ap-1827	155	8	the	the	DET
ap-1827	155	9	inefficiency	inefficiency	NOUN
ap-1827	155	10	claim	claim	NOUN
ap-1827	155	11	concerning	concern	VERB
ap-1827	155	12	the	the	DET
ap-1827	155	13	equivalence	equivalence	NOUN
ap-1827	155	14	class	class	NOUN
ap-1827	155	15	approach	approach	NOUN
ap-1827	155	16	is	be	AUX
ap-1827	155	17	valid	valid	ADJ
ap-1827	155	18	if	if	SCONJ
ap-1827	155	19	we	we	PRON
ap-1827	155	20	consider	consider	VERB
ap-1827	155	21	the	the	DET
ap-1827	155	22	naïve	naïve	ADJ
ap-1827	155	23	procedure	procedure	NOUN
ap-1827	155	24	suggested	suggest	VERB
ap-1827	155	25	by	by	ADP
ap-1827	155	26	example	example	NOUN
ap-1827	155	27	1	1	NUM
ap-1827	155	28	.	.	PUNCT
ap-1827	156	1	the	the	DET
ap-1827	156	2	precise	precise	ADJ
ap-1827	156	3	computational	computational	ADJ
ap-1827	156	4	complexity	complexity	NOUN
ap-1827	156	5	of	of	ADP
ap-1827	156	6	algorithm	algorithm	PROPN
ap-1827	156	7	b	b	PROPN
ap-1827	156	8	goes	go	VERB
ap-1827	156	9	beyond	beyond	ADP
ap-1827	156	10	the	the	DET
ap-1827	156	11	scope	scope	NOUN
ap-1827	156	12	of	of	ADP
ap-1827	156	13	this	this	DET
ap-1827	156	14	paper	paper	NOUN
ap-1827	156	15	(	(	PUNCT
ap-1827	156	16	see	see	VERB
ap-1827	156	17	the	the	DET
ap-1827	156	18	discussion	discussion	NOUN
ap-1827	156	19	in	in	ADP
ap-1827	156	20	[	[	X
ap-1827	156	21	3	3	NUM
ap-1827	156	22	]	]	NUM
ap-1827	156	23	)	)	PUNCT
ap-1827	156	24	.	.	PUNCT
ap-1827	157	1	one	one	NUM
ap-1827	157	2	possible	possible	ADJ
ap-1827	157	3	drawback	drawback	NOUN
ap-1827	157	4	can	can	AUX
ap-1827	157	5	be	be	AUX
ap-1827	157	6	a	a	DET
ap-1827	157	7	bit	bit	NOUN
ap-1827	157	8	discouraging	discouraging	ADJ
ap-1827	157	9	notation	notation	NOUN
ap-1827	157	10	like	like	ADP
ap-1827	157	11	∼p	∼p	PROPN
ap-1827	157	12	,	,	PUNCT
ap-1827	157	13	k	k	NOUN
ap-1827	157	14	,	,	PUNCT
ap-1827	157	15	and	and	CCONJ
ap-1827	157	16	the	the	DET
ap-1827	157	17	fact	fact	NOUN
ap-1827	157	18	that	that	SCONJ
ap-1827	157	19	notions	notion	NOUN
ap-1827	157	20	like	like	ADP
ap-1827	157	21	“	"	PUNCT
ap-1827	157	22	equivalence	equivalence	NOUN
ap-1827	157	23	closure	closure	NOUN
ap-1827	157	24	”	"	PUNCT
ap-1827	157	25	may	may	AUX
ap-1827	157	26	sound	sound	VERB
ap-1827	157	27	“	"	PUNCT
ap-1827	157	28	too	too	ADV
ap-1827	157	29	algebraic	algebraic	ADJ
ap-1827	157	30	”	"	PUNCT
ap-1827	157	31	to	to	ADP
ap-1827	157	32	some	some	DET
ap-1827	157	33	ears	ear	NOUN
ap-1827	157	34	.	.	PUNCT
ap-1827	158	1	computer	computer	NOUN
ap-1827	158	2	theorists	theorist	NOUN
ap-1827	158	3	could	could	AUX
ap-1827	158	4	therefore	therefore	ADV
ap-1827	158	5	like	like	VERB
ap-1827	158	6	to	to	PART
ap-1827	158	7	translate	translate	VERB
ap-1827	158	8	the	the	DET
ap-1827	158	9	exposition	exposition	NOUN
ap-1827	158	10	into	into	ADP
ap-1827	158	11	graph	graph	NOUN
ap-1827	158	12	language	language	NOUN
