id	sid	tid	token	lemma	pos
cana-5314	1	1	communications	communication	NOUN
cana-5314	1	2	on	on	ADP
cana-5314	1	3	applied	apply	VERB
cana-5314	1	4	nonlinear	nonlinear	ADJ
cana-5314	1	5	analysis	analysis	NOUN
cana-5314	1	6	issn	issn	NOUN
cana-5314	1	7	:	:	PUNCT
cana-5314	1	8	1074	1074	NUM
cana-5314	1	9	-	-	PUNCT
cana-5314	1	10	133x	133x	NUM
cana-5314	1	11	vol	vol	NOUN
cana-5314	1	12	31	31	NUM
cana-5314	1	13	no	no	NOUN
cana-5314	1	14	.	.	PUNCT
cana-5314	2	1	8s	8s	PROPN
cana-5314	2	2	(	(	PUNCT
cana-5314	2	3	2024	2024	NUM
cana-5314	2	4	)	)	PUNCT
cana-5314	2	5	945	945	NUM
cana-5314	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5314	2	7	the	the	DET
cana-5314	2	8	p	p	X
cana-5314	2	9	versus	versus	ADP
cana-5314	2	10	np	np	ADP
cana-5314	2	11	problem	problem	NOUN
cana-5314	2	12	insights	insight	NOUN
cana-5314	2	13	into	into	ADP
cana-5314	2	14	computational	computational	ADJ
cana-5314	2	15	complexity	complexity	NOUN
cana-5314	2	16	1s	1	NOUN
cana-5314	2	17	.	.	PUNCT
cana-5314	3	1	balamuralitharan	balamuralitharan	PROPN
cana-5314	3	2	,	,	PUNCT
cana-5314	3	3	2r	2r	NUM
cana-5314	3	4	.	.	PUNCT
cana-5314	4	1	arulprakasam	arulprakasam	PROPN
cana-5314	4	2	,	,	PUNCT
cana-5314	4	3	3n.sujatha	3n.sujatha	NUM
cana-5314	4	4	,	,	PUNCT
cana-5314	4	5	4	4	NUM
cana-5314	4	6	m	m	NOUN
cana-5314	4	7	bala	bala	NOUN
cana-5314	4	8	prabhakar	prabhakar	NOUN
cana-5314	4	9	,	,	PUNCT
cana-5314	4	10	1adjunct	1adjunct	NUM
cana-5314	4	11	faculty	faculty	NOUN
cana-5314	4	12	,	,	PUNCT
cana-5314	4	13	department	department	NOUN
cana-5314	4	14	of	of	ADP
cana-5314	4	15	pure	pure	ADJ
cana-5314	4	16	and	and	CCONJ
cana-5314	4	17	applied	applied	ADJ
cana-5314	4	18	mathematics	mathematic	NOUN
cana-5314	4	19	,	,	PUNCT
cana-5314	4	20	saveetha	saveetha	PROPN
cana-5314	4	21	school	school	PROPN
cana-5314	4	22	of	of	ADP
cana-5314	4	23	engineering	engineering	NOUN
cana-5314	4	24	,	,	PUNCT
cana-5314	4	25	simats	simat	NOUN
cana-5314	4	26	,	,	PUNCT
cana-5314	4	27	chennai	chennai	PROPN
cana-5314	4	28	,	,	PUNCT
cana-5314	4	29	tamil	tamil	PROPN
cana-5314	4	30	nadu	nadu	PROPN
cana-5314	4	31	,	,	PUNCT
cana-5314	4	32	india	india	PROPN
cana-5314	4	33	email	email	NOUN
cana-5314	5	1	i	i	PROPN
cana-5314	5	2	d	d	PROPN
cana-5314	5	3	:	:	PUNCT
cana-5314	5	4	balamurali.maths@gmail.com	balamurali.maths@gmail.com	X
cana-5314	5	5	2department	2department	NUM
cana-5314	5	6	of	of	ADP
cana-5314	5	7	mathematics	mathematic	NOUN
cana-5314	5	8	,	,	PUNCT
cana-5314	5	9	college	college	NOUN
cana-5314	5	10	of	of	ADP
cana-5314	5	11	engineering	engineering	NOUN
cana-5314	5	12	and	and	CCONJ
cana-5314	5	13	technology	technology	NOUN
cana-5314	5	14	,	,	PUNCT
cana-5314	5	15	srm	srm	PROPN
cana-5314	5	16	institute	institute	PROPN
cana-5314	5	17	of	of	ADP
cana-5314	5	18	science	science	NOUN
cana-5314	5	19	and	and	CCONJ
cana-5314	5	20	technology	technology	NOUN
cana-5314	5	21	,	,	PUNCT
cana-5314	5	22	srm	srm	NOUN
cana-5314	5	23	nagar	nagar	NOUN
cana-5314	5	24	,	,	PUNCT
cana-5314	5	25	kattankulathur	kattankulathur	PROPN
cana-5314	5	26	603203	603203	NUM
cana-5314	5	27	,	,	PUNCT
cana-5314	5	28	chengalpattu	chengalpattu	ADJ
cana-5314	5	29	district	district	NOUN
cana-5314	5	30	,	,	PUNCT
cana-5314	5	31	tamilnadu	tamilnadu	PROPN
cana-5314	5	32	,	,	PUNCT
cana-5314	5	33	india	india	PROPN
cana-5314	5	34	r.aruljeeva@gmail.com	r.aruljeeva@gmail.com	PROPN
cana-5314	5	35	3associate	3associate	NUM
cana-5314	5	36	professor	professor	NOUN
cana-5314	5	37	,	,	PUNCT
cana-5314	5	38	department	department	NOUN
cana-5314	5	39	of	of	ADP
cana-5314	5	40	mathematics	mathematics	PROPN
cana-5314	5	41	,	,	PUNCT
cana-5314	5	42	aditya	aditya	PROPN
cana-5314	5	43	university	university	PROPN
cana-5314	5	44	,	,	PUNCT
cana-5314	5	45	surampalem	surampalem	NOUN
cana-5314	5	46	,	,	PUNCT
cana-5314	5	47	india	india	PROPN
cana-5314	5	48	,	,	PUNCT
cana-5314	5	49	sujatha.nanduri@aec.edu.in	sujatha.nanduri@aec.edu.in	PROPN
cana-5314	5	50	4associate	4associate	NUM
cana-5314	5	51	professor	professor	NOUN
cana-5314	5	52	,	,	PUNCT
cana-5314	5	53	dept	dept	NOUN
cana-5314	5	54	of	of	ADP
cana-5314	5	55	mathematics	mathematic	NOUN
cana-5314	5	56	,	,	PUNCT
cana-5314	5	57	aditya	aditya	PROPN
cana-5314	5	58	university	university	PROPN
cana-5314	5	59	,	,	PUNCT
cana-5314	5	60	surampalem	surampalem	NOUN
cana-5314	5	61	,	,	PUNCT
cana-5314	5	62	india	india	PROPN
cana-5314	5	63	,	,	PUNCT
cana-5314	5	64	balaprabhakar.mattaparthi@aec.edu.in	balaprabhakar.mattaparthi@aec.edu.in	NOUN
cana-5314	5	65	article	article	NOUN
cana-5314	5	66	history	history	NOUN
cana-5314	5	67	:	:	PUNCT
cana-5314	5	68	received	receive	VERB
cana-5314	5	69	:	:	PUNCT
cana-5314	5	70	12	12	NUM
cana-5314	5	71	-	-	SYM
cana-5314	5	72	10	10	NUM
cana-5314	5	73	-	-	PUNCT
cana-5314	5	74	2024	2024	NUM
cana-5314	5	75	revised	revise	VERB
cana-5314	5	76	:	:	PUNCT
cana-5314	5	77	15	15	NUM
cana-5314	5	78	-	-	SYM
cana-5314	5	79	11	11	NUM
cana-5314	5	80	-	-	PUNCT
cana-5314	5	81	2024	2024	NUM
cana-5314	5	82	accepted	accept	VERB
cana-5314	5	83	:	:	PUNCT
cana-5314	5	84	19	19	NUM
cana-5314	5	85	-	-	SYM
cana-5314	5	86	12	12	NUM
cana-5314	5	87	-	-	PUNCT
cana-5314	5	88	2024	2024	NUM
cana-5314	5	89	abstract	abstract	NOUN
cana-5314	5	90	:	:	PUNCT
cana-5314	5	91	theoretical	theoretical	ADJ
cana-5314	5	92	computer	computer	NOUN
cana-5314	5	93	science	science	NOUN
cana-5314	5	94	along	along	ADP
cana-5314	5	95	with	with	ADP
cana-5314	5	96	mathematics	mathematic	NOUN
cana-5314	5	97	face	face	VERB
cana-5314	5	98	an	an	DET
cana-5314	5	99	ultimate	ultimate	ADJ
cana-5314	5	100	problem	problem	NOUN
cana-5314	5	101	which	which	PRON
cana-5314	5	102	remains	remain	VERB
cana-5314	5	103	unsettled	unsettled	ADJ
cana-5314	5	104	because	because	SCONJ
cana-5314	5	105	of	of	ADP
cana-5314	5	106	its	its	PRON
cana-5314	5	107	deep	deep	ADJ
cana-5314	5	108	significance	significance	NOUN
cana-5314	5	109	as	as	ADP
cana-5314	5	110	p	p	NOUN
cana-5314	5	111	versus	versus	ADP
cana-5314	5	112	np	np	PROPN
cana-5314	5	113	.	.	PUNCT
cana-5314	6	1	the	the	DET
cana-5314	6	2	problem	problem	NOUN
cana-5314	6	3	seeks	seek	VERB
cana-5314	6	4	to	to	PART
cana-5314	6	5	know	know	VERB
cana-5314	6	6	if	if	SCONJ
cana-5314	6	7	all	all	DET
cana-5314	6	8	the	the	DET
cana-5314	6	9	problems	problem	NOUN
cana-5314	6	10	that	that	PRON
cana-5314	6	11	can	can	AUX
cana-5314	6	12	be	be	AUX
cana-5314	6	13	validated	validate	VERB
cana-5314	6	14	quickly	quickly	ADV
cana-5314	6	15	in	in	ADP
cana-5314	6	16	polynomial	polynomial	ADJ
cana-5314	6	17	time	time	NOUN
cana-5314	6	18	can	can	AUX
cana-5314	6	19	also	also	ADV
cana-5314	6	20	be	be	AUX
cana-5314	6	21	solved	solve	VERB
cana-5314	6	22	quickly	quickly	ADV
cana-5314	6	23	.	.	PUNCT
cana-5314	7	1	researchers	researcher	NOUN
cana-5314	7	2	have	have	AUX
cana-5314	7	3	spent	spend	VERB
cana-5314	7	4	multiple	multiple	ADJ
cana-5314	7	5	decades	decade	NOUN
cana-5314	7	6	exploring	explore	VERB
cana-5314	7	7	this	this	DET
cana-5314	7	8	question	question	NOUN
cana-5314	7	9	alongside	alongside	ADP
cana-5314	7	10	significant	significant	ADJ
cana-5314	7	11	practical	practical	ADJ
cana-5314	7	12	applications	application	NOUN
cana-5314	7	13	yet	yet	ADV
cana-5314	7	14	the	the	DET
cana-5314	7	15	issue	issue	NOUN
cana-5314	7	16	has	have	AUX
cana-5314	7	17	not	not	PART
cana-5314	7	18	been	be	AUX
cana-5314	7	19	resolved	resolve	VERB
cana-5314	7	20	.	.	PUNCT
cana-5314	8	1	this	this	DET
cana-5314	8	2	paper	paper	NOUN
cana-5314	8	3	delivers	deliver	VERB
cana-5314	8	4	an	an	DET
cana-5314	8	5	efficient	efficient	ADJ
cana-5314	8	6	exploration	exploration	NOUN
cana-5314	8	7	of	of	ADP
cana-5314	8	8	the	the	DET
cana-5314	8	9	p	p	NOUN
cana-5314	8	10	vs.	vs.	ADP
cana-5314	8	11	np	np	INTJ
cana-5314	8	12	problem	problem	NOUN
cana-5314	8	13	by	by	ADP
cana-5314	8	14	studying	study	VERB
cana-5314	8	15	its	its	PRON
cana-5314	8	16	core	core	ADJ
cana-5314	8	17	components	component	NOUN
cana-5314	8	18	in	in	ADP
cana-5314	8	19	computational	computational	ADJ
cana-5314	8	20	complexity	complexity	NOUN
cana-5314	8	21	theory	theory	NOUN
cana-5314	8	22	while	while	SCONJ
cana-5314	8	23	analyzing	analyze	VERB
cana-5314	8	24	historical	historical	ADJ
cana-5314	8	25	and	and	CCONJ
cana-5314	8	26	contemporary	contemporary	ADJ
cana-5314	8	27	studies	study	NOUN
cana-5314	8	28	alongside	alongside	ADP
cana-5314	8	29	methodological	methodological	ADJ
cana-5314	8	30	frameworks	framework	NOUN
cana-5314	8	31	for	for	ADP
cana-5314	8	32	solving	solve	VERB
cana-5314	8	33	this	this	DET
cana-5314	8	34	problem	problem	NOUN
cana-5314	8	35	.	.	PUNCT
cana-5314	9	1	the	the	DET
cana-5314	9	2	research	research	NOUN
cana-5314	9	3	identifies	identify	VERB
cana-5314	9	4	outcomes	outcome	NOUN
cana-5314	9	5	together	together	ADV
cana-5314	9	6	with	with	ADP
cana-5314	9	7	their	their	PRON
cana-5314	9	8	interpretive	interpretive	ADJ
cana-5314	9	9	values	value	NOUN
cana-5314	9	10	and	and	CCONJ
cana-5314	9	11	implications	implication	NOUN
cana-5314	9	12	to	to	PART
cana-5314	9	13	offer	offer	VERB
cana-5314	9	14	extensive	extensive	ADJ
cana-5314	9	15	comprehension	comprehension	NOUN
cana-5314	9	16	between	between	ADP
cana-5314	9	17	technical	technical	ADJ
cana-5314	9	18	aspects	aspect	NOUN
cana-5314	9	19	and	and	CCONJ
cana-5314	9	20	philosophical	philosophical	ADJ
cana-5314	9	21	evaluations	evaluation	NOUN
cana-5314	9	22	of	of	ADP
cana-5314	9	23	the	the	DET
cana-5314	9	24	problem	problem	NOUN
cana-5314	9	25	which	which	PRON
cana-5314	9	26	enables	enable	VERB
cana-5314	9	27	advanced	advanced	ADJ
cana-5314	9	28	understanding	understanding	NOUN
cana-5314	9	29	of	of	ADP
cana-5314	9	30	algorithm	algorithm	NOUN
cana-5314	9	31	development	development	NOUN
cana-5314	9	32	and	and	CCONJ
cana-5314	9	33	cryptographic	cryptographic	ADJ
cana-5314	9	34	practices	practice	NOUN
cana-5314	9	35	along	along	ADP
cana-5314	9	36	with	with	ADP
cana-5314	9	37	optimization	optimization	NOUN
cana-5314	9	38	techniques	technique	NOUN
cana-5314	9	39	and	and	CCONJ
cana-5314	9	40	artificial	artificial	ADJ
cana-5314	9	41	intelligence	intelligence	NOUN
cana-5314	9	42	methodologies	methodology	NOUN
cana-5314	9	43	.	.	PUNCT
cana-5314	10	1	keywords	keyword	NOUN
cana-5314	10	2	—	—	PUNCT
cana-5314	10	3	p	p	X
cana-5314	10	4	vs.	vs.	ADP
cana-5314	10	5	np	np	INTJ
cana-5314	10	6	,	,	PUNCT
cana-5314	10	7	computational	computational	ADJ
cana-5314	10	8	complexity	complexity	NOUN
cana-5314	10	9	,	,	PUNCT
cana-5314	10	10	polynomial	polynomial	ADJ
cana-5314	10	11	time	time	NOUN
cana-5314	10	12	,	,	PUNCT
cana-5314	10	13	np	np	NOUN
cana-5314	10	14	-	-	PUNCT
cana-5314	10	15	completeness	completeness	NOUN
cana-5314	10	16	,	,	PUNCT
cana-5314	10	17	algorithms	algorithm	NOUN
cana-5314	10	18	,	,	PUNCT
cana-5314	10	19	cryptography	cryptography	NOUN
cana-5314	10	20	,	,	PUNCT
cana-5314	10	21	theoretical	theoretical	ADJ
cana-5314	10	22	computer	computer	NOUN
cana-5314	10	23	science	science	PROPN
cana-5314	10	24	i.	i.	PROPN
cana-5314	10	25	introduction	introduction	NOUN
cana-5314	10	26	the	the	DET
cana-5314	10	27	main	main	ADJ
cana-5314	10	28	question	question	NOUN
cana-5314	10	29	of	of	ADP
cana-5314	10	30	the	the	DET
cana-5314	10	31	problem	problem	NOUN
cana-5314	10	32	concerns	concern	VERB
cana-5314	10	33	whether	whether	SCONJ
cana-5314	10	34	every	every	DET
cana-5314	10	35	checking	checking	NOUN
cana-5314	10	36	problem	problem	NOUN
cana-5314	10	37	that	that	PRON
cana-5314	10	38	uses	use	VERB
cana-5314	10	39	polynomial	polynomial	ADJ
cana-5314	10	40	time	time	NOUN
cana-5314	10	41	verification	verification	NOUN
cana-5314	10	42	also	also	ADV
cana-5314	10	43	has	have	VERB
cana-5314	10	44	polynomial	polynomial	ADJ
cana-5314	10	45	time	time	NOUN
cana-5314	10	46	solutions	solution	NOUN
cana-5314	10	47	.	.	PUNCT
cana-5314	11	1	the	the	DET
cana-5314	11	2	p	p	PROPN
cana-5314	11	3	versus	versus	ADP
cana-5314	11	4	np	np	NUM
cana-5314	11	5	question	question	NOUN
cana-5314	11	6	explores	explore	NOUN
cana-5314	11	7	whether	whether	SCONJ
cana-5314	11	8	every	every	DET
cana-5314	11	9	polynomial	polynomial	ADJ
cana-5314	11	10	time	time	NOUN
cana-5314	11	11	solvable	solvable	ADJ
cana-5314	11	12	problem	problem	NOUN
cana-5314	11	13	by	by	ADP
cana-5314	11	14	a	a	DET
cana-5314	11	15	deterministic	deterministic	ADJ
cana-5314	11	16	turing	ture	VERB