ap-1827	158	13	and	and	CCONJ
ap-1827	158	14	speak	speak	VERB
ap-1827	158	15	about	about	ADP
ap-1827	158	16	edges	edge	NOUN
ap-1827	158	17	instead	instead	ADV
ap-1827	158	18	of	of	ADP
ap-1827	158	19	generating	generate	VERB
ap-1827	158	20	relations	relation	NOUN
ap-1827	158	21	,	,	PUNCT
ap-1827	158	22	and	and	CCONJ
ap-1827	158	23	about	about	ADP
ap-1827	158	24	connected	connected	ADJ
ap-1827	158	25	components	component	NOUN
ap-1827	158	26	instead	instead	ADV
ap-1827	158	27	of	of	ADP
ap-1827	158	28	equivalence	equivalence	NOUN
ap-1827	158	29	classes	class	NOUN
ap-1827	158	30	.	.	PUNCT
ap-1827	159	1	the	the	DET
ap-1827	159	2	rest	rest	NOUN
ap-1827	159	3	will	will	AUX
ap-1827	159	4	be	be	AUX
ap-1827	159	5	the	the	DET
ap-1827	159	6	same	same	ADJ
ap-1827	159	7	.	.	PUNCT
ap-1827	160	1	acknowledgements	acknowledgement	NOUN
ap-1827	160	2	this	this	DET
ap-1827	160	3	work	work	NOUN
ap-1827	160	4	was	be	AUX
ap-1827	160	5	supported	support	VERB
ap-1827	160	6	by	by	ADP
ap-1827	160	7	czech	czech	PROPN
ap-1827	160	8	science	science	NOUN
ap-1827	160	9	foundation	foundation	NOUN
ap-1827	160	10	grant	grant	VERB
ap-1827	160	11	13	13	NUM
ap-1827	160	12	-	-	PUNCT
ap-1827	160	13	01832s	01832s	NUM
ap-1827	160	14	.	.	PUNCT
ap-1827	161	1	references	reference	NOUN
ap-1827	161	2	[	[	X
ap-1827	161	3	1	1	NUM
ap-1827	161	4	]	]	PUNCT
ap-1827	161	5	s.	s.	PROPN
ap-1827	161	6	constantinescu	constantinescu	PROPN
ap-1827	161	7	,	,	PUNCT
ap-1827	161	8	et	et	PROPN
ap-1827	161	9	al	al	PROPN
ap-1827	161	10	.	.	PROPN
ap-1827	161	11	generalised	generalise	VERB
ap-1827	161	12	fine	fine	ADJ
ap-1827	161	13	and	and	CCONJ
ap-1827	161	14	wilf	wilf	PROPN
ap-1827	161	15	’s	’s	PART
ap-1827	161	16	theorem	theorem	NOUN
ap-1827	161	17	for	for	ADP
ap-1827	161	18	arbitrary	arbitrary	ADJ
ap-1827	161	19	number	number	NOUN
ap-1827	161	20	of	of	ADP
ap-1827	161	21	periods	period	NOUN
ap-1827	161	22	.	.	PUNCT
ap-1827	162	1	theoret	theoret	VERB
ap-1827	162	2	comput	comput	ADP
ap-1827	162	3	sci	sci	PROPN
ap-1827	162	4	339(1):49–60	339(1):49–60	NOUN
ap-1827	162	5	,	,	PUNCT
ap-1827	162	6	2005	2005	NUM
ap-1827	162	7	.	.	PUNCT
ap-1827	163	1	[	[	X
ap-1827	163	2	2	2	NUM
ap-1827	163	3	]	]	PUNCT
ap-1827	163	4	r.	r.	PROPN
ap-1827	163	5	tijdeman	tijdeman	PROPN
ap-1827	163	6	,	,	PUNCT
ap-1827	163	7	et	et	PROPN
ap-1827	163	8	al	al	PROPN
ap-1827	163	9	.	.	PROPN
ap-1827	163	10	fine	fine	PROPN
ap-1827	163	11	and	and	CCONJ
ap-1827	163	12	wilf	wilf	NOUN
ap-1827	163	13	words	word	NOUN
ap-1827	163	14	for	for	ADP
ap-1827	163	15	any	any	DET
ap-1827	163	16	periods	period	NOUN
ap-1827	163	17	.	.	PUNCT
ap-1827	164	1	indag	indag	PROPN
ap-1827	164	2	math	math	NOUN
ap-1827	164	3	(	(	PUNCT
ap-1827	164	4	ns	ns	PROPN
ap-1827	164	5	)	)	PUNCT
ap-1827	164	6	14(1):135–147	14(1):135–147	PROPN
ap-1827	164	7	,	,	PUNCT