cana-5314	11	17	machine	machine	NOUN
cana-5314	11	18	also	also	ADV
cana-5314	11	19	features	feature	VERB
cana-5314	11	20	a	a	DET
cana-5314	11	21	polynomial	polynomial	ADJ
cana-5314	11	22	time	time	NOUN
cana-5314	11	23	checking	checking	NOUN
cana-5314	11	24	capability	capability	NOUN
cana-5314	11	25	when	when	SCONJ
cana-5314	11	26	using	use	VERB
cana-5314	11	27	a	a	DET
cana-5314	11	28	nondeterministic	nondeterministic	ADJ
cana-5314	11	29	turing	ture	VERB
cana-5314	11	30	machine	machine	NOUN
cana-5314	11	31	.	.	PUNCT
cana-5314	12	1	both	both	DET
cana-5314	12	2	computer	computer	NOUN
cana-5314	12	3	science	science	NOUN
cana-5314	12	4	and	and	CCONJ
cana-5314	12	5	the	the	DET
cana-5314	12	6	world	world	NOUN
cana-5314	12	7	at	at	ADP
cana-5314	12	8	large	large	ADJ
cana-5314	12	9	explore	explore	NOUN
cana-5314	12	10	this	this	DET
cana-5314	12	11	central	central	ADJ
cana-5314	12	12	subject	subject	NOUN
cana-5314	12	13	after	after	SCONJ
cana-5314	12	14	stephen	stephen	PROPN
cana-5314	12	15	cook	cook	PROPN
cana-5314	12	16	formally	formally	ADV
cana-5314	12	17	introduced	introduce	VERB
cana-5314	12	18	the	the	DET
cana-5314	12	19	question	question	NOUN
cana-5314	12	20	in	in	ADP
cana-5314	12	21	1971	1971	NUM
cana-5314	12	22	through	through	ADP
cana-5314	12	23	“	"	PUNCT
cana-5314	12	24	the	the	DET
cana-5314	12	25	complexity	complexity	NOUN
cana-5314	12	26	of	of	ADP
cana-5314	12	27	theoremproving	theoremprove	VERB
cana-5314	12	28	procedures	procedure	NOUN
cana-5314	12	29	[	[	X
cana-5314	12	30	1	1	NUM
cana-5314	12	31	-	-	SYM
cana-5314	12	32	2	2	NUM
cana-5314	12	33	]	]	PUNCT
cana-5314	12	34	.	.	PUNCT
cana-5314	13	1	communications	communication	NOUN
cana-5314	13	2	on	on	ADP
cana-5314	13	3	applied	apply	VERB
cana-5314	13	4	nonlinear	nonlinear	ADJ
cana-5314	13	5	analysis	analysis	NOUN
cana-5314	13	6	issn	issn	NOUN
cana-5314	13	7	:	:	PUNCT
cana-5314	13	8	1074	1074	NUM
cana-5314	13	9	-	-	PUNCT
cana-5314	13	10	133x	133x	NUM
cana-5314	13	11	vol	vol	NOUN
cana-5314	13	12	31	31	NUM
cana-5314	13	13	no	no	NOUN
cana-5314	13	14	.	.	PUNCT
cana-5314	14	1	8s	8s	PROPN
cana-5314	14	2	(	(	PUNCT
cana-5314	14	3	2024	2024	NUM
cana-5314	14	4	)	)	PUNCT
cana-5314	14	5	946	946	NUM
cana-5314	14	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5314	14	7	the	the	DET
cana-5314	14	8	answer	answer	NOUN
cana-5314	14	9	to	to	ADP
cana-5314	14	10	this	this	DET
cana-5314	14	11	question	question	NOUN
cana-5314	14	12	would	would	AUX
cana-5314	14	13	affect	affect	VERB
cana-5314	14	14	fundamental	fundamental	ADJ
cana-5314	14	15	computer	computer	NOUN
cana-5314	14	16	science	science	NOUN
cana-5314	14	17	inquiries	inquiry	NOUN
cana-5314	14	18	and	and	CCONJ
cana-5314	14	19	theoretical	theoretical	ADJ
cana-5314	14	20	research	research	NOUN
cana-5314	14	21	.	.	PUNCT
cana-5314	15	1	the	the	DET
cana-5314	15	2	solution	solution	NOUN
cana-5314	15	3	of	of	ADP
cana-5314	15	4	p	p	NOUN
cana-5314	15	5	=	=	X
cana-5314	15	6	np	np	INTJ
cana-5314	15	7	would	would	AUX
cana-5314	15	8	enable	enable	VERB
cana-5314	15	9	computers	computer	NOUN
cana-5314	15	10	to	to	PART
cana-5314	15	11	address	address	VERB
cana-5314	15	12	several	several	ADJ
cana-5314	15	13	hard	hard	ADJ
cana-5314	15	14	problems	problem	NOUN
cana-5314	15	15	including	include	VERB
cana-5314	15	16	traveling	travel	VERB
cana-5314	15	17	salesman	salesman	ADJ
cana-5314	15	18	problem	problem	NOUN
cana-5314	15	19	(	(	PUNCT
cana-5314	15	20	tsp	tsp	NOUN
cana-5314	15	21	)	)	PUNCT
cana-5314	15	22	,	,	PUNCT
cana-5314	15	23	integer	integer	NOUN
cana-5314	15	24	factorization	factorization	NOUN
cana-5314	15	25	along	along	ADP
cana-5314	15	26	with	with	ADP
cana-5314	15	27	boolean	boolean	ADJ
cana-5314	15	28	satisfiability	satisfiability	NOUN
cana-5314	15	29	problem	problem	NOUN
cana-5314	15	30	(	(	PUNCT
cana-5314	15	31	sat	sit	VERB
cana-5314	15	32	)	)	PUNCT
cana-5314	15	33	with	with	ADP
cana-5314	15	34	high	high	ADJ
cana-5314	15	35	operational	operational	ADJ
cana-5314	15	36	effectiveness	effectiveness	NOUN
cana-5314	15	37	.	.	PUNCT
cana-5314	16	1	the	the	DET
cana-5314	16	2	solution	solution	NOUN
cana-5314	16	3	of	of	ADP
cana-5314	16	4	p	p	NOUN
cana-5314	16	5	=	=	X
cana-5314	16	6	np	np	INTJ
cana-5314	16	7	would	would	AUX
cana-5314	16	8	transform	transform	VERB
cana-5314	16	9	optimization	optimization	NOUN
cana-5314	16	10	along	along	ADP
cana-5314	16	11	with	with	ADP
cana-5314	16	12	cryptography	cryptography	NOUN
cana-5314	16	13	machine	machine	NOUN
cana-5314	16	14	learning	learning	NOUN
cana-5314	16	15	and	and	CCONJ
cana-5314	16	16	artificial	artificial	ADJ
cana-5314	16	17	intelligence	intelligence	NOUN
cana-5314	16	18	fields	field	NOUN
cana-5314	16	19	.	.	PUNCT
cana-5314	17	1	the	the	DET
cana-5314	17	2	discovery	discovery	NOUN
cana-5314	17	3	of	of	ADP
cana-5314	17	4	p	p	PROPN
cana-5314	17	5	≠	≠	PROPN
cana-5314	17	6	np	np	PRON
cana-5314	17	7	would	would	AUX
cana-5314	17	8	create	create	VERB
cana-5314	17	9	essential	essential	ADJ
cana-5314	17	10	limits	limit	NOUN
cana-5314	17	11	to	to	ADP
cana-5314	17	12	what	what	PRON
cana-5314	17	13	computers	computer	NOUN
cana-5314	17	14	can	can	AUX
cana-5314	17	15	efficiently	efficiently	ADV
cana-5314	17	16	compute	compute	VERB
cana-5314	17	17	which	which	PRON
cana-5314	17	18	would	would	AUX
cana-5314	17	19	provide	provide	VERB
cana-5314	17	20	better	well	ADJ
cana-5314	17	21	boundaries	boundary	NOUN
cana-5314	17	22	between	between	ADP
cana-5314	17	23	complicated	complicated	ADJ
cana-5314	17	24	and	and	CCONJ
cana-5314	17	25	simple	simple	ADJ
cana-5314	17	26	problems	problem	NOUN
cana-5314	17	27	.	.	PUNCT
cana-5314	18	1	it	it	PRON
cana-5314	18	2	becomes	become	VERB
cana-5314	18	3	difficult	difficult	ADJ
cana-5314	18	4	to	to	PART
cana-5314	18	5	establish	establish	VERB
cana-5314	18	6	either	either	DET
cana-5314	18	7	type	type	NOUN
cana-5314	18	8	of	of	ADP
cana-5314	18	9	proof	proof	NOUN
cana-5314	18	10	because	because	SCONJ
cana-5314	18	11	of	of	ADP
cana-5314	18	12	the	the	DET
cana-5314	18	13	challenge	challenge	NOUN
cana-5314	18	14	.	.	PUNCT
cana-5314	19	1	thousands	thousand	NOUN
cana-5314	19	2	of	of	ADP
cana-5314	19	3	mathematicians	mathematician	NOUN
cana-5314	19	4	have	have	AUX
cana-5314	19	5	looked	look	VERB
cana-5314	19	6	for	for	ADP
cana-5314	19	7	polynomial	polynomial	ADJ
cana-5314	19	8	-	-	PUNCT
cana-5314	19	9	time	time	NOUN
cana-5314	19	10	algorithms	algorithm	NOUN
cana-5314	19	11	to	to	PART
cana-5314	19	12	solve	solve	VERB
cana-5314	19	13	any	any	PRON
cana-5314	19	14	of	of	ADP
cana-5314	19	15	the	the	DET
cana-5314	19	16	np	np	NOUN
cana-5314	19	17	-	-	PUNCT
cana-5314	19	18	complete	complete	ADJ
cana-5314	19	19	problems	problem	NOUN
cana-5314	19	20	without	without	ADP
cana-5314	19	21	success	success	NOUN
cana-5314	19	22	since	since	SCONJ
cana-5314	19	23	these	these	DET
cana-5314	19	24	problems	problem	NOUN
cana-5314	19	25	stand	stand	VERB
cana-5314	19	26	among	among	ADP
cana-5314	19	27	the	the	DET
cana-5314	19	28	toughest	tough	ADJ
cana-5314	19	29	to	to	PART
cana-5314	19	30	solve	solve	VERB
cana-5314	19	31	within	within	ADP
cana-5314	19	32	the	the	DET
cana-5314	19	33	np	np	ADJ
cana-5314	19	34	class	class	NOUN
cana-5314	19	35	[	[	X
cana-5314	19	36	11	11	NUM
cana-5314	19	37	]	]	PUNCT
cana-5314	19	38	.	.	PUNCT
cana-5314	20	1	according	accord	VERB
cana-5314	20	2	to	to	ADP
cana-5314	20	3	the	the	DET
cana-5314	20	4	cook	cook	NOUN
cana-5314	20	5	-	-	PUNCT
cana-5314	20	6	levin	levin	PROPN
cana-5314	20	7	theorem	theorem	PROPN
cana-5314	20	8	(	(	PUNCT
cana-5314	20	9	1971	1971	NUM
cana-5314	20	10	)	)	PUNCT
cana-5314	20	11	sat	sit	VERB
cana-5314	20	12	was	be	AUX
cana-5314	20	13	proven	prove	VERB
cana-5314	20	14	to	to	PART
cana-5314	20	15	be	be	AUX
cana-5314	20	16	npcomplete	npcomplete	ADJ
cana-5314	20	17	thus	thus	ADV
cana-5314	20	18	demonstrating	demonstrate	VERB
cana-5314	20	19	that	that	SCONJ
cana-5314	20	20	solving	solve	VERB
cana-5314	20	21	any	any	DET
cana-5314	20	22	np	np	NOUN
cana-5314	20	23	-	-	PUNCT
cana-5314	20	24	complete	complete	ADJ
cana-5314	20	25	problem	problem	NOUN
cana-5314	20	26	in	in	ADP
cana-5314	20	27	polynomial	polynomial	ADJ
cana-5314	20	28	time	time	NOUN
cana-5314	20	29	would	would	AUX
cana-5314	20	30	lead	lead	VERB
cana-5314	20	31	to	to	ADP
cana-5314	20	32	the	the	DET
cana-5314	20	33	ability	ability	NOUN
cana-5314	20	34	to	to	PART
cana-5314	20	35	solve	solve	VERB
cana-5314	20	36	all	all	DET
cana-5314	20	37	problems	problem	NOUN
cana-5314	20	38	within	within	ADP
cana-5314	20	39	the	the	DET
cana-5314	20	40	np	np	NOUN
cana-5314	20	41	class	class	NOUN
cana-5314	20	42	in	in	ADP
cana-5314	20	43	polynomial	polynomial	ADJ
cana-5314	20	44	time	time	NOUN
cana-5314	20	45	also	also	ADV
cana-5314	20	46	.	.	PUNCT
cana-5314	21	1	besides	besides	SCONJ
cana-5314	21	2	sat	sit	VERB
cana-5314	21	3	the	the	DET
cana-5314	21	4	concept	concept	NOUN
cana-5314	21	5	now	now	ADV
cana-5314	21	6	extends	extend	VERB
cana-5314	21	7	to	to	ADP
cana-5314	21	8	various	various	ADJ
cana-5314	21	9	additional	additional	ADJ
cana-5314	21	10	problems	problem	NOUN
cana-5314	21	11	including	include	VERB
cana-5314	21	12	knapsack	knapsack	NOUN
cana-5314	21	13	along	along	ADV
cana-5314	21	14	with	with	ADP
cana-5314	21	15	clique	clique	NOUN
cana-5314	21	16	and	and	CCONJ
cana-5314	21	17	vertex	vertex	NOUN
cana-5314	21	18	cover	cover	NOUN
cana-5314	21	19	.	.	PUNCT
cana-5314	22	1	rsa	rsa	NOUN
cana-5314	22	2	encryption	encryption	NOUN
cana-5314	22	3	together	together	ADV
cana-5314	22	4	with	with	ADP
cana-5314	22	5	other	other	ADJ
cana-5314	22	6	cryptographic	cryptographic	ADJ
cana-5314	22	7	systems	system	NOUN
cana-5314	22	8	relies	rely	VERB
cana-5314	22	9	on	on	ADP
cana-5314	22	10	the	the	DET
cana-5314	22	11	fundamental	fundamental	ADJ
cana-5314	22	12	concept	concept	NOUN
cana-5314	22	13	of	of	ADP
cana-5314	22	14	p	p	NOUN
cana-5314	22	15	versus	versus	ADP
cana-5314	22	16	np	np	INTJ
cana-5314	22	17	to	to	PART
cana-5314	22	18	protect	protect	VERB
cana-5314	22	19	critical	critical	ADJ
cana-5314	22	20	data	datum	NOUN
cana-5314	22	21	.	.	PUNCT
cana-5314	23	1	this	this	DET
cana-5314	23	2	problem	problem	NOUN
cana-5314	23	3	stands	stand	VERB
cana-5314	23	4	as	as	ADP
cana-5314	23	5	the	the	DET
cana-5314	23	6	foundation	foundation	NOUN
cana-5314	23	7	behind	behind	ADP
cana-5314	23	8	cryptographic	cryptographic	ADJ
cana-5314	23	9	encryption	encryption	NOUN
cana-5314	23	10	because	because	SCONJ
cana-5314	23	11	it	it	PRON
cana-5314	23	12	remains	remain	VERB
cana-5314	23	13	unproven	unproven	ADJ
cana-5314	23	14	whether	whether	SCONJ
cana-5314	23	15	particular	particular	ADJ
cana-5314	23	16	problems	problem	NOUN
cana-5314	23	17	require	require	VERB
cana-5314	23	18	long	long	ADJ
cana-5314	23	19	periods	period	NOUN
cana-5314	23	20	to	to	PART
cana-5314	23	21	solve	solve	VERB
cana-5314	23	22	.	.	PUNCT
cana-5314	24	1	the	the	DET
cana-5314	24	2	discovery	discovery	NOUN
cana-5314	24	3	of	of	ADP
cana-5314	24	4	p	p	NOUN
cana-5314	24	5	=	=	X
cana-5314	24	6	np	np	INTJ
cana-5314	24	7	would	would	AUX
cana-5314	24	8	allow	allow	VERB
cana-5314	24	9	quick	quick	ADJ
cana-5314	24	10	solutions	solution	NOUN
cana-5314	24	11	to	to	PART
cana-5314	24	12	break	break	VERB
cana-5314	24	13	encryption	encryption	NOUN
cana-5314	24	14	methods	method	NOUN
cana-5314	24	15	thereby	thereby	ADV
cana-5314	24	16	requiring	require	VERB
cana-5314	24	17	a	a	DET
cana-5314	24	18	rapid	rapid	ADJ
cana-5314	24	19	development	development	NOUN
cana-5314	24	20	of	of	ADP
cana-5314	24	21	new	new	ADJ
cana-5314	24	22	cryptographic	cryptographic	ADJ
cana-5314	24	23	methods	method	NOUN
cana-5314	24	24	.	.	PUNCT
cana-5314	25	1	the	the	DET
cana-5314	25	2	belief	belief	NOUN
cana-5314	25	3	that	that	SCONJ
cana-5314	25	4	some	some	DET
cana-5314	25	5	problems	problem	NOUN
cana-5314	25	6	(	(	PUNCT
cana-5314	25	7	including	include	VERB
cana-5314	25	8	the	the	DET
cana-5314	25	9	training	training	NOUN
cana-5314	25	10	of	of	ADP
cana-5314	25	11	large	large	ADJ
cana-5314	25	12	neural	neural	ADJ
cana-5314	25	13	networks	network	NOUN
cana-5314	25	14	)	)	PUNCT
cana-5314	25	15	can	can	AUX
cana-5314	25	16	not	not	PART
cana-5314	25	17	be	be	AUX
cana-5314	25	18	solved	solve	VERB
cana-5314	25	19	within	within	ADP
cana-5314	25	20	polynomial	polynomial	ADJ
cana-5314	25	21	time	time	NOUN
cana-5314	25	22	functions	function	NOUN
cana-5314	25	23	as	as	ADP
cana-5314	25	24	fundamental	fundamental	ADJ
cana-5314	25	25	base	base	NOUN
cana-5314	25	26	for	for	ADP
cana-5314	25	27	ai	ai	VERB
cana-5314	25	28	along	along	ADP
cana-5314	25	29	with	with	ADP
cana-5314	25	30	machine	machine	NOUN
cana-5314	25	31	learning	learning	NOUN
cana-5314	25	32	and	and	CCONJ
cana-5314	25	33	optimization	optimization	NOUN
cana-5314	25	34	algorithms	algorithm	NOUN
cana-5314	25	35	which	which	PRON
cana-5314	25	36	determine	determine	VERB
cana-5314	25	37	heuristic	heuristic	ADJ
cana-5314	25	38	design	design	NOUN
cana-5314	26	1	[	[	X
cana-5314	26	2	14	14	NUM
cana-5314	26	3	-	-	SYM
cana-5314	26	4	15	15	NUM
cana-5314	26	5	]	]	PUNCT
cana-5314	26	6	.	.	PUNCT
cana-5314	27	1	research	research	NOUN
cana-5314	27	2	activities	activity	NOUN
cana-5314	27	3	about	about	ADP
cana-5314	27	4	this	this	DET
cana-5314	27	5	unsolved	unsolved	ADJ
cana-5314	27	6	problem	problem	NOUN
cana-5314	27	7	have	have	AUX
cana-5314	27	8	been	be	AUX
cana-5314	27	9	substantial	substantial	ADJ
cana-5314	27	10	during	during	ADP
cana-5314	27	11	the	the	DET
cana-5314	27	12	last	last	ADJ
cana-5314	27	13	fifty	fifty	NUM
cana-5314	27	14	years	year	NOUN
cana-5314	27	15	although	although	SCONJ
cana-5314	27	16	a	a	DET
cana-5314	27	17	solution	solution	NOUN
cana-5314	27	18	has	have	AUX
cana-5314	27	19	not	not	PART
cana-5314	27	20	been	be	AUX
cana-5314	27	21	found	find	VERB
cana-5314	27	22	.	.	PUNCT
cana-5314	28	1	due	due	ADP
cana-5314	28	2	to	to	ADP
cana-5314	28	3	p	p	NOUN
cana-5314	28	4	vs.	vs.	ADP
cana-5314	28	5	np	np	INTJ
cana-5314	28	6	most	most	ADJ
cana-5314	28	7	researchers	researcher	NOUN
cana-5314	28	8	study	study	VERB
cana-5314	28	9	the	the	DET
cana-5314	28	10	structure	structure	NOUN
cana-5314	28	11	of	of	ADP
cana-5314	28	12	np	np	NOUN
cana-5314	28	13	-	-	PUNCT
cana-5314	28	14	complete	complete	ADJ
cana-5314	28	15	problems	problem	NOUN
cana-5314	28	16	together	together	ADV
cana-5314	28	17	with	with	ADP
cana-5314	28	18	searching	search	VERB
cana-5314	28	19	for	for	ADP
cana-5314	28	20	polynomial	polynomial	ADJ
cana-5314	28	21	-	-	PUNCT
cana-5314	28	22	time	time	NOUN
cana-5314	28	23	solutions	solution	NOUN
cana-5314	28	24	for	for	ADP
cana-5314	28	25	these	these	DET
cana-5314	28	26	problems	problem	NOUN
cana-5314	28	27	.	.	PUNCT
cana-5314	29	1	toolmakers	toolmaker	NOUN
cana-5314	29	2	developed	develop	VERB
cana-5314	29	3	approximation	approximation	NOUN
cana-5314	29	4	algorithms	algorithm	NOUN
cana-5314	29	5	coupled	couple	VERB
cana-5314	29	6	with	with	ADP
cana-5314	29	7	randomized	randomized	ADJ
cana-5314	29	8	algorithms	algorithm	NOUN
cana-5314	29	9	and	and	CCONJ
cana-5314	29	10	heuristic	heuristic	ADJ
cana-5314	29	11	algorithms	algorithm	NOUN
cana-5314	29	12	to	to	PART
cana-5314	29	13	produce	produce	VERB
cana-5314	29	14	workable	workable	ADJ
cana-5314	29	15	solutions	solution	NOUN
cana-5314	29	16	for	for	ADP
cana-5314	29	17	many	many	ADJ
cana-5314	29	18	practical	practical	ADJ
cana-5314	29	19	situations	situation	NOUN
cana-5314	29	20	although	although	SCONJ
cana-5314	29	21	such	such	ADJ
cana-5314	29	22	systems	system	NOUN
cana-5314	29	23	ensure	ensure	VERB
cana-5314	29	24	only	only	ADV
cana-5314	29	25	approximate	approximate	ADJ
cana-5314	29	26	results	result	NOUN
cana-5314	29	27	.	.	PUNCT
cana-5314	30	1	the	the	DET
cana-5314	30	2	scientific	scientific	ADJ
cana-5314	30	3	community	community	NOUN
cana-5314	30	4	strongly	strongly	ADV
cana-5314	30	5	believes	believe	VERB
cana-5314	30	6	p	p	NOUN
cana-5314	30	7	is	be	AUX
cana-5314	30	8	not	not	PART
cana-5314	30	9	equal	equal	ADJ
cana-5314	30	10	to	to	ADP
cana-5314	30	11	np	np	INTJ
cana-5314	31	1	yet	yet	ADV
cana-5314	31	2	no	no	DET
cana-5314	31	3	final	final	ADJ
cana-5314	31	4	verification	verification	NOUN
cana-5314	31	5	exists	exist	NOUN
cana-5314	31	6	which	which	PRON
cana-5314	31	7	continues	continue	VERB
cana-5314	31	8	to	to	PART
cana-5314	31	9	fascinate	fascinate	VERB
cana-5314	31	10	math	math	NOUN
cana-5314	31	11	and	and	CCONJ
cana-5314	31	12	computer	computer	NOUN
cana-5314	31	13	science	science	NOUN
cana-5314	31	14	researchers	researcher	NOUN
cana-5314	31	15	.	.	PUNCT
cana-5314	32	1	many	many	ADJ
cana-5314	32	2	consider	consider	VERB
cana-5314	32	3	this	this	DET
cana-5314	32	4	core	core	NOUN
cana-5314	32	5	question	question	NOUN
cana-5314	32	6	important	important	ADJ
cana-5314	32	7	enough	enough	ADV
cana-5314	32	8	for	for	SCONJ
cana-5314	32	9	the	the	DET
cana-5314	32	10	clay	clay	NOUN
cana-5314	32	11	mathematics	mathematics	PROPN
cana-5314	32	12	institute	institute	PROPN
cana-5314	32	13	to	to	PART
cana-5314	32	14	select	select	VERB
cana-5314	32	15	it	it	PRON
cana-5314	32	16	as	as	ADP
cana-5314	32	17	one	one	NUM
cana-5314	32	18	of	of	ADP
cana-5314	32	19	seven	seven	NUM
cana-5314	32	20	millennium	millennium	NOUN
cana-5314	32	21	prize	prize	NOUN
cana-5314	32	22	problems	problem	NOUN
cana-5314	32	23	with	with	ADP
cana-5314	32	24	a	a	DET
cana-5314	32	25	$	$	SYM
cana-5314	32	26	1	1	NUM
cana-5314	32	27	million	million	NUM
cana-5314	32	28	prize	prize	NOUN
cana-5314	32	29	reward	reward	NOUN
cana-5314	32	30	for	for	ADP
cana-5314	32	31	its	its	PRON
cana-5314	32	32	successful	successful	ADJ
cana-5314	32	33	resolution	resolution	NOUN
cana-5314	32	34	[	[	X
cana-5314	32	35	12	12	NUM
cana-5314	32	36	]	]	PUNCT
cana-5314	32	37	.	.	PUNCT
cana-5314	33	1	the	the	DET
cana-5314	33	2	relationship	relationship	NOUN
cana-5314	33	3	between	between	ADP
cana-5314	33	4	p	p	PROPN
cana-5314	33	5	and	and	CCONJ
cana-5314	33	6	np	np	PROPN
cana-5314	33	7	would	would	AUX
cana-5314	33	8	indicate	indicate	VERB
cana-5314	33	9	the	the	DET
cana-5314	33	10	existence	existence	NOUN
cana-5314	33	11	of	of	ADP
cana-5314	33	12	a	a	DET
cana-5314	33	13	hidden	hide	VERB
cana-5314	33	14	practical	practical	ADJ
cana-5314	33	15	computational	computational	ADJ
cana-5314	33	16	approach	approach	NOUN
cana-5314	33	17	if	if	SCONJ
cana-5314	33	18	p	p	NOUN
cana-5314	33	19	=	=	VERB
cana-5314	33	20	np	np	NOUN
cana-5314	33	21	turns	turn	VERB
cana-5314	33	22	out	out	ADP
cana-5314	33	23	to	to	PART
cana-5314	33	24	be	be	AUX
cana-5314	33	25	true	true	ADJ
cana-5314	33	26	.	.	PUNCT
cana-5314	34	1	if	if	SCONJ
cana-5314	34	2	p	p	PROPN
cana-5314	34	3	≠	≠	PROPN
cana-5314	34	4	np	np	INTJ
cana-5314	34	5	then	then	ADV
cana-5314	34	6	researchers	researcher	NOUN
cana-5314	34	7	would	would	AUX
cana-5314	34	8	gain	gain	VERB
cana-5314	34	9	further	further	ADJ
cana-5314	34	10	confirmation	confirmation	NOUN
cana-5314	34	11	that	that	SCONJ
cana-5314	34	12	human	human	ADJ
cana-5314	34	13	computation	computation	NOUN
cana-5314	34	14	has	have	AUX
cana-5314	34	15	inherent	inherent	ADJ
cana-5314	34	16	restrictions	restriction	NOUN
cana-5314	34	17	.	.	PUNCT
cana-5314	35	1	the	the	DET
cana-5314	35	2	solution	solution	NOUN
cana-5314	35	3	of	of	ADP
cana-5314	35	4	this	this	DET
cana-5314	35	5	communications	communication	NOUN
cana-5314	35	6	on	on	ADP
cana-5314	35	7	applied	apply	VERB
cana-5314	35	8	nonlinear	nonlinear	ADJ
cana-5314	35	9	analysis	analysis	NOUN
cana-5314	35	10	issn	issn	NOUN
cana-5314	35	11	:	:	PUNCT
cana-5314	35	12	1074	1074	NUM
cana-5314	35	13	-	-	PUNCT
cana-5314	35	14	133x	133x	NUM
cana-5314	35	15	vol	vol	NOUN
cana-5314	35	16	31	31	NUM
cana-5314	35	17	no	no	NOUN
cana-5314	35	18	.	.	PUNCT
cana-5314	36	1	8s	8s	PROPN
cana-5314	36	2	(	(	PUNCT
cana-5314	36	3	2024	2024	NUM
cana-5314	36	4	)	)	PUNCT
cana-5314	36	5	947	947	NUM
cana-5314	36	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5314	36	7	mathematical	mathematical	ADJ
cana-5314	36	8	problem	problem	NOUN
cana-5314	36	9	will	will	AUX
cana-5314	36	10	bring	bring	VERB
cana-5314	36	11	scientific	scientific	ADJ
cana-5314	36	12	progress	progress	NOUN
cana-5314	36	13	to	to	ADP
cana-5314	36	14	theoretical	theoretical	ADJ
cana-5314	36	15	computer	computer	NOUN
cana-5314	36	16	science	science	NOUN
cana-5314	36	17	and	and	CCONJ
cana-5314	36	18	reshape	reshape	VERB
cana-5314	36	19	our	our	PRON
cana-5314	36	20	comprehension	comprehension	NOUN
cana-5314	36	21	of	of	ADP
cana-5314	36	22	what	what	PRON
cana-5314	36	23	the	the	DET
cana-5314	36	24	computational	computational	ADJ
cana-5314	36	25	universe	universe	NOUN
cana-5314	36	26	entails	entail	VERB
cana-5314	36	27	.	.	PUNCT
cana-5314	37	1	novelty	novelty	NOUN
cana-5314	37	2	and	and	CCONJ
cana-5314	37	3	contribution	contribution	NOUN
cana-5314	37	4	the	the	DET
cana-5314	37	5	research	research	NOUN
cana-5314	37	6	intends	intend	VERB
cana-5314	37	7	to	to	PART
cana-5314	37	8	conduct	conduct	VERB
cana-5314	37	9	a	a	DET
cana-5314	37	10	detailed	detailed	ADJ
cana-5314	37	11	analysis	analysis	NOUN
cana-5314	37	12	of	of	ADP
cana-5314	37	13	the	the	DET
cana-5314	37	14	p	p	NOUN
cana-5314	37	15	versus	versus	ADP
cana-5314	37	16	np	np	ADP
cana-5314	37	17	problem	problem	NOUN
cana-5314	37	18	by	by	ADP
cana-5314	37	19	tracing	trace	VERB
cana-5314	37	20	its	its	PRON
cana-5314	37	21	historical	historical	ADJ
cana-5314	37	22	progression	progression	NOUN
cana-5314	37	23	together	together	ADV
cana-5314	37	24	with	with	ADP
cana-5314	37	25	its	its	PRON
cana-5314	37	26	practical	practical	ADJ
cana-5314	37	27	effects	effect	NOUN
cana-5314	37	28	and	and	CCONJ
cana-5314	37	29	active	active	ADJ
cana-5314	37	30	resolution	resolution	NOUN
cana-5314	37	31	activities	activity	NOUN
cana-5314	37	32	.	.	PUNCT
cana-5314	38	1	the	the	DET
cana-5314	38	2	novel	novel	ADJ
cana-5314	38	3	aspect	aspect	NOUN
cana-5314	38	4	of	of	ADP
cana-5314	38	5	this	this	DET
cana-5314	38	6	research	research	NOUN
cana-5314	38	7	combines	combine	VERB
cana-5314	38	8	theoretical	theoretical	ADJ
cana-5314	38	9	perspectives	perspective	NOUN
cana-5314	38	10	from	from	ADP
cana-5314	38	11	computer	computer	NOUN
cana-5314	38	12	science	science	NOUN
cana-5314	38	13	with	with	ADP
cana-5314	38	14	practical	practical	ADJ
cana-5314	38	15	insights	insight	NOUN
cana-5314	38	16	to	to	PART
cana-5314	38	17	study	study	VERB
cana-5314	38	18	the	the	DET
cana-5314	38	19	problem	problem	NOUN
cana-5314	38	20	[	[	X
cana-5314	38	21	8	8	NUM
cana-5314	38	22	]	]	PUNCT
cana-5314	38	23	.	.	PUNCT
cana-5314	39	1	this	this	DET
cana-5314	39	2	paper	paper	NOUN
cana-5314	39	3	conducts	conduct	VERB
cana-5314	39	4	a	a	DET
cana-5314	39	5	thorough	thorough	ADJ
cana-5314	39	6	assessment	assessment	NOUN
cana-5314	39	7	of	of	ADP
cana-5314	39	8	contemporary	contemporary	ADJ
cana-5314	39	9	advancements	advancement	NOUN
cana-5314	39	10	in	in	ADP
cana-5314	39	11	complexity	complexity	NOUN
cana-5314	39	12	theory	theory	NOUN
cana-5314	39	13	around	around	ADP
cana-5314	39	14	np	np	NOUN
cana-5314	39	15	-	-	PUNCT
cana-5314	39	16	complete	complete	ADJ
cana-5314	39	17	issues	issue	NOUN
cana-5314	39	18	.	.	PUNCT
cana-5314	40	1	the	the	DET
cana-5314	40	2	paper	paper	NOUN
cana-5314	40	3	connects	connect	VERB
cana-5314	40	4	theoretical	theoretical	ADJ
cana-5314	40	5	analysis	analysis	NOUN
cana-5314	40	6	of	of	ADP
cana-5314	40	7	p	p	NOUN
cana-5314	40	8	vs.	vs.	ADP
cana-5314	40	9	np	np	INTJ
cana-5314	40	10	with	with	ADP
cana-5314	40	11	practical	practical	ADJ
cana-5314	40	12	applications	application	NOUN
cana-5314	40	13	which	which	PRON
cana-5314	40	14	include	include	VERB
cana-5314	40	15	cryptography	cryptography	NOUN
cana-5314	40	16	together	together	ADV
cana-5314	40	17	with	with	ADP
cana-5314	40	18	machine	machine	NOUN
cana-5314	40	19	learning	learn	VERB
cana-5314	40	20	optimization	optimization	NOUN
cana-5314	40	21	and	and	CCONJ
cana-5314	40	22	artificial	artificial	ADJ
cana-5314	40	23	intelligence	intelligence	NOUN
cana-5314	40	24	.	.	PUNCT
cana-5314	41	1	this	this	DET
cana-5314	41	2	paper	paper	NOUN
cana-5314	41	3	uses	use	VERB
cana-5314	41	4	theoretical	theoretical	ADJ
cana-5314	41	5	problem	problem	NOUN
cana-5314	41	6	background	background	NOUN
cana-5314	41	7	together	together	ADV
cana-5314	41	8	with	with	ADP
cana-5314	41	9	practical	practical	ADJ
cana-5314	41	10	effects	effect	NOUN
cana-5314	41	11	to	to	PART
cana-5314	41	12	offer	offer	VERB
cana-5314	41	13	improved	improved	ADJ
cana-5314	41	14	comprehension	comprehension	NOUN
cana-5314	41	15	of	of	ADP
cana-5314	41	16	p	p	NOUN
cana-5314	41	17	vs.	vs.	ADP