ap-1827	164	8	2003	2003	NUM
ap-1827	164	9	.	.	PUNCT
ap-1827	165	1	[	[	X
ap-1827	165	2	3	3	X
ap-1827	165	3	]	]	X
ap-1827	165	4	r.	r.	PROPN
ap-1827	165	5	tijdeman	tijdeman	PROPN
ap-1827	165	6	,	,	PUNCT
ap-1827	165	7	et	et	PROPN
ap-1827	165	8	al	al	PROPN
ap-1827	165	9	.	.	PROPN
ap-1827	165	10	fine	fine	PROPN
ap-1827	165	11	and	and	CCONJ
ap-1827	165	12	wilf	wilf	NOUN
ap-1827	165	13	words	word	NOUN
ap-1827	165	14	for	for	ADP
ap-1827	165	15	any	any	DET
ap-1827	165	16	periods	periods	PROPN
ap-1827	165	17	ii	ii	PROPN
ap-1827	165	18	.	.	PUNCT
ap-1827	166	1	theor	theor	PROPN
ap-1827	166	2	comput	comput	PROPN
ap-1827	166	3	sci	sci	PROPN
ap-1827	166	4	410(30	410(30	PROPN
ap-1827	166	5	-	-	PROPN
ap-1827	166	6	32):3027–3034	32):3027–3034	PROPN
ap-1827	166	7	,	,	PUNCT
ap-1827	166	8	2009	2009	NUM
ap-1827	166	9	.	.	PUNCT
ap-1827	167	1	[	[	X
ap-1827	167	2	4	4	NUM
ap-1827	167	3	]	]	X
ap-1827	167	4	š	š	PROPN
ap-1827	167	5	.	.	PUNCT
ap-1827	167	6	holub	holub	PROPN
ap-1827	167	7	.	.	PUNCT
ap-1827	168	1	on	on	ADP
ap-1827	168	2	multiperiodic	multiperiodic	ADJ
ap-1827	168	3	words	word	NOUN
ap-1827	168	4	.	.	PUNCT
ap-1827	169	1	theor	theor	PROPN
ap-1827	169	2	inform	inform	VERB
ap-1827	169	3	appl	appl	PROPN
ap-1827	169	4	40(4):583–591	40(4):583–591	PROPN
ap-1827	169	5	,	,	PUNCT
ap-1827	169	6	2006	2006	NUM
ap-1827	169	7	.	.	PUNCT
ap-1827	170	1	[	[	X
ap-1827	170	2	5	5	NUM
ap-1827	170	3	]	]	SYM
ap-1827	170	4	š	š	PROPN
ap-1827	170	5	.	.	PUNCT
ap-1827	170	6	holub	holub	PROPN
ap-1827	170	7	.	.	PUNCT
ap-1827	171	1	corrigendum	corrigendum	NOUN
ap-1827	171	2	:	:	PUNCT
ap-1827	171	3	on	on	ADP
ap-1827	171	4	multiperiodic	multiperiodic	ADJ
ap-1827	171	5	words	word	NOUN
ap-1827	171	6	.	.	PUNCT
ap-1827	172	1	theor	theor	PROPN
ap-1827	172	2	inform	inform	VERB
ap-1827	172	3	appl	appl	PROPN
ap-1827	172	4	45(4):467–469	45(4):467–469	PROPN
ap-1827	172	5	,	,	PUNCT
ap-1827	172	6	2011	2011	NUM
ap-1827	172	7	.	.	PUNCT
ap-1827	173	1	346	346	NUM
ap-1827	173	2	acta	acta	PROPN
ap-1827	173	3	polytechnica	polytechnica	PROPN
ap-1827	173	4	53(4):344–346	53(4):344–346	PROPN
ap-1827	173	5	,	,	PUNCT
ap-1827	173	6	2013	2013	NUM
ap-1827	173	7	1	1	NUM
ap-1827	173	8	a	a	DET
ap-1827	173	9	short	short	ADJ
ap-1827	173	10	(	(	PUNCT
ap-1827	173	11	personal	personal	ADJ
ap-1827	173	12	)	)	PUNCT
ap-1827	173	13	history	history	NOUN
ap-1827	173	14	2	2	NUM
ap-1827	173	15	notation	notation	NOUN
ap-1827	173	16	3	3	NUM
ap-1827	173	17	classes	class	NOUN
ap-1827	173	18	of	of	ADP
ap-1827	173	19	equivalence	equivalence	NOUN
ap-1827	173	20	4	4	NUM
ap-1827	173	21	the	the	DET
ap-1827	173	22	algorithm	algorithm	NOUN
ap-1827	173	23	5	5	NUM
ap-1827	173	24	concluding	conclude	VERB
ap-1827	173	25	remarks	remark	VERB
ap-1827	173	26	acknowledgements	acknowledgement	NOUN
ap-1827	173	27	references	reference	NOUN