cana-5314	41	18	np	np	INTJ
cana-5314	41	19	solutions	solution	NOUN
cana-5314	41	20	for	for	ADP
cana-5314	41	21	various	various	ADJ
cana-5314	41	22	fields	field	NOUN
cana-5314	41	23	.	.	PUNCT
cana-5314	42	1	the	the	DET
cana-5314	42	2	paper	paper	NOUN
cana-5314	42	3	presents	present	VERB
cana-5314	42	4	a	a	DET
cana-5314	42	5	fresh	fresh	ADJ
cana-5314	42	6	framework	framework	NOUN
cana-5314	42	7	that	that	PRON
cana-5314	42	8	deals	deal	VERB
cana-5314	42	9	with	with	ADP
cana-5314	42	10	the	the	DET
cana-5314	42	11	problem	problem	NOUN
cana-5314	42	12	.	.	PUNCT
cana-5314	43	1	the	the	DET
cana-5314	43	2	article	article	NOUN
cana-5314	43	3	investigates	investigate	VERB
cana-5314	43	4	computational	computational	ADJ
cana-5314	43	5	models	model	NOUN
cana-5314	43	6	beyond	beyond	ADP
cana-5314	43	7	turing	ture	VERB
cana-5314	43	8	machines	machine	NOUN
cana-5314	43	9	by	by	ADP
cana-5314	43	10	studying	study	VERB
cana-5314	43	11	quantum	quantum	NOUN
cana-5314	43	12	computing	computing	NOUN
cana-5314	43	13	and	and	CCONJ
cana-5314	43	14	probabilistic	probabilistic	ADJ
cana-5314	43	15	computation	computation	NOUN
cana-5314	43	16	to	to	PART
cana-5314	43	17	obtain	obtain	VERB
cana-5314	43	18	fresh	fresh	ADJ
cana-5314	43	19	perspectives	perspective	NOUN
cana-5314	43	20	about	about	ADP
cana-5314	43	21	p	p	PROPN
cana-5314	43	22	vs.	vs.	ADP
cana-5314	43	23	np	np	INTJ
cana-5314	43	24	.	.	PUNCT
cana-5314	44	1	new	new	ADJ
cana-5314	44	2	computational	computational	ADJ
cana-5314	44	3	models	model	NOUN
cana-5314	44	4	emerging	emerge	VERB
cana-5314	44	5	today	today	NOUN
cana-5314	44	6	create	create	VERB
cana-5314	44	7	distinct	distinct	ADJ
cana-5314	44	8	pathways	pathway	NOUN
cana-5314	44	9	to	to	PART
cana-5314	44	10	solve	solve	VERB
cana-5314	44	11	the	the	DET
cana-5314	44	12	p	p	NOUN
cana-5314	44	13	=	=	X
cana-5314	44	14	np	np	NOUN
cana-5314	44	15	question	question	NOUN
cana-5314	44	16	through	through	ADP
cana-5314	44	17	p	p	NOUN
cana-5314	44	18	=	=	PUNCT
cana-5314	45	1	np	np	PRON
cana-5314	45	2	evidence	evidence	NOUN
cana-5314	45	3	or	or	CCONJ
cana-5314	45	4	evidence	evidence	NOUN
cana-5314	45	5	that	that	SCONJ
cana-5314	45	6	p	p	NOUN
cana-5314	45	7	is	be	AUX
cana-5314	45	8	not	not	PART
cana-5314	45	9	equal	equal	ADJ
cana-5314	45	10	to	to	ADP
cana-5314	45	11	np	np	INTJ
cana-5314	45	12	.	.	PUNCT
cana-5314	46	1	the	the	DET
cana-5314	46	2	paper	paper	NOUN
cana-5314	46	3	explores	explore	VERB
cana-5314	46	4	fundamental	fundamental	ADJ
cana-5314	46	5	philosophical	philosophical	ADJ
cana-5314	46	6	questions	question	NOUN
cana-5314	46	7	associated	associate	VERB
cana-5314	46	8	with	with	ADP
cana-5314	46	9	the	the	DET
cana-5314	46	10	problem	problem	NOUN
cana-5314	46	11	which	which	PRON
cana-5314	46	12	frequently	frequently	ADV
cana-5314	46	13	escape	escape	VERB
cana-5314	46	14	attention	attention	NOUN
cana-5314	46	15	during	during	ADP
cana-5314	46	16	technical	technical	ADJ
cana-5314	46	17	p	p	PROPN
cana-5314	46	18	vs.	vs.	ADP
cana-5314	46	19	np	np	PROPN
cana-5314	46	20	talks	talk	NOUN
cana-5314	46	21	.	.	PUNCT
cana-5314	47	1	the	the	DET
cana-5314	47	2	research	research	NOUN
cana-5314	47	3	delves	delve	VERB
cana-5314	47	4	into	into	ADP
cana-5314	47	5	philosophical	philosophical	ADJ
cana-5314	47	6	areas	area	NOUN
cana-5314	47	7	of	of	ADP
cana-5314	47	8	the	the	DET
cana-5314	47	9	p	p	NOUN
cana-5314	47	10	vs.	vs.	ADP
cana-5314	47	11	np	np	INTJ
cana-5314	47	12	problem	problem	NOUN
cana-5314	47	13	to	to	PART
cana-5314	47	14	support	support	VERB
cana-5314	47	15	a	a	DET
cana-5314	47	16	wider	wide	ADJ
cana-5314	47	17	examination	examination	NOUN
cana-5314	47	18	of	of	ADP
cana-5314	47	19	computation	computation	NOUN
cana-5314	47	20	nature	nature	NOUN
cana-5314	47	21	and	and	CCONJ
cana-5314	47	22	human	human	ADJ
cana-5314	47	23	knowledge	knowledge	NOUN
cana-5314	47	24	boundaries	boundary	NOUN
cana-5314	47	25	together	together	ADV
cana-5314	47	26	with	with	ADP
cana-5314	47	27	advances	advance	NOUN
cana-5314	47	28	in	in	ADP
cana-5314	47	29	fundamental	fundamental	ADJ
cana-5314	47	30	properties	property	NOUN
cana-5314	47	31	of	of	ADP
cana-5314	47	32	computational	computational	ADJ
cana-5314	47	33	processes	process	NOUN
cana-5314	47	34	[	[	X
cana-5314	47	35	10	10	NUM
cana-5314	47	36	]	]	PUNCT
cana-5314	47	37	.	.	PUNCT
cana-5314	48	1	the	the	DET
cana-5314	48	2	paper	paper	NOUN
cana-5314	48	3	provides	provide	VERB
cana-5314	48	4	a	a	DET
cana-5314	48	5	discussion	discussion	NOUN
cana-5314	48	6	on	on	ADP
cana-5314	48	7	prospective	prospective	ADJ
cana-5314	48	8	research	research	NOUN
cana-5314	48	9	pathways	pathway	NOUN
cana-5314	48	10	for	for	ADP
cana-5314	48	11	the	the	DET
cana-5314	48	12	p	p	NOUN
cana-5314	48	13	vs.	vs.	ADP
cana-5314	48	14	np	np	INTJ
cana-5314	48	15	problem	problem	NOUN
cana-5314	48	16	together	together	ADV
cana-5314	48	17	with	with	ADP
cana-5314	48	18	open	open	ADJ
cana-5314	48	19	questions	question	NOUN
cana-5314	48	20	and	and	CCONJ
cana-5314	48	21	existing	exist	VERB
cana-5314	48	22	conjectures	conjecture	NOUN
cana-5314	48	23	which	which	PRON
cana-5314	48	24	could	could	AUX
cana-5314	48	25	potentially	potentially	ADV
cana-5314	48	26	lead	lead	VERB
cana-5314	48	27	to	to	ADP
cana-5314	48	28	breakthrough	breakthrough	NOUN
cana-5314	48	29	solutions	solution	NOUN
cana-5314	48	30	.	.	PUNCT
cana-5314	49	1	the	the	DET
cana-5314	49	2	research	research	NOUN
cana-5314	49	3	investigates	investigate	VERB
cana-5314	49	4	the	the	DET
cana-5314	49	5	present	present	ADJ
cana-5314	49	6	situation	situation	NOUN
cana-5314	49	7	of	of	ADP
cana-5314	49	8	this	this	DET
cana-5314	49	9	problem	problem	NOUN
cana-5314	49	10	pointby	pointby	NOUN
cana-5314	49	11	-	-	PUNCT
cana-5314	49	12	point	point	NOUN
cana-5314	49	13	along	along	ADV
cana-5314	49	14	with	with	ADP
cana-5314	49	15	establishing	establish	VERB
cana-5314	49	16	future	future	ADJ
cana-5314	49	17	development	development	NOUN
cana-5314	49	18	paths	path	NOUN
cana-5314	49	19	towards	towards	ADP
cana-5314	49	20	progress	progress	NOUN
cana-5314	49	21	.	.	PUNCT
cana-5314	50	1	ii	ii	X
cana-5314	50	2	.	.	PROPN
cana-5314	50	3	related	relate	VERB
cana-5314	50	4	works	work	NOUN
cana-5314	50	5	in	in	ADP
cana-5314	50	6	2022	2022	NUM
cana-5314	50	7	d.	d.	PROPN
cana-5314	50	8	bianco	bianco	PROPN
cana-5314	50	9	et	et	PROPN
cana-5314	50	10	al	al	PROPN
cana-5314	50	11	.	.	PROPN
cana-5314	50	12	,	,	PUNCT
cana-5314	51	1	[	[	X
cana-5314	51	2	13	13	NUM
cana-5314	51	3	]	]	PUNCT
cana-5314	51	4	introduced	introduce	VERB
cana-5314	51	5	the	the	DET
cana-5314	51	6	p	p	NOUN
cana-5314	51	7	versus	versus	ADP
cana-5314	51	8	np	np	PRON
cana-5314	51	9	problem	problem	NOUN
cana-5314	51	10	became	become	VERB
cana-5314	51	11	the	the	DET
cana-5314	51	12	main	main	ADJ
cana-5314	51	13	focus	focus	NOUN
cana-5314	51	14	of	of	ADP
cana-5314	51	15	computational	computational	ADJ
cana-5314	51	16	complexity	complexity	NOUN
cana-5314	51	17	theory	theory	NOUN
cana-5314	51	18	research	research	NOUN
cana-5314	51	19	when	when	SCONJ
cana-5314	51	20	it	it	PRON
cana-5314	51	21	emerged	emerge	VERB
cana-5314	51	22	and	and	CCONJ
cana-5314	51	23	caused	cause	VERB
cana-5314	51	24	extensive	extensive	ADJ
cana-5314	51	25	academic	academic	ADJ
cana-5314	51	26	discussions	discussion	NOUN
cana-5314	51	27	about	about	ADP
cana-5314	51	28	efficient	efficient	ADJ
cana-5314	51	29	computing	computing	NOUN
cana-5314	51	30	.	.	PUNCT
cana-5314	52	1	scientists	scientist	NOUN
cana-5314	52	2	pursue	pursue	VERB
cana-5314	52	3	this	this	DET
cana-5314	52	4	topic	topic	NOUN
cana-5314	52	5	because	because	SCONJ
cana-5314	52	6	they	they	PRON
cana-5314	52	7	seek	seek	VERB
cana-5314	52	8	to	to	PART
cana-5314	52	9	identify	identify	VERB
cana-5314	52	10	the	the	DET
cana-5314	52	11	limits	limit	NOUN
cana-5314	52	12	of	of	ADP
cana-5314	52	13	efficient	efficient	ADJ
cana-5314	52	14	computation	computation	NOUN
cana-5314	52	15	.	.	PUNCT
cana-5314	53	1	the	the	DET
cana-5314	53	2	main	main	ADJ
cana-5314	53	3	obstacles	obstacle	NOUN
cana-5314	53	4	in	in	ADP
cana-5314	53	5	problem	problem	NOUN
cana-5314	53	6	classification	classification	NOUN
cana-5314	53	7	involve	involve	VERB
cana-5314	53	8	separating	separate	VERB
cana-5314	53	9	p	p	NOUN
cana-5314	53	10	from	from	ADP
cana-5314	53	11	np	np	INTJ
cana-5314	53	12	as	as	SCONJ
cana-5314	53	13	p	p	NOUN
cana-5314	53	14	contains	contain	VERB
cana-5314	53	15	problems	problem	NOUN
cana-5314	53	16	that	that	PRON
cana-5314	53	17	require	require	VERB
cana-5314	53	18	polynomial	polynomial	ADJ
cana-5314	53	19	time	time	NOUN
cana-5314	53	20	solutions	solution	NOUN
cana-5314	53	21	while	while	SCONJ
cana-5314	53	22	np	np	INTJ
cana-5314	53	23	includes	include	VERB
cana-5314	53	24	problems	problem	NOUN
cana-5314	53	25	where	where	SCONJ
cana-5314	53	26	polynomial	polynomial	ADJ
cana-5314	53	27	time	time	NOUN
cana-5314	53	28	verification	verification	NOUN
cana-5314	53	29	exists	exist	VERB
cana-5314	53	30	.	.	PUNCT
cana-5314	54	1	during	during	ADP
cana-5314	54	2	the	the	DET
cana-5314	54	3	early	early	ADJ
cana-5314	54	4	period	period	NOUN
cana-5314	54	5	researchers	researcher	NOUN
cana-5314	54	6	examined	examine	VERB
cana-5314	54	7	np	np	ADJ
cana-5314	54	8	-	-	PUNCT
cana-5314	54	9	complete	complete	ADJ
cana-5314	54	10	problems	problem	NOUN
cana-5314	54	11	to	to	PART
cana-5314	54	12	understand	understand	VERB
cana-5314	54	13	their	their	PRON
cana-5314	54	14	traits	trait	NOUN
cana-5314	54	15	since	since	SCONJ
cana-5314	54	16	these	these	DET
cana-5314	54	17	problems	problem	NOUN
cana-5314	54	18	represent	represent	VERB
cana-5314	54	19	the	the	DET
cana-5314	54	20	most	most	ADV
cana-5314	54	21	challenging	challenging	ADJ
cana-5314	54	22	problems	problem	NOUN
cana-5314	54	23	in	in	ADP
cana-5314	54	24	the	the	DET
cana-5314	54	25	np	np	ADJ
cana-5314	54	26	category	category	NOUN
cana-5314	54	27	.	.	PUNCT
cana-5314	55	1	the	the	DET
cana-5314	55	2	communications	communication	NOUN
cana-5314	55	3	on	on	ADP
cana-5314	55	4	applied	apply	VERB
cana-5314	55	5	nonlinear	nonlinear	ADJ
cana-5314	55	6	analysis	analysis	NOUN
cana-5314	55	7	issn	issn	NOUN
cana-5314	55	8	:	:	PUNCT
cana-5314	55	9	1074	1074	NUM
cana-5314	55	10	-	-	PUNCT
cana-5314	55	11	133x	133x	NUM
cana-5314	55	12	vol	vol	NOUN
cana-5314	55	13	31	31	NUM
cana-5314	55	14	no	no	NOUN
cana-5314	55	15	.	.	PUNCT
cana-5314	56	1	8s	8s	PROPN
cana-5314	56	2	(	(	PUNCT
cana-5314	56	3	2024	2024	NUM
cana-5314	56	4	)	)	PUNCT
cana-5314	56	5	948	948	NUM
cana-5314	56	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5314	56	7	significance	significance	NOUN
cana-5314	56	8	of	of	ADP
cana-5314	56	9	np	np	NOUN
cana-5314	56	10	-	-	PUNCT
cana-5314	56	11	complete	complete	ADJ
cana-5314	56	12	problems	problem	NOUN
cana-5314	56	13	lies	lie	VERB
cana-5314	56	14	in	in	ADP
cana-5314	56	15	their	their	PRON
cana-5314	56	16	ability	ability	NOUN
cana-5314	56	17	to	to	PART
cana-5314	56	18	solve	solve	VERB
cana-5314	56	19	every	every	DET
cana-5314	56	20	problem	problem	NOUN
cana-5314	56	21	in	in	ADP
cana-5314	56	22	np	np	INTJ
cana-5314	56	23	if	if	SCONJ
cana-5314	56	24	a	a	DET
cana-5314	56	25	single	single	ADJ
cana-5314	56	26	np	np	INTJ
cana-5314	56	27	-	-	PUNCT
cana-5314	56	28	complete	complete	ADJ
cana-5314	56	29	problem	problem	NOUN
cana-5314	56	30	receives	receive	VERB
cana-5314	56	31	polynomial	polynomial	ADJ
cana-5314	56	32	-	-	PUNCT
cana-5314	56	33	time	time	NOUN
cana-5314	56	34	solution	solution	NOUN
cana-5314	56	35	thus	thus	ADV
cana-5314	56	36	equating	equate	VERB
cana-5314	56	37	p	p	PRON
cana-5314	56	38	to	to	ADP
cana-5314	56	39	np	np	INTJ
cana-5314	56	40	.	.	PUNCT
cana-5314	57	1	scientists	scientist	NOUN
cana-5314	57	2	during	during	ADP
cana-5314	57	3	early	early	ADJ
cana-5314	57	4	research	research	NOUN
cana-5314	57	5	identified	identify	VERB
cana-5314	57	6	fresh	fresh	ADJ
cana-5314	57	7	np	np	NOUN
cana-5314	57	8	-	-	PUNCT
cana-5314	57	9	complete	complete	ADJ
cana-5314	57	10	challenges	challenge	NOUN
cana-5314	57	11	and	and	CCONJ
cana-5314	57	12	examined	examine	VERB
cana-5314	57	13	these	these	DET
cana-5314	57	14	problems	problem	NOUN
cana-5314	57	15	extensively	extensively	ADV
cana-5314	57	16	.	.	PUNCT
cana-5314	58	1	np	np	X
cana-5314	58	2	-	-	PUNCT
cana-5314	58	3	complete	complete	ADJ
cana-5314	58	4	problems	problem	NOUN
cana-5314	58	5	proved	prove	VERB
cana-5314	58	6	to	to	PART
cana-5314	58	7	be	be	AUX
cana-5314	58	8	a	a	DET
cana-5314	58	9	wide	wide	ADV
cana-5314	58	10	-	-	PUNCT
cana-5314	58	11	ranging	range	VERB
cana-5314	58	12	group	group	NOUN
cana-5314	58	13	that	that	PRON
cana-5314	58	14	exists	exist	VERB
cana-5314	58	15	across	across	ADP
cana-5314	58	16	multiple	multiple	ADJ
cana-5314	58	17	subject	subject	ADJ
cana-5314	58	18	domains	domain	NOUN
cana-5314	58	19	including	include	VERB
cana-5314	58	20	logical	logical	ADJ
cana-5314	58	21	analysis	analysis	NOUN
cana-5314	58	22	besides	besides	SCONJ
cana-5314	58	23	scheduling	scheduling	NOUN
cana-5314	58	24	and	and	CCONJ
cana-5314	58	25	network	network	NOUN
cana-5314	58	26	planning	planning	NOUN
cana-5314	58	27	and	and	CCONJ
cana-5314	58	28	optimization	optimization	NOUN
cana-5314	58	29	techniques	technique	NOUN
cana-5314	58	30	[	[	X
cana-5314	58	31	9	9	NUM
cana-5314	58	32	]	]	PUNCT
cana-5314	58	33	.	.	PUNCT
cana-5314	59	1	in	in	ADP
cana-5314	59	2	2022	2022	NUM
cana-5314	59	3	d.	d.	PROPN
cana-5314	59	4	gamarnik	gamarnik	PROPN
cana-5314	59	5	et.al	et.al	PROPN
cana-5314	59	6	.	.	PROPN
cana-5314	59	7	,	,	PUNCT
cana-5314	59	8	c.	c.	PROPN
cana-5314	59	9	moore	moore	PROPN
cana-5314	59	10	et.al	et.al	PROPN
cana-5314	59	11	.	.	PROPN
cana-5314	59	12	,	,	PUNCT
cana-5314	59	13	and	and	CCONJ
cana-5314	59	14	l.	l.	PROPN
cana-5314	59	15	zdeborová	zdeborová	PROPN
cana-5314	59	16	et.al	et.al	PROPN
cana-5314	59	17	.	.	PROPN
cana-5314	59	18	,	,	PUNCT
cana-5314	59	19	[	[	X
cana-5314	59	20	3	3	X
cana-5314	59	21	]	]	PUNCT
cana-5314	59	22	suggested	suggest	VERB
cana-5314	59	23	the	the	DET
cana-5314	59	24	scientists	scientist	NOUN
cana-5314	59	25	have	have	AUX
cana-5314	59	26	extensively	extensively	ADV
cana-5314	59	27	studied	study	VERB
cana-5314	59	28	approximation	approximation	NOUN
cana-5314	59	29	algorithms	algorithm	NOUN
cana-5314	59	30	and	and	CCONJ
cana-5314	59	31	heuristic	heuristic	ADJ
cana-5314	59	32	methods	method	NOUN
cana-5314	59	33	as	as	ADP
cana-5314	59	34	solutions	solution	NOUN
cana-5314	59	35	for	for	ADP
cana-5314	59	36	np	np	NOUN
cana-5314	59	37	-	-	PUNCT
cana-5314	59	38	complete	complete	ADJ
cana-5314	59	39	problems	problem	NOUN
cana-5314	59	40	when	when	SCONJ
cana-5314	59	41	used	use	VERB
cana-5314	59	42	in	in	ADP
cana-5314	59	43	practical	practical	ADJ
cana-5314	59	44	applications	application	NOUN
cana-5314	59	45	.	.	PUNCT
cana-5314	60	1	research	research	NOUN
cana-5314	60	2	focuses	focus	VERB
cana-5314	60	3	on	on	ADP
cana-5314	60	4	developing	develop	VERB
cana-5314	60	5	approximation	approximation	NOUN
cana-5314	60	6	algorithms	algorithm	NOUN
cana-5314	60	7	that	that	PRON
cana-5314	60	8	generate	generate	VERB
cana-5314	60	9	acceptable	acceptable	ADJ
cana-5314	60	10	solutions	solution	NOUN
cana-5314	60	11	within	within	ADP
cana-5314	60	12	specific	specific	ADJ
cana-5314	60	13	time	time	NOUN
cana-5314	60	14	limits	limit	NOUN
cana-5314	60	15	because	because	SCONJ
cana-5314	60	16	the	the	DET
cana-5314	60	17	exact	exact	ADJ
cana-5314	60	18	solution	solution	NOUN
cana-5314	60	19	of	of	ADP
cana-5314	60	20	these	these	DET
cana-5314	60	21	problems	problem	NOUN
cana-5314	60	22	demonstrates	demonstrate	VERB
cana-5314	60	23	unlikely	unlikely	ADJ
cana-5314	60	24	polynomial	polynomial	ADJ
cana-5314	60	25	-	-	PUNCT
cana-5314	60	26	time	time	NOUN
cana-5314	60	27	feasibility	feasibility	NOUN
cana-5314	60	28	under	under	ADP
cana-5314	60	29	p	p	PROPN
cana-5314	60	30	≠	≠	PROPN
cana-5314	60	31	np	np	NOUN
cana-5314	60	32	assumptions	assumption	NOUN
cana-5314	60	33	.	.	PUNCT
cana-5314	61	1	such	such	ADJ
cana-5314	61	2	solution	solution	NOUN
cana-5314	61	3	approaches	approach	NOUN
cana-5314	61	4	hold	hold	VERB
cana-5314	61	5	great	great	ADJ
cana-5314	61	6	importance	importance	NOUN
cana-5314	61	7	in	in	ADP
cana-5314	61	8	optimization	optimization	NOUN
cana-5314	61	9	applications	application	NOUN
cana-5314	61	10	because	because	SCONJ
cana-5314	61	11	they	they	PRON
cana-5314	61	12	yield	yield	VERB
cana-5314	61	13	valuable	valuable	ADJ
cana-5314	61	14	close	close	VERB
cana-5314	61	15	-	-	PUNCT
cana-5314	61	16	to	to	ADP
cana-5314	61	17	-	-	PUNCT
cana-5314	61	18	optimal	optimal	ADJ
cana-5314	61	19	results	result	NOUN
cana-5314	61	20	for	for	ADP
cana-5314	61	21	tasks	task	NOUN
cana-5314	61	22	including	include	VERB
cana-5314	61	23	resource	resource	NOUN
cana-5314	61	24	management	management	NOUN
cana-5314	61	25	and	and	CCONJ
cana-5314	61	26	route	route	NOUN
cana-5314	61	27	design	design	NOUN
cana-5314	61	28	and	and	CCONJ
cana-5314	61	29	artificial	artificial	ADJ
cana-5314	61	30	intelligence	intelligence	NOUN
cana-5314	61	31	models	model	NOUN
cana-5314	61	32	.	.	PUNCT
cana-5314	62	1	the	the	DET
cana-5314	62	2	relationship	relationship	NOUN
cana-5314	62	3	between	between	ADP
cana-5314	62	4	p	p	PROPN
cana-5314	62	5	and	and	CCONJ
cana-5314	62	6	np	np	PROPN
cana-5314	62	7	has	have	AUX
cana-5314	62	8	been	be	AUX
cana-5314	62	9	studied	study	VERB
cana-5314	62	10	using	use	VERB
cana-5314	62	11	different	different	ADJ
cana-5314	62	12	complexity	complexity	NOUN
cana-5314	62	13	classes	class	NOUN
cana-5314	62	14	which	which	PRON
cana-5314	62	15	exist	exist	VERB
cana-5314	62	16	between	between	ADP
cana-5314	62	17	p	p	PROPN
cana-5314	62	18	and	and	CCONJ
cana-5314	62	19	np	np	INTJ
cana-5314	62	20	.	.	PUNCT
cana-5314	63	1	the	the	DET
cana-5314	63	2	research	research	NOUN
cana-5314	63	3	community	community	NOUN
cana-5314	63	4	continues	continue	VERB
cana-5314	63	5	to	to	PART
cana-5314	63	6	analyze	analyze	VERB
cana-5314	63	7	the	the	DET
cana-5314	63	8	boundaries	boundary	NOUN
cana-5314	63	9	which	which	PRON
cana-5314	63	10	define	define	VERB
cana-5314	63	11	np	np	NOUN
cana-5314	63	12	-	-	PUNCT
cana-5314	63	13	hard	hard	ADJ
cana-5314	63	14	and	and	CCONJ
cana-5314	63	15	np	np	NOUN
cana-5314	63	16	-	-	PUNCT
cana-5314	63	17	easy	easy	ADJ
cana-5314	63	18	categories	category	NOUN
cana-5314	63	19	even	even	ADV
cana-5314	63	20	though	though	SCONJ
cana-5314	63	21	these	these	DET
cana-5314	63	22	boundaries	boundary	NOUN
cana-5314	63	23	lie	lie	VERB
cana-5314	63	24	between	between	ADP
cana-5314	63	25	p	p	PROPN
cana-5314	63	26	and	and	CCONJ
cana-5314	63	27	np	np	INTJ
cana-5314	63	28	.	.	PROPN
cana-5314	63	29	problem	problem	NOUN
cana-5314	63	30	classification	classification	NOUN
cana-5314	63	31	under	under	ADP
cana-5314	63	32	these	these	DET
cana-5314	63	33	subcategories	subcategorie	NOUN
cana-5314	63	34	determines	determine	VERB
cana-5314	63	35	the	the	DET
cana-5314	63	36	difficulty	difficulty	NOUN
cana-5314	63	37	level	level	NOUN
cana-5314	63	38	of	of	ADP
cana-5314	63	39	unverified	unverified	ADJ
cana-5314	63	40	and	and	CCONJ
cana-5314	63	41	unsolvable	unsolvable	ADJ
cana-5314	63	42	problems	problem	NOUN
cana-5314	63	43	that	that	PRON
cana-5314	63	44	do	do	AUX
cana-5314	63	45	not	not	PART
cana-5314	63	46	belong	belong	VERB
cana-5314	63	47	to	to	ADP
cana-5314	63	48	np	np	NOUN
cana-5314	63	49	-	-	PUNCT
cana-5314	63	50	complete	complete	ADJ
cana-5314	63	51	.	.	PUNCT
cana-5314	64	1	research	research	NOUN
cana-5314	64	2	about	about	ADP
cana-5314	64	3	computational	computational	ADJ
cana-5314	64	4	theory	theory	NOUN
cana-5314	64	5	depends	depend	VERB
cana-5314	64	6	heavily	heavily	ADV
cana-5314	64	7	on	on	ADP
cana-5314	64	8	our	our	PRON
cana-5314	64	9	comprehension	comprehension	NOUN
cana-5314	64	10	of	of	ADP
cana-5314	64	11	these	these	DET
cana-5314	64	12	labeled	label	VERB
cana-5314	64	13	problem	problem	NOUN
cana-5314	64	14	classes	class	NOUN
cana-5314	64	15	.	.	PUNCT
cana-5314	65	1	the	the	DET
cana-5314	65	2	p	p	NOUN
cana-5314	65	3	vs.	vs.	ADP
cana-5314	65	4	np	np	PRON
cana-5314	65	5	question	question	NOUN
cana-5314	65	6	leads	lead	VERB
cana-5314	65	7	theoretical	theoretical	ADJ
cana-5314	65	8	cryptography	cryptography	NOUN
cana-5314	65	9	to	to	PART
cana-5314	65	10	experience	experience	VERB
cana-5314	65	11	important	important	ADJ
cana-5314	65	12	developments	development	NOUN
cana-5314	65	13	.	.	PUNCT
cana-5314	66	1	the	the	DET
cana-5314	66	2	security	security	NOUN
cana-5314	66	3	of	of	ADP
cana-5314	66	4	many	many	ADJ
cana-5314	66	5	encryption	encryption	NOUN
cana-5314	66	6	systems	system	NOUN
cana-5314	66	7	depends	depend	VERB
cana-5314	66	8	on	on	ADP
cana-5314	66	9	hard	hard	ADJ
cana-5314	66	10	problems	problem	NOUN
cana-5314	66	11	that	that	PRON
cana-5314	66	12	need	need	VERB
cana-5314	66	13	polynomial	polynomial	ADJ
cana-5314	66	14	time	time	NOUN
cana-5314	66	15	resolution	resolution	NOUN
cana-5314	66	16	to	to	PART
cana-5314	66	17	maintain	maintain	VERB
cana-5314	66	18	their	their	PRON
cana-5314	66	19	strength	strength	NOUN
cana-5314	66	20	after	after	ADP
cana-5314	66	21	validating	validate	VERB
cana-5314	66	22	whether	whether	SCONJ
cana-5314	66	23	p	p	PRON
cana-5314	66	24	equals	equal	VERB
cana-5314	66	25	np	np	INTJ
cana-5314	66	26	.	.	PUNCT
cana-5314	67	1	the	the	DET
cana-5314	67	2	equivalence	equivalence	NOUN
cana-5314	67	3	of	of	ADP
cana-5314	67	4	p	p	NOUN
cana-5314	67	5	and	and	CCONJ
cana-5314	67	6	np	np	PROPN
cana-5314	67	7	would	would	AUX
cana-5314	67	8	degrade	degrade	VERB
cana-5314	67	9	the	the	DET
cana-5314	67	10	security	security	NOUN
cana-5314	67	11	of	of	ADP
cana-5314	67	12	cryptographic	cryptographic	ADJ
cana-5314	67	13	systems	system	NOUN
cana-5314	67	14	thus	thus	ADV
cana-5314	67	15	leading	lead	VERB
cana-5314	67	16	to	to	ADP
cana-5314	67	17	the	the	DET
cana-5314	67	18	need	need	NOUN
cana-5314	67	19	for	for	ADP
cana-5314	67	20	new	new	ADJ
cana-5314	67	21	cryptographic	cryptographic	ADJ
cana-5314	67	22	protocols	protocol	NOUN
cana-5314	67	23	altogether	altogether	ADV
cana-5314	67	24	.	.	PUNCT
cana-5314	68	1	in	in	ADP
cana-5314	68	2	2020	2020	NUM
cana-5314	68	3	n.	n.	PROPN
cana-5314	68	4	almasarwah	almasarwah	PROPN
cana-5314	68	5	et.al	et.al	PROPN
cana-5314	68	6	.	.	PUNCT
cana-5314	69	1	and	and	CCONJ
cana-5314	69	2	g.	g.	PROPN
cana-5314	69	3	a.	a.	PROPN
cana-5314	69	4	süer	süer	PROPN
cana-5314	69	5	et.al	et.al	PROPN
cana-5314	69	6	.	.	PUNCT
cana-5314	69	7	,	,	PUNCT
cana-5314	70	1	[	[	X
cana-5314	70	2	7	7	X
cana-5314	70	3	]	]	PUNCT
cana-5314	70	4	proposed	propose	VERB
cana-5314	70	5	the	the	DET
cana-5314	70	6	research	research	NOUN
cana-5314	70	7	focusing	focus	VERB
cana-5314	70	8	on	on	ADP
cana-5314	70	9	philosophical	philosophical	ADJ
cana-5314	70	10	aspects	aspect	NOUN
cana-5314	70	11	regarding	regard	VERB
cana-5314	70	12	p	p	NOUN
cana-5314	70	13	vs	vs	ADP
cana-5314	70	14	np	np	PRON
cana-5314	70	15	problem	problem	NOUN
cana-5314	70	16	theory	theory	NOUN
cana-5314	70	17	has	have	AUX
cana-5314	70	18	become	become	VERB
cana-5314	70	19	increasingly	increasingly	ADV
cana-5314	70	20	prevalent	prevalent	ADJ
cana-5314	70	21	during	during	ADP
cana-5314	70	22	the	the	DET
cana-5314	70	23	last	last	ADJ
cana-5314	70	24	few	few	ADJ
cana-5314	70	25	years	year	NOUN
cana-5314	70	26	.	.	PUNCT
cana-5314	71	1	numerous	numerous	ADJ
cana-5314	71	2	philosophers	philosopher	NOUN
cana-5314	71	3	along	along	ADP
cana-5314	71	4	with	with	ADP
cana-5314	71	5	theoretical	theoretical	ADJ
cana-5314	71	6	experts	expert	NOUN
cana-5314	71	7	continue	continue	VERB
cana-5314	71	8	to	to	PART
cana-5314	71	9	discuss	discuss	VERB
cana-5314	71	10	whether	whether	SCONJ
cana-5314	71	11	current	current	ADJ
cana-5314	71	12	computational	computational	ADJ
cana-5314	71	13	methods	method	NOUN
cana-5314	71	14	are	be	AUX
cana-5314	71	15	sufficient	sufficient	ADJ
cana-5314	71	16	for	for	ADP
cana-5314	71	17	resolving	resolve	VERB
cana-5314	71	18	this	this	DET
cana-5314	71	19	problem	problem	NOUN
cana-5314	71	20	or	or	CCONJ
cana-5314	71	21	if	if	SCONJ
cana-5314	71	22	an	an	DET
cana-5314	71	23	alternative	alternative	ADJ
cana-5314	71	24	computing	compute	VERB
cana-5314	71	25	approach	approach	NOUN
cana-5314	71	26	must	must	AUX
cana-5314	71	27	be	be	AUX
cana-5314	71	28	developed	develop	VERB
cana-5314	71	29	.	.	PUNCT
cana-5314	72	1	discussions	discussion	NOUN
cana-5314	72	2	explore	explore	VERB
cana-5314	72	3	knowledge	knowledge	NOUN
cana-5314	72	4	definitions	definition	NOUN
cana-5314	72	5	and	and	CCONJ
cana-5314	72	6	human	human	ADJ
cana-5314	72	7	creative	creative	ADJ
cana-5314	72	8	potential	potential	NOUN
cana-5314	72	9	since	since	SCONJ
cana-5314	72	10	they	they	PRON
cana-5314	72	11	involve	involve	VERB
cana-5314	72	12	understanding	understand	VERB
cana-5314	72	13	how	how	SCONJ
cana-5314	72	14	people	people	NOUN
cana-5314	72	15	think	think	VERB
cana-5314	72	16	when	when	SCONJ
cana-5314	72	17	handling	handle	VERB
cana-5314	72	18	complex	complex	ADJ
cana-5314	72	19	brain	brain	NOUN
cana-5314	72	20	or	or	CCONJ
cana-5314	72	21	artificial	artificial	ADJ
cana-5314	72	22	intelligence	intelligence	NOUN
cana-5314	72	23	systems	system	NOUN
cana-5314	72	24	.	.	PUNCT
cana-5314	73	1	quantum	quantum	PROPN
cana-5314	73	2	computing	compute	VERB
cana-5314	73	3	developments	development	NOUN
cana-5314	73	4	represent	represent	VERB
cana-5314	73	5	the	the	DET
cana-5314	73	6	newest	new	ADJ
cana-5314	73	7	addition	addition	NOUN
cana-5314	73	8	to	to	ADP
cana-5314	73	9	p	p	NOUN
cana-5314	73	10	vs.	vs.	ADP
cana-5314	73	11	np	np	DET
cana-5314	73	12	research	research	NOUN
cana-5314	73	13	.	.	PUNCT
cana-5314	74	1	quantum	quantum	PROPN
cana-5314	74	2	computing	computing	NOUN
cana-5314	74	3	technology	technology	NOUN
cana-5314	74	4	demonstrates	demonstrate	VERB
cana-5314	74	5	ability	ability	NOUN
cana-5314	74	6	to	to	PART
cana-5314	74	7	tackle	tackle	VERB
cana-5314	74	8	specific	specific	ADJ
cana-5314	74	9	problems	problem	NOUN
cana-5314	74	10	with	with	ADP
cana-5314	74	11	exponential	exponential	ADJ
cana-5314	74	12	speed	speed	NOUN
cana-5314	74	13	relative	relative	ADJ
cana-5314	74	14	to	to	ADP
cana-5314	74	15	traditional	traditional	ADJ
cana-5314	74	16	computing	computing	NOUN
cana-5314	74	17	systems	system	NOUN
cana-5314	74	18	thus	thus	ADV
cana-5314	74	19	creating	create	VERB
cana-5314	74	20	new	new	ADJ
cana-5314	74	21	perspectives	perspective	NOUN
cana-5314	74	22	regarding	regard	VERB
cana-5314	74	23	p	p	NOUN
cana-5314	74	24	vs.	vs.	ADP
cana-5314	74	25	np	np	PRON
cana-5314	74	26	problem	problem	NOUN
cana-5314	74	27	resolution	resolution	NOUN
cana-5314	74	28	.	.	PUNCT
cana-5314	75	1	research	research	NOUN
cana-5314	75	2	on	on	ADP
cana-5314	75	3	quantum	quantum	NOUN
cana-5314	75	4	computing	computing	NOUN
cana-5314	75	5	continues	continue	VERB
cana-5314	75	6	to	to	PART
cana-5314	75	7	establish	establish	VERB
cana-5314	75	8	its	its	PRON
cana-5314	75	9	potential	potential	ADJ
cana-5314	75	10	effect	effect	NOUN
cana-5314	75	11	on	on	ADP
cana-5314	75	12	computational	computational	ADJ
cana-5314	75	13	complexity	complexity	NOUN
cana-5314	75	14	which	which	PRON
cana-5314	75	15	could	could	AUX
cana-5314	75	16	create	create	VERB
cana-5314	75	17	either	either	CCONJ
cana-5314	75	18	enhanced	enhanced	ADJ
cana-5314	75	19	or	or	CCONJ
cana-5314	75	20	barriers	barrier	NOUN
cana-5314	75	21	in	in	ADP
cana-5314	75	22	the	the	DET
cana-5314	75	23	understanding	understanding	NOUN
cana-5314	75	24	of	of	ADP
cana-5314	75	25	p	p	PROPN
cana-5314	75	26	and	and	CCONJ
cana-5314	75	27	np	np	INTJ
cana-5314	75	28	.	.	PUNCT
cana-5314	75	29	communications	communication	NOUN
cana-5314	75	30	on	on	ADP
cana-5314	75	31	applied	apply	VERB
cana-5314	75	32	nonlinear	nonlinear	ADJ
cana-5314	75	33	analysis	analysis	NOUN
cana-5314	75	34	issn	issn	NOUN
cana-5314	75	35	:	:	PUNCT
cana-5314	75	36	1074	1074	NUM
cana-5314	75	37	-	-	PUNCT
cana-5314	75	38	133x	133x	NUM
cana-5314	75	39	vol	vol	NOUN
cana-5314	75	40	31	31	NUM
cana-5314	75	41	no	no	NOUN
cana-5314	75	42	.	.	PUNCT
cana-5314	76	1	8s	8s	PROPN
cana-5314	76	2	(	(	PUNCT
cana-5314	76	3	2024	2024	NUM
cana-5314	76	4	)	)	PUNCT
cana-5314	76	5	949	949	NUM
cana-5314	76	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5314	77	1	these	these	DET
cana-5314	77	2	areas	area	NOUN
cana-5314	77	3	of	of	ADP
cana-5314	77	4	research	research	NOUN
cana-5314	77	5	collectively	collectively	ADV
cana-5314	77	6	expand	expand	VERB
cana-5314	77	7	understanding	understanding	NOUN
cana-5314	77	8	about	about	ADP
cana-5314	77	9	the	the	DET
cana-5314	77	10	p	p	NOUN
cana-5314	77	11	versus	versus	ADP
cana-5314	77	12	np	np	ADP
cana-5314	77	13	problem	problem	NOUN
cana-5314	77	14	by	by	ADP
cana-5314	77	15	demonstrating	demonstrate	VERB
cana-5314	77	16	both	both	CCONJ
cana-5314	77	17	the	the	DET
cana-5314	77	18	complications	complication	NOUN
cana-5314	77	19	and	and	CCONJ
cana-5314	77	20	solutions	solution	NOUN
cana-5314	77	21	which	which	PRON
cana-5314	77	22	could	could	AUX
cana-5314	77	23	transform	transform	VERB
cana-5314	77	24	both	both	DET
cana-5314	77	25	computer	computer	NOUN
cana-5314	77	26	science	science	NOUN
cana-5314	77	27	and	and	CCONJ
cana-5314	77	28	numerous	numerous	ADJ
cana-5314	77	29	practical	practical	ADJ
cana-5314	77	30	fields	field	NOUN
cana-5314	77	31	that	that	PRON
cana-5314	77	32	require	require	VERB
cana-5314	77	33	speedy	speedy	ADJ
cana-5314	77	34	digital	digital	ADJ
cana-5314	77	35	processing	processing	NOUN
cana-5314	77	36	.	.	PUNCT
cana-5314	78	1	iii	iii	PROPN
cana-5314	78	2	.	.	PROPN
cana-5314	78	3	proposed	propose	VERB
cana-5314	78	4	methodology	methodology	NOUN
cana-5314	78	5	computational	computational	ADJ
cana-5314	78	6	complexity	complexity	NOUN
cana-5314	78	7	theory	theory	NOUN
cana-5314	78	8	deals	deal	VERB
cana-5314	78	9	with	with	ADP
cana-5314	78	10	the	the	DET
cana-5314	78	11	fundamental	fundamental	ADJ
cana-5314	78	12	challenge	challenge	NOUN
cana-5314	78	13	presented	present	VERB
cana-5314	78	14	by	by	ADP
cana-5314	78	15	p	p	PROPN
cana-5314	78	16	versus	versus	ADP
cana-5314	78	17	np	np	PRON
cana-5314	78	18	problem	problem	NOUN
cana-5314	78	19	.	.	PUNCT
cana-5314	79	1	the	the	DET
cana-5314	79	2	proposed	propose	VERB
cana-5314	79	3	paper	paper	NOUN
cana-5314	79	4	introduces	introduce	VERB
cana-5314	79	5	a	a	DET
cana-5314	79	6	new	new	ADJ
cana-5314	79	7	method	method	NOUN
cana-5314	79	8	to	to	PART
cana-5314	79	9	investigate	investigate	VERB
cana-5314	79	10	the	the	DET
cana-5314	79	11	problem	problem	NOUN
cana-5314	79	12	through	through	ADP
cana-5314	79	13	different	different	ADJ
cana-5314	79	14	computational	computational	ADJ
cana-5314	79	15	algorithms	algorithm	NOUN
cana-5314	79	16	and	and	CCONJ
cana-5314	79	17	theoretical	theoretical	ADJ
cana-5314	79	18	analysis	analysis	NOUN
cana-5314	79	19	of	of	ADP
cana-5314	79	20	models	model	NOUN
cana-5314	79	21	along	along	ADP
cana-5314	79	22	with	with	ADP
cana-5314	79	23	algorithmic	algorithmic	ADJ
cana-5314	79	24	strategies	strategy	NOUN
cana-5314	79	25	.	.	PUNCT
cana-5314	80	1	the	the	DET
cana-5314	80	2	methodology	methodology	NOUN
cana-5314	80	3	uses	use	VERB
cana-5314	80	4	theoretical	theoretical	ADJ
cana-5314	80	5	examinations	examination	NOUN
cana-5314	80	6	which	which	PRON
cana-5314	80	7	are	be	AUX
cana-5314	80	8	combined	combine	VERB
cana-5314	80	9	with	with	ADP
cana-5314	80	10	experimental	experimental	ADJ
cana-5314	80	11	tests	test	NOUN
cana-5314	80	12	to	to	PART
cana-5314	80	13	research	research	VERB
cana-5314	80	14	the	the	DET
cana-5314	80	15	relationship	relationship	NOUN
cana-5314	80	16	possibilities	possibility	NOUN
cana-5314	80	17	between	between	ADP
cana-5314	80	18	p	p	PROPN
cana-5314	80	19	and	and	CCONJ
cana-5314	80	20	np	np	INTJ
cana-5314	80	21	.	.	PUNCT
cana-5314	81	1	the	the	DET
cana-5314	81	2	goal	goal	NOUN
cana-5314	81	3	consists	consist	VERB
cana-5314	81	4	of	of	ADP
cana-5314	81	5	establishing	establish	VERB
cana-5314	81	6	whether	whether	SCONJ
cana-5314	81	7	p	p	PROPN
cana-5314	81	8	and	and	CCONJ
cana-5314	81	9	np	np	INTJ
cana-5314	81	10	are	be	AUX
cana-5314	81	11	equivalent	equivalent	ADJ
cana-5314	81	12	powers	power	NOUN
cana-5314	81	13	and	and	CCONJ
cana-5314	81	14	exploring	explore	VERB
cana-5314	81	15	practical	practical	ADJ
cana-5314	81	16	effects	effect	NOUN
cana-5314	81	17	on	on	ADP
cana-5314	81	18	current	current	ADJ
cana-5314	81	19	computational	computational	ADJ
cana-5314	81	20	systems	system	NOUN
cana-5314	81	21	[	[	X
cana-5314	81	22	4	4	NUM
cana-5314	81	23	]	]	PUNCT
cana-5314	81	24	.	.	PUNCT
cana-5314	82	1	the	the	DET
cana-5314	82	2	reduction	reduction	NOUN
cana-5314	82	3	method	method	NOUN
cana-5314	82	4	demonstrates	demonstrate	VERB
cana-5314	82	5	the	the	DET
cana-5314	82	6	creation	creation	NOUN
cana-5314	82	7	of	of	ADP
cana-5314	82	8	links	link	NOUN
cana-5314	82	9	between	between	ADP
cana-5314	82	10	two	two	NUM
cana-5314	82	11	problems	problem	NOUN
cana-5314	82	12	so	so	SCONJ
cana-5314	82	13	that	that	SCONJ
cana-5314	82	14	tackling	tackle	VERB
cana-5314	82	15	the	the	DET
cana-5314	82	16	first	first	ADJ
cana-5314	82	17	could	could	AUX
cana-5314	82	18	generate	generate	VERB
cana-5314	82	19	solutions	solution	NOUN
cana-5314	82	20	to	to	ADP
cana-5314	82	21	the	the	DET
cana-5314	82	22	second	second	ADJ
cana-5314	82	23	within	within	ADP
cana-5314	82	24	polynomial	polynomial	ADJ
cana-5314	82	25	time	time	NOUN
cana-5314	82	26	.	.	PUNCT
cana-5314	83	1	establishing	establish	VERB
cana-5314	83	2	these	these	DET
cana-5314	83	3	reductions	reduction	NOUN
cana-5314	83	4	enables	enable	VERB
cana-5314	83	5	us	we	PRON
cana-5314	83	6	to	to	PART
cana-5314	83	7	understand	understand	VERB
cana-5314	83	8	np	np	ADJ
cana-5314	83	9	-	-	PUNCT
cana-5314	83	10	complete	complete	ADJ
cana-5314	83	11	problems	problem	NOUN
cana-5314	83	12	better	well	ADV
cana-5314	83	13	and	and	CCONJ
cana-5314	83	14	determine	determine	VERB
cana-5314	83	15	their	their	PRON
cana-5314	83	16	relationship	relationship	NOUN
cana-5314	83	17	to	to	ADP
cana-5314	83	18	p.	p.	NOUN
cana-5314	83	19	the	the	DET
cana-5314	83	20	focus	focus	NOUN
cana-5314	83	21	of	of	ADP
cana-5314	83	22	our	our	PRON
cana-5314	83	23	investigation	investigation	NOUN
cana-5314	83	24	involves	involve	VERB
cana-5314	83	25	determining	determine	VERB
cana-5314	83	26	if	if	SCONJ
cana-5314	83	27	boolean	boolean	ADJ
cana-5314	83	28	satisfiability	satisfiability	NOUN
cana-5314	83	29	(	(	PUNCT
cana-5314	83	30	sat	sit	VERB
cana-5314	83	31	)	)	PUNCT
cana-5314	83	32	can	can	AUX
cana-5314	83	33	be	be	AUX
cana-5314	83	34	solved	solve	VERB
cana-5314	83	35	within	within	ADP
cana-5314	83	36	polynomial	polynomial	ADJ
cana-5314	83	37	time	time	NOUN
cana-5314	83	38	.	.	PUNCT
cana-5314	84	1	when	when	SCONJ
cana-5314	84	2	sat	sit	VERB
cana-5314	84	3	demonstrates	demonstrate	VERB
cana-5314	84	4	reducibility	reducibility	NOUN
cana-5314	84	5	to	to	ADP
cana-5314	84	6	a	a	DET
cana-5314	84	7	problem	problem	NOUN
cana-5314	84	8	which	which	PRON
cana-5314	84	9	has	have	VERB
cana-5314	84	10	polynomial	polynomial	ADJ
cana-5314	84	11	-	-	PUNCT
cana-5314	84	12	time	time	NOUN
cana-5314	84	13	solvability	solvability	NOUN
cana-5314	84	14	it	it	PRON
cana-5314	84	15	necessarily	necessarily	ADV
cana-5314	84	16	confirms	confirm	VERB
cana-5314	84	17	p	p	X
cana-5314	84	18	=	=	NOUN
cana-5314	84	19	np	np	NOUN
cana-5314	84	20	.	.	PUNCT
cana-5314	85	1	first	first	ADV
cana-5314	85	2	we	we	PRON
cana-5314	85	3	analyze	analyze	VERB
cana-5314	85	4	how	how	SCONJ
cana-5314	85	5	np	np	ADJ
cana-5314	85	6	-	-	PUNCT
cana-5314	85	7	complete	complete	ADJ
cana-5314	85	8	problems	problem	NOUN
cana-5314	85	9	are	be	AUX
cana-5314	85	10	constructed	construct	VERB
cana-5314	86	1	but	but	CCONJ
cana-5314	86	2	then	then	ADV
cana-5314	86	3	we	we	PRON
cana-5314	86	4	explore	explore	VERB
cana-5314	86	5	whether	whether	SCONJ
cana-5314	86	6	a	a	DET
cana-5314	86	7	polynomial	polynomial	ADJ
cana-5314	86	8	-	-	PUNCT
cana-5314	86	9	time	time	NOUN
cana-5314	86	10	algorithm	algorithm	NOUN
cana-5314	86	11	exists	exist	VERB
cana-5314	86	12	for	for	ADP
cana-5314	86	13	solving	solve	VERB
cana-5314	86	14	these	these	DET
cana-5314	86	15	problems	problem	NOUN
cana-5314	86	16	.	.	PUNCT
cana-5314	87	1	the	the	DET
cana-5314	87	2	proposed	propose	VERB
cana-5314	87	3	algorithm	algorithm	NOUN
cana-5314	87	4	for	for	ADP
cana-5314	87	5	any	any	DET
cana-5314	87	6	np	np	NOUN
cana-5314	87	7	-	-	PUNCT
cana-5314	87	8	complete	complete	ADJ
cana-5314	87	9	problem	problem	NOUN
cana-5314	87	10	can	can	AUX
cana-5314	87	11	serve	serve	VERB
cana-5314	87	12	other	other	ADJ
cana-5314	87	13	np	np	ADP
cana-5314	87	14	problems	problem	NOUN
cana-5314	87	15	because	because	SCONJ
cana-5314	87	16	reduction	reduction	NOUN
cana-5314	87	17	properties	property	NOUN
cana-5314	87	18	maintain	maintain	VERB
cana-5314	87	19	transitivity	transitivity	NOUN
cana-5314	87	20	.	.	PUNCT
cana-5314	88	1	the	the	DET
cana-5314	88	2	systematic	systematic	ADJ
cana-5314	88	3	method	method	NOUN
cana-5314	88	4	establishes	establish	VERB
cana-5314	88	5	procedures	procedure	NOUN
cana-5314	88	6	for	for	ADP
cana-5314	88	7	building	build	VERB
cana-5314	88	8	verification	verification	NOUN
cana-5314	88	9	algorithms	algorithm	NOUN
cana-5314	88	10	which	which	PRON
cana-5314	88	11	check	check	VERB
cana-5314	88	12	solutions	solution	NOUN
cana-5314	88	13	efficiently	efficiently	ADV
cana-5314	88	14	while	while	SCONJ
cana-5314	88	15	investigating	investigate	VERB
cana-5314	88	16	polynomial	polynomial	ADJ
cana-5314	88	17	-	-	PUNCT
cana-5314	88	18	time	time	NOUN
cana-5314	88	19	solutions	solution	NOUN
cana-5314	88	20	for	for	ADP
cana-5314	88	21	np	np	NOUN
cana-5314	88	22	-	-	PUNCT
cana-5314	88	23	complete	complete	ADJ
cana-5314	88	24	problems	problem	NOUN
cana-5314	88	25	[	[	X
cana-5314	88	26	5	5	NUM
cana-5314	88	27	]	]	PUNCT
cana-5314	88	28	.	.	PUNCT
cana-5314	89	1	the	the	DET
cana-5314	89	2	proposed	propose	VERB
cana-5314	89	3	method	method	NOUN
cana-5314	89	4	requires	require	VERB
cana-5314	89	5	these	these	DET
cana-5314	89	6	mathematical	mathematical	ADJ
cana-5314	89	7	expressions	expression	NOUN
cana-5314	89	8	to	to	PART
cana-5314	89	9	work	work	VERB
cana-5314	89	10	.	.	PUNCT
cana-5314	90	1	the	the	DET
cana-5314	90	2	equations	equation	NOUN
cana-5314	90	3	present	present	VERB
cana-5314	90	4	multiple	multiple	ADJ
cana-5314	90	5	computational	computational	ADJ
cana-5314	90	6	models	model	NOUN
cana-5314	90	7	that	that	PRON
cana-5314	90	8	serve	serve	VERB
cana-5314	90	9	as	as	ADP
cana-5314	90	10	both	both	DET
cana-5314	90	11	decision	decision	NOUN
cana-5314	90	12	functions	function	NOUN
cana-5314	90	13	and	and	CCONJ
cana-5314	90	14	to	to	PART
cana-5314	90	15	confirm	confirm	VERB
cana-5314	90	16	complex	complex	ADJ
cana-5314	90	17	problem	problem	NOUN
cana-5314	90	18	verification	verification	NOUN
cana-5314	90	19	through	through	ADP
cana-5314	90	20	reductions	reduction	NOUN
cana-5314	90	21	.	.	PUNCT
cana-5314	91	1	in	in	ADP
cana-5314	91	2	this	this	DET
cana-5314	91	3	workplace	workplace	NOUN
cana-5314	91	4	we	we	PRON
cana-5314	91	5	first	first	ADV
cana-5314	91	6	establish	establish	VERB
cana-5314	91	7	decision	decision	NOUN
cana-5314	91	8	problems	problem	NOUN
cana-5314	91	9	as	as	ADP
cana-5314	91	10	tasks	task	NOUN
cana-5314	91	11	that	that	PRON
cana-5314	91	12	need	need	VERB
cana-5314	91	13	to	to	PART
cana-5314	91	14	verify	verify	VERB
cana-5314	91	15	if	if	SCONJ
cana-5314	91	16	solutions	solution	NOUN
cana-5314	91	17	exist	exist	VERB
cana-5314	91	18	inside	inside	ADP
cana-5314	91	19	specific	specific	ADJ
cana-5314	91	20	computational	computational	ADJ
cana-5314	91	21	models	model	NOUN
cana-5314	91	22	.	.	PUNCT
cana-5314	92	1	the	the	DET
cana-5314	92	2	decision	decision	NOUN
cana-5314	92	3	problem	problem	NOUN
cana-5314	92	4	x	x	PUNCT
cana-5314	92	5	contains	contain	VERB
cana-5314	92	6	its	its	PRON
cana-5314	92	7	solution	solution	NOUN
cana-5314	92	8	space	space	NOUN
cana-5314	92	9	defined	define	VERB
cana-5314	92	10	as	as	ADP
cana-5314	92	11	s	s	PROPN
cana-5314	92	12	,	,	PUNCT
cana-5314	92	13	where	where	SCONJ
cana-5314	92	14	:	:	PUNCT
cana-5314	92	15	𝑆	𝑆	PROPN
cana-5314	92	16	=	=	SYM
cana-5314	92	17	{	{	PUNCT
cana-5314	92	18	𝑥	𝑥	PROPN
cana-5314	92	19	∣	∣	ADJ
cana-5314	92	20	𝑓(𝑥	𝑓(𝑥	NOUN
cana-5314	92	21	)	)	PUNCT
cana-5314	92	22	=	=	SYM
cana-5314	92	23	1	1	X
cana-5314	92	24	}	}	PUNCT
cana-5314	92	25	here	here	ADV
cana-5314	92	26	,	,	PUNCT
cana-5314	92	27	𝑓(𝑥	𝑓(𝑥	NOUN
cana-5314	92	28	)	)	PUNCT
cana-5314	92	29	is	be	AUX
cana-5314	92	30	the	the	DET
cana-5314	92	31	decision	decision	NOUN
cana-5314	92	32	function	function	NOUN
cana-5314	92	33	for	for	ADP
cana-5314	92	34	the	the	DET
cana-5314	92	35	problem	problem	NOUN
cana-5314	92	36	𝑋	𝑋	PROPN
cana-5314	92	37	,	,	PUNCT
cana-5314	92	38	returning	return	VERB
cana-5314	92	39	a	a	DET
cana-5314	92	40	binary	binary	ADJ
cana-5314	92	41	outcome	outcome	NOUN
cana-5314	92	42	.	.	PUNCT
cana-5314	93	1	for	for	ADP
cana-5314	93	2	a	a	DET
cana-5314	93	3	problem	problem	NOUN
cana-5314	93	4	in	in	ADP
cana-5314	93	5	𝑁𝑃	𝑁𝑃	PROPN
cana-5314	93	6	,	,	PUNCT
cana-5314	93	7	the	the	DET
cana-5314	93	8	function	function	NOUN
cana-5314	93	9	𝑓(𝑥	𝑓(𝑥	NOUN
cana-5314	93	10	)	)	PUNCT
cana-5314	93	11	must	must	AUX
cana-5314	93	12	be	be	AUX
cana-5314	93	13	verifiable	verifiable	ADJ
cana-5314	93	14	in	in	ADP
cana-5314	93	15	polynomial	polynomial	ADJ
cana-5314	93	16	time	time	NOUN
cana-5314	93	17	.	.	PUNCT
cana-5314	94	1	in	in	ADP
cana-5314	94	2	order	order	NOUN
cana-5314	94	3	to	to	PART
cana-5314	94	4	model	model	VERB
cana-5314	94	5	reduction	reduction	NOUN
cana-5314	94	6	between	between	ADP
cana-5314	94	7	problems	problem	NOUN
cana-5314	94	8	,	,	PUNCT
cana-5314	94	9	we	we	PRON
cana-5314	94	10	use	use	VERB
cana-5314	94	11	the	the	DET
cana-5314	94	12	concept	concept	NOUN
cana-5314	94	13	of	of	ADP
cana-5314	94	14	polynomial	polynomial	ADJ
cana-5314	94	15	-	-	PUNCT
cana-5314	94	16	time	time	NOUN
cana-5314	94	17	transformations	transformation	NOUN
cana-5314	94	18	.	.	PUNCT
cana-5314	95	1	let	let	VERB
cana-5314	95	2	𝐴	𝐴	PROPN
cana-5314	95	3	be	be	AUX
cana-5314	95	4	a	a	DET
cana-5314	95	5	problem	problem	NOUN
cana-5314	95	6	in	in	ADP
cana-5314	95	7	np	np	INTJ
cana-5314	95	8	and	and	CCONJ
cana-5314	95	9	𝐵	𝐵	PRON
cana-5314	95	10	a	a	DET
cana-5314	95	11	problem	problem	NOUN
cana-5314	95	12	in	in	ADP
cana-5314	95	13	p.	p.	NOUN
cana-5314	95	14	a	a	DET
cana-5314	95	15	reduction	reduction	NOUN
cana-5314	95	16	from	from	ADP
cana-5314	95	17	𝐴	𝐴	PROPN
cana-5314	95	18	to	to	ADP
cana-5314	95	19	𝐵	𝐵	PROPN
cana-5314	95	20	can	can	AUX
cana-5314	95	21	be	be	AUX
cana-5314	95	22	defined	define	VERB
cana-5314	95	23	as	as	ADP
cana-5314	95	24	a	a	DET
cana-5314	95	25	function	function	NOUN
cana-5314	95	26	𝑅	𝑅	NOUN
cana-5314	95	27	such	such	ADJ
cana-5314	95	28	that	that	SCONJ
cana-5314	95	29	:	:	PUNCT
cana-5314	95	30	communications	communication	NOUN
cana-5314	95	31	on	on	ADP
cana-5314	95	32	applied	apply	VERB
cana-5314	95	33	nonlinear	nonlinear	ADJ
cana-5314	95	34	analysis	analysis	NOUN
cana-5314	95	35	issn	issn	NOUN
cana-5314	95	36	:	:	PUNCT
cana-5314	95	37	1074	1074	NUM
cana-5314	95	38	-	-	PUNCT
cana-5314	95	39	133x	133x	NUM
cana-5314	95	40	vol	vol	NOUN
cana-5314	95	41	31	31	NUM
cana-5314	95	42	no	no	NOUN
cana-5314	95	43	.	.	PUNCT
cana-5314	96	1	8s	8s	PROPN
cana-5314	96	2	(	(	PUNCT
cana-5314	96	3	2024	2024	NUM
cana-5314	96	4	)	)	PUNCT
cana-5314	96	5	950	950	NUM
cana-5314	96	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5314	96	7	𝐴(𝑥	𝐴(𝑥	NOUN
cana-5314	96	8	)	)	PUNCT
cana-5314	96	9	≤𝑃	≤𝑃	NOUN
cana-5314	96	10	𝐵(𝑅(𝑥	𝐵(𝑅(𝑥	NOUN
cana-5314	96	11	)	)	PUNCT
cana-5314	96	12	)	)	PUNCT
cana-5314	96	13	where	where	SCONJ
cana-5314	96	14	≤𝑃	≤𝑃	NOUN
cana-5314	96	15	represents	represent	VERB
cana-5314	96	16	polynomial	polynomial	ADJ
cana-5314	96	17	-	-	PUNCT
cana-5314	96	18	time	time	NOUN
cana-5314	96	19	reducibility	reducibility	NOUN
cana-5314	96	20	.	.	PUNCT
cana-5314	97	1	if	if	SCONJ
cana-5314	97	2	𝐴	𝐴	PROPN
cana-5314	97	3	can	can	AUX
cana-5314	97	4	be	be	AUX
cana-5314	97	5	reduced	reduce	VERB
cana-5314	97	6	to	to	ADP
cana-5314	97	7	𝐵	𝐵	PROPN
cana-5314	97	8	in	in	ADP
cana-5314	97	9	polynomial	polynomial	ADJ
cana-5314	97	10	time	time	NOUN
cana-5314	97	11	,	,	PUNCT
cana-5314	97	12	solving	solve	VERB
cana-5314	97	13	𝐴	𝐴	PROPN
cana-5314	97	14	becomes	become	VERB
cana-5314	97	15	equivalent	equivalent	ADJ
cana-5314	97	16	to	to	ADP
cana-5314	97	17	solving	solve	VERB
cana-5314	97	18	𝐵.	𝐵.	PROPN
cana-5314	97	19	next	next	ADV
cana-5314	97	20	,	,	PUNCT
cana-5314	97	21	we	we	PRON
cana-5314	97	22	define	define	VERB
cana-5314	97	23	polynomial	polynomial	ADJ
cana-5314	97	24	-	-	PUNCT
cana-5314	97	25	time	time	NOUN
cana-5314	97	26	algorithms	algorithm	NOUN
cana-5314	97	27	that	that	PRON
cana-5314	97	28	verify	verify	VERB
cana-5314	97	29	solutions	solution	NOUN
cana-5314	97	30	for	for	ADP
cana-5314	97	31	np	np	NOUN
cana-5314	97	32	problems	problem	NOUN
cana-5314	97	33	.	.	PUNCT
cana-5314	98	1	for	for	ADP
cana-5314	98	2	any	any	DET
cana-5314	98	3	problem	problem	NOUN
cana-5314	98	4	𝑋	𝑋	PROPN
cana-5314	98	5	∈	∈	PROPN
cana-5314	98	6	𝑁𝑃	𝑁𝑃	PROPN
cana-5314	98	7	,	,	PUNCT
cana-5314	98	8	there	there	PRON
cana-5314	98	9	exists	exist	VERB
cana-5314	98	10	a	a	DET
cana-5314	98	11	verification	verification	NOUN
cana-5314	98	12	function	function	NOUN
cana-5314	98	13	𝑉(𝑥	𝑉(𝑥	ADP
cana-5314	98	14	,	,	PUNCT
cana-5314	98	15	𝑦	𝑦	NOUN
cana-5314	98	16	)	)	PUNCT
cana-5314	98	17	where	where	SCONJ
cana-5314	98	18	𝑦	𝑦	NOUN
cana-5314	98	19	is	be	AUX
cana-5314	98	20	a	a	DET
cana-5314	98	21	proposed	propose	VERB
cana-5314	98	22	solution	solution	NOUN
cana-5314	98	23	and	and	CCONJ
cana-5314	98	24	𝑉(𝑥	𝑉(𝑥	PROPN
cana-5314	98	25	,	,	PUNCT
cana-5314	98	26	𝑦	𝑦	NOUN
cana-5314	98	27	)	)	PUNCT
cana-5314	98	28	checks	check	VERB
cana-5314	98	29	whether	whether	SCONJ
cana-5314	98	30	𝒚	𝒚	PROPN
cana-5314	98	31	satisfies	satisfy	VERB
cana-5314	98	32	the	the	DET
cana-5314	98	33	conditions	condition	NOUN
cana-5314	98	34	of	of	ADP
cana-5314	98	35	𝑋.	𝑋.	PROPN
cana-5314	98	36	the	the	DET
cana-5314	98	37	time	time	NOUN
cana-5314	98	38	complexity	complexity	NOUN
cana-5314	98	39	of	of	ADP
cana-5314	98	40	the	the	DET
cana-5314	98	41	verification	verification	NOUN
cana-5314	98	42	function	function	NOUN
cana-5314	98	43	is	be	AUX
cana-5314	98	44	denoted	denote	VERB
cana-5314	98	45	as	as	ADP
cana-5314	98	46	:	:	PUNCT
cana-5314	98	47	𝑇𝑉(𝑛	𝑇𝑉(𝑛	ADV
cana-5314	98	48	)	)	PUNCT
cana-5314	99	1	=	=	SYM
cana-5314	99	2	𝑂(𝑛𝑘	𝑂(𝑛𝑘	NOUN
cana-5314	99	3	)	)	PUNCT
cana-5314	99	4	where	where	SCONJ
cana-5314	99	5	𝑘	𝑘	NOUN
cana-5314	99	6	is	be	AUX
cana-5314	99	7	the	the	DET
cana-5314	99	8	degree	degree	NOUN
cana-5314	99	9	of	of	ADP
cana-5314	99	10	the	the	DET
cana-5314	99	11	polynomial	polynomial	NOUN
cana-5314	99	12	.	.	PUNCT
cana-5314	100	1	this	this	DET
cana-5314	100	2	polynomial	polynomial	ADJ
cana-5314	100	3	-	-	PUNCT
cana-5314	100	4	time	time	NOUN
cana-5314	100	5	verification	verification	NOUN
cana-5314	100	6	is	be	AUX
cana-5314	100	7	a	a	DET
cana-5314	100	8	key	key	ADJ
cana-5314	100	9	characteristic	characteristic	NOUN
cana-5314	100	10	of	of	ADP
cana-5314	100	11	np	np	ADP
cana-5314	100	12	problems	problem	NOUN
cana-5314	100	13	.	.	PUNCT
cana-5314	101	1	consider	consider	VERB
cana-5314	101	2	the	the	DET
cana-5314	101	3	boolean	boolean	ADJ
cana-5314	101	4	satisfiability	satisfiability	NOUN
cana-5314	101	5	problem	problem	NOUN
cana-5314	101	6	(	(	PUNCT
cana-5314	101	7	sat	sit	VERB
cana-5314	101	8	)	)	PUNCT
cana-5314	101	9	.	.	PUNCT
cana-5314	102	1	the	the	DET
cana-5314	102	2	boolean	boolean	ADJ
cana-5314	102	3	formula	formula	NOUN
cana-5314	102	4	𝜙	𝜙	NOUN
cana-5314	102	5	in	in	ADP
cana-5314	102	6	sat	sit	VERB
cana-5314	102	7	can	can	AUX
cana-5314	102	8	be	be	AUX
cana-5314	102	9	represented	represent	VERB
cana-5314	102	10	as	as	ADP
cana-5314	102	11	:	:	PUNCT
cana-5314	102	12	𝜙	𝜙	X
cana-5314	102	13	=	=	SYM
cana-5314	102	14	(	(	PUNCT
cana-5314	102	15	𝑥1	𝑥1	NOUN
cana-5314	102	16	∨	∨	NOUN
cana-5314	102	17	𝑥2	𝑥2	PROPN
cana-5314	102	18	∨	∨	NUM
cana-5314	102	19	⋯∨	⋯∨	NOUN
cana-5314	102	20	𝑥𝑛	𝑥𝑛	PROPN
cana-5314	102	21	)	)	PUNCT
cana-5314	102	22	where	where	SCONJ
cana-5314	102	23	v	v	NOUN
cana-5314	102	24	represents	represent	VERB
cana-5314	102	25	the	the	DET
cana-5314	102	26	logical	logical	ADJ
cana-5314	102	27	or	or	CCONJ
cana-5314	102	28	operation	operation	NOUN
cana-5314	102	29	,	,	PUNCT
cana-5314	102	30	and	and	CCONJ
cana-5314	102	31	𝑥𝑖	𝑥𝑖	PROPN
cana-5314	102	32	are	be	AUX
cana-5314	102	33	boolean	boolean	ADJ
cana-5314	102	34	variables	variable	NOUN
cana-5314	102	35	.	.	PUNCT
cana-5314	103	1	a	a	DET
cana-5314	103	2	solution	solution	NOUN
cana-5314	103	3	𝛼	𝛼	NOUN
cana-5314	103	4	is	be	AUX
cana-5314	103	5	a	a	DET
cana-5314	103	6	truth	truth	NOUN
cana-5314	103	7	assignment	assignment	NOUN
cana-5314	103	8	to	to	ADP
cana-5314	103	9	the	the	DET
cana-5314	103	10	variables	variables	PROPN
cana-5314	103	11	𝑥1	𝑥1	PROPN
cana-5314	103	12	,	,	PUNCT
cana-5314	103	13	𝑥2	𝑥2	NOUN
cana-5314	103	14	,	,	PUNCT
cana-5314	103	15	…	…	PUNCT
cana-5314	103	16	,	,	PUNCT
cana-5314	103	17	𝑥𝑛	𝑥𝑛	PROPN
cana-5314	103	18	,	,	PUNCT
cana-5314	103	19	and	and	CCONJ
cana-5314	103	20	we	we	PRON
cana-5314	103	21	want	want	VERB
cana-5314	103	22	to	to	PART
cana-5314	103	23	check	check	VERB
cana-5314	103	24	whether	whether	SCONJ
cana-5314	103	25	there	there	PRON
cana-5314	103	26	exists	exist	VERB
cana-5314	103	27	an	an	DET
cana-5314	103	28	assignment	assignment	NOUN
cana-5314	103	29	such	such	ADJ
cana-5314	103	30	that	that	SCONJ
cana-5314	103	31	𝜙	𝜙	PROPN
cana-5314	103	32	evaluates	evaluate	VERB
cana-5314	103	33	to	to	ADP
cana-5314	103	34	true	true	ADJ
cana-5314	103	35	.	.	PUNCT
cana-5314	104	1	the	the	DET
cana-5314	104	2	problem	problem	NOUN
cana-5314	104	3	is	be	AUX
cana-5314	104	4	np	np	NOUN
cana-5314	104	5	-	-	PUNCT
cana-5314	104	6	complete	complete	ADJ
cana-5314	104	7	,	,	PUNCT
cana-5314	104	8	and	and	CCONJ
cana-5314	104	9	if	if	SCONJ
cana-5314	104	10	sat	sit	VERB
cana-5314	104	11	can	can	AUX
cana-5314	104	12	be	be	AUX
cana-5314	104	13	solved	solve	VERB
cana-5314	104	14	in	in	ADP
cana-5314	104	15	polynomial	polynomial	ADJ
cana-5314	104	16	time	time	NOUN
cana-5314	104	17	,	,	PUNCT
cana-5314	104	18	then	then	ADV
cana-5314	104	19	all	all	DET
cana-5314	104	20	problems	problem	NOUN
cana-5314	104	21	in	in	ADP
cana-5314	104	22	np	np	INTJ
cana-5314	104	23	can	can	AUX
cana-5314	104	24	also	also	ADV
cana-5314	104	25	be	be	AUX
cana-5314	104	26	solved	solve	VERB
cana-5314	104	27	in	in	ADP
cana-5314	104	28	polynomial	polynomial	ADJ
cana-5314	104	29	time	time	NOUN
cana-5314	104	30	.	.	PUNCT
cana-5314	105	1	to	to	PART
cana-5314	105	2	analyze	analyze	VERB
cana-5314	105	3	the	the	DET
cana-5314	105	4	complexity	complexity	NOUN
cana-5314	105	5	of	of	ADP
cana-5314	105	6	np	np	PROPN
cana-5314	105	7	problems	problem	NOUN
cana-5314	105	8	,	,	PUNCT
cana-5314	105	9	we	we	PRON
cana-5314	105	10	define	define	VERB
cana-5314	105	11	the	the	DET
cana-5314	105	12	complexity	complexity	NOUN
cana-5314	105	13	class	class	NOUN
cana-5314	105	14	of	of	ADP
cana-5314	105	15	a	a	DET
cana-5314	105	16	problem	problem	NOUN
cana-5314	105	17	𝑋	𝑋	NOUN
cana-5314	105	18	as	as	ADP
cana-5314	105	19	:	:	PUNCT
cana-5314	105	20	complexity(𝑋	complexity(𝑋	PROPN
cana-5314	105	21	)	)	PUNCT
cana-5314	106	1	=	=	SYM
cana-5314	106	2	min(𝑇(𝑛	min(𝑇(𝑛	NOUN
cana-5314	106	3	)	)	PUNCT
cana-5314	106	4	∣	∣	NOUN
cana-5314	106	5	∃𝑦	∃𝑦	NOUN
cana-5314	106	6	such	such	ADJ
cana-5314	106	7	that	that	SCONJ
cana-5314	106	8	𝑉(𝑥	𝑉(𝑥	PROPN
cana-5314	106	9	,	,	PUNCT
cana-5314	106	10	𝑦	𝑦	NOUN
cana-5314	106	11	)	)	PUNCT
cana-5314	106	12	runs	run	VERB
cana-5314	106	13	in	in	ADP
cana-5314	106	14	𝑂(𝑛𝑘	𝑂(𝑛𝑘	NOUN
cana-5314	106	15	)	)	PUNCT
cana-5314	106	16	)	)	PUNCT
cana-5314	106	17	where	where	SCONJ
cana-5314	106	18	𝑇(𝑛	𝑇(𝑛	NOUN
cana-5314	106	19	)	)	PUNCT
cana-5314	106	20	represents	represent	VERB
cana-5314	106	21	the	the	DET
cana-5314	106	22	time	time	NOUN
cana-5314	106	23	required	require	VERB
cana-5314	106	24	to	to	PART
cana-5314	106	25	solve	solve	VERB
cana-5314	106	26	the	the	DET
cana-5314	106	27	problem	problem	NOUN
cana-5314	106	28	.	.	PUNCT
cana-5314	107	1	if	if	SCONJ
cana-5314	107	2	complexity(𝑋	complexity(𝑋	NOUN
cana-5314	107	3	)	)	PUNCT
cana-5314	107	4	=	=	SYM
cana-5314	107	5	𝑂(𝑛𝑘	𝑂(𝑛𝑘	NOUN
cana-5314	107	6	)	)	PUNCT
cana-5314	107	7	for	for	ADP
cana-5314	107	8	some	some	DET
cana-5314	107	9	polynomial	polynomial	ADJ
cana-5314	107	10	𝑘	𝑘	NOUN
cana-5314	107	11	,	,	PUNCT
cana-5314	107	12	then	then	ADV
cana-5314	107	13	𝑋	𝑋	PROPN
cana-5314	107	14	belongs	belong	VERB
cana-5314	107	15	to	to	ADP
cana-5314	107	16	np	np	INTJ
cana-5314	107	17	.	.	PUNCT
cana-5314	108	1	we	we	PRON
cana-5314	108	2	also	also	ADV
cana-5314	108	3	explore	explore	VERB
cana-5314	108	4	the	the	DET
cana-5314	108	5	role	role	NOUN
cana-5314	108	6	of	of	ADP
cana-5314	108	7	probabilistic	probabilistic	ADJ
cana-5314	108	8	algorithms	algorithm	NOUN
cana-5314	108	9	in	in	ADP
cana-5314	108	10	solving	solve	VERB
cana-5314	108	11	np	np	ADP
cana-5314	108	12	problems	problem	NOUN
cana-5314	108	13	.	.	PUNCT
cana-5314	109	1	a	a	DET
cana-5314	109	2	probabilistic	probabilistic	ADJ
cana-5314	109	3	turing	ture	VERB
cana-5314	109	4	machine	machine	NOUN
cana-5314	109	5	(	(	PUNCT
cana-5314	109	6	ptm	ptm	NOUN
cana-5314	109	7	)	)	PUNCT
cana-5314	109	8	has	have	VERB
cana-5314	109	9	access	access	NOUN
cana-5314	109	10	to	to	ADP
cana-5314	109	11	random	random	ADJ
cana-5314	109	12	bits	bit	NOUN
cana-5314	109	13	and	and	CCONJ
cana-5314	109	14	operates	operate	VERB
cana-5314	109	15	with	with	ADP
cana-5314	109	16	a	a	DET
cana-5314	109	17	probability	probability	NOUN
cana-5314	109	18	of	of	ADP
cana-5314	109	19	error	error	NOUN
cana-5314	109	20	.	.	PUNCT
cana-5314	110	1	let	let	VERB
cana-5314	110	2	𝑃	𝑃	PRON
cana-5314	110	3	be	be	AUX
cana-5314	110	4	a	a	DET
cana-5314	110	5	probabilistic	probabilistic	ADJ
cana-5314	110	6	algorithm	algorithm	NOUN
cana-5314	110	7	and	and	CCONJ
cana-5314	110	8	𝑋	𝑋	PROPN
cana-5314	110	9	an	an	DET
cana-5314	110	10	np	np	PROPN
cana-5314	110	11	problem	problem	NOUN
cana-5314	110	12	,	,	PUNCT
cana-5314	110	13	where	where	SCONJ
cana-5314	110	14	the	the	DET
cana-5314	110	15	time	time	NOUN
cana-5314	110	16	complexity	complexity	NOUN
cana-5314	110	17	of	of	ADP
cana-5314	110	18	𝑃	𝑃	PROPN
cana-5314	110	19	is	be	AUX
cana-5314	110	20	denoted	denote	VERB
cana-5314	110	21	by	by	ADP
cana-5314	110	22	:	:	PUNCT
cana-5314	110	23	𝑇𝑃(𝑛	𝑇𝑃(𝑛	PROPN
cana-5314	110	24	)	)	PUNCT
cana-5314	111	1	=	=	PUNCT
cana-5314	111	2	𝑂(𝑛𝑘	𝑂(𝑛𝑘	ADP
cana-5314	111	3	⋅	⋅	PROPN
cana-5314	111	4	log⁡	log⁡	X
cana-5314	111	5	𝑛	𝑛	PROPN
cana-5314	111	6	)	)	PUNCT
cana-5314	111	7	this	this	DET
cana-5314	111	8	approach	approach	NOUN
cana-5314	111	9	explores	explore	VERB
cana-5314	111	10	the	the	DET
cana-5314	111	11	possibility	possibility	NOUN
cana-5314	111	12	of	of	ADP
cana-5314	111	13	using	use	VERB
cana-5314	111	14	randomness	randomness	NOUN
cana-5314	111	15	to	to	PART
cana-5314	111	16	solve	solve	VERB
cana-5314	111	17	np	np	PRON
cana-5314	111	18	problems	problem	NOUN
cana-5314	111	19	more	more	ADV
cana-5314	111	20	efficiently	efficiently	ADV
cana-5314	111	21	.	.	PUNCT
cana-5314	112	1	the	the	DET
cana-5314	112	2	relationship	relationship	NOUN
cana-5314	112	3	between	between	ADP
cana-5314	112	4	𝐏	𝐏	PROPN
cana-5314	112	5	and	and	CCONJ
cana-5314	112	6	𝐍𝐏	𝐍𝐏	PROPN
cana-5314	112	7	is	be	AUX
cana-5314	112	8	further	far	ADV
cana-5314	112	9	explored	explore	VERB
cana-5314	112	10	through	through	ADP
cana-5314	112	11	the	the	DET
cana-5314	112	12	circuit	circuit	NOUN
cana-5314	112	13	complexity	complexity	NOUN
cana-5314	112	14	of	of	ADP
cana-5314	112	15	boolean	boolean	ADJ
cana-5314	112	16	functions	function	NOUN
cana-5314	112	17	.	.	PUNCT
cana-5314	113	1	the	the	DET
cana-5314	113	2	circuit	circuit	NOUN
cana-5314	113	3	size	size	NOUN
cana-5314	113	4	of	of	ADP
cana-5314	113	5	a	a	DET
cana-5314	113	6	boolean	boolean	ADJ
cana-5314	113	7	function	function	NOUN
cana-5314	113	8	𝑓	𝑓	PROPN
cana-5314	113	9	is	be	AUX
cana-5314	113	10	defined	define	VERB
cana-5314	113	11	as	as	ADP
cana-5314	113	12	the	the	DET
cana-5314	113	13	smallest	small	ADJ
cana-5314	113	14	number	number	NOUN
cana-5314	113	15	of	of	ADP
cana-5314	113	16	gates	gate	NOUN
cana-5314	113	17	required	require	VERB
cana-5314	113	18	to	to	PART
cana-5314	113	19	compute	compute	VERB
cana-5314	113	20	𝑓	𝑓	PRON
cana-5314	113	21	,	,	PUNCT
cana-5314	113	22	and	and	CCONJ
cana-5314	113	23	is	be	AUX
cana-5314	113	24	given	give	VERB
cana-5314	113	25	by	by	ADP
cana-5314	113	26	:	:	PUNCT
cana-5314	113	27	communications	communication	NOUN
cana-5314	113	28	on	on	ADP
cana-5314	113	29	applied	apply	VERB
cana-5314	113	30	nonlinear	nonlinear	ADJ
cana-5314	113	31	analysis	analysis	NOUN
cana-5314	113	32	issn	issn	NOUN
cana-5314	113	33	:	:	PUNCT
cana-5314	113	34	1074	1074	NUM
cana-5314	113	35	-	-	PUNCT
cana-5314	113	36	133x	133x	NUM
cana-5314	113	37	vol	vol	NOUN
cana-5314	113	38	31	31	NUM
cana-5314	113	39	no	no	NOUN
cana-5314	113	40	.	.	PUNCT
cana-5314	114	1	8s	8s	PROPN
cana-5314	114	2	(	(	PUNCT
cana-5314	114	3	2024	2024	NUM
cana-5314	114	4	)	)	PUNCT
cana-5314	114	5	951	951	NUM
cana-5314	114	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5314	114	7	circuitsize(𝑓	circuitsize(𝑓	NOUN
cana-5314	114	8	)	)	PUNCT
cana-5314	114	9	=	=	SYM
cana-5314	114	10	min	min	NOUN
cana-5314	114	11	(	(	PUNCT
cana-5314	114	12	∑	∑	INTJ
cana-5314	114	13	  	  	SPACE
cana-5314	114	14	𝑛	𝑛	PRON
cana-5314	114	15	𝑖=1	𝑖=1	PROPN
cana-5314	114	16	 	 	SPACE
cana-5314	114	17	𝑔𝑖	𝑔𝑖	PROPN
cana-5314	114	18	∣	∣	ADJ
cana-5314	114	19	𝑔𝑖	𝑔𝑖	NOUN
cana-5314	114	20	∈	∈	NOUN
cana-5314	114	21	gates	gate	NOUN
cana-5314	114	22	used	use	VERB
cana-5314	114	23	in	in	ADP
cana-5314	114	24	the	the	DET
cana-5314	114	25	circuit	circuit	NOUN
cana-5314	114	26	)	)	PUNCT
cana-5314	114	27	by	by	ADP
cana-5314	114	28	analyzing	analyze	VERB
cana-5314	114	29	the	the	DET
cana-5314	114	30	circuit	circuit	NOUN
cana-5314	114	31	complexity	complexity	NOUN
cana-5314	114	32	of	of	ADP
cana-5314	114	33	np	np	NOUN
cana-5314	114	34	-	-	PUNCT
cana-5314	114	35	complete	complete	ADJ
cana-5314	114	36	problems	problem	NOUN
cana-5314	114	37	,	,	PUNCT
cana-5314	114	38	we	we	PRON
cana-5314	114	39	aim	aim	VERB
cana-5314	114	40	to	to	PART
cana-5314	114	41	identify	identify	VERB
cana-5314	114	42	structural	structural	ADJ
cana-5314	114	43	patterns	pattern	NOUN
cana-5314	114	44	that	that	PRON
cana-5314	114	45	may	may	AUX
cana-5314	114	46	lead	lead	VERB
cana-5314	114	47	to	to	ADP
cana-5314	114	48	polynomial	polynomial	ADJ
cana-5314	114	49	-	-	PUNCT
cana-5314	114	50	time	time	NOUN
cana-5314	114	51	algorithms	algorithm	NOUN
cana-5314	114	52	or	or	CCONJ
cana-5314	114	53	further	further	ADJ
cana-5314	114	54	evidence	evidence	NOUN
cana-5314	114	55	of	of	ADP
cana-5314	114	56	the	the	DET
cana-5314	114	57	separation	separation	NOUN
cana-5314	114	58	between	between	ADP
cana-5314	114	59	p	p	PROPN
cana-5314	114	60	and	and	CCONJ
cana-5314	114	61	np	np	INTJ
cana-5314	114	62	.	.	PUNCT
cana-5314	115	1	finally	finally	ADV
cana-5314	115	2	,	,	PUNCT
cana-5314	115	3	the	the	DET
cana-5314	115	4	search	search	NOUN
cana-5314	115	5	space	space	NOUN
cana-5314	115	6	for	for	ADP
cana-5314	115	7	finding	find	VERB
cana-5314	115	8	polynomial	polynomial	ADJ
cana-5314	115	9	-	-	PUNCT
cana-5314	115	10	time	time	NOUN
cana-5314	115	11	solutions	solution	NOUN
cana-5314	115	12	to	to	ADP
cana-5314	115	13	np	np	NOUN
cana-5314	115	14	-	-	PUNCT
cana-5314	115	15	complete	complete	ADJ
cana-5314	115	16	problems	problem	NOUN
cana-5314	115	17	is	be	AUX
cana-5314	115	18	examined	examine	VERB
cana-5314	115	19	using	use	VERB
cana-5314	115	20	dynamic	dynamic	ADJ
cana-5314	115	21	programming	programming	NOUN
cana-5314	115	22	.	.	PUNCT
cana-5314	116	1	given	give	VERB
cana-5314	116	2	a	a	DET
cana-5314	116	3	problem	problem	NOUN
cana-5314	116	4	with	with	ADP
cana-5314	116	5	a	a	DET
cana-5314	116	6	solution	solution	NOUN
cana-5314	116	7	space	space	NOUN
cana-5314	116	8	of	of	ADP
cana-5314	116	9	size	size	NOUN
cana-5314	116	10	2𝑛	2𝑛	NUM
cana-5314	116	11	,	,	PUNCT
cana-5314	116	12	a	a	DET
cana-5314	116	13	dynamic	dynamic	ADJ
cana-5314	116	14	programming	programming	NOUN
cana-5314	116	15	approach	approach	NOUN
cana-5314	116	16	breaks	break	VERB
cana-5314	116	17	down	down	ADP
cana-5314	116	18	the	the	DET
cana-5314	116	19	problem	problem	NOUN
cana-5314	116	20	into	into	ADP
cana-5314	116	21	subproblems	subproblem	NOUN
cana-5314	116	22	with	with	ADP
cana-5314	116	23	overlapping	overlap	VERB
cana-5314	116	24	substructure	substructure	NOUN
cana-5314	116	25	,	,	PUNCT
cana-5314	116	26	reducing	reduce	VERB
cana-5314	116	27	the	the	DET
cana-5314	116	28	overall	overall	ADJ
cana-5314	116	29	complexity	complexity	NOUN
cana-5314	116	30	.	.	PUNCT
cana-5314	117	1	the	the	DET
cana-5314	117	2	dynamic	dynamic	ADJ
cana-5314	117	3	programming	programming	NOUN
cana-5314	117	4	recurrence	recurrence	NOUN
cana-5314	117	5	can	can	AUX
cana-5314	117	6	be	be	AUX
cana-5314	117	7	written	write	VERB
cana-5314	117	8	as	as	ADP
cana-5314	117	9	:	:	PUNCT
cana-5314	117	10	𝑑𝑝(𝑖	𝑑𝑝(𝑖	NUM
cana-5314	117	11	,	,	PUNCT
cana-5314	117	12	𝑗	𝑗	NOUN
cana-5314	117	13	)	)	PUNCT
cana-5314	117	14	=	=	SYM
cana-5314	117	15	min(𝑑𝑝(𝑖	min(𝑑𝑝(𝑖	NOUN
cana-5314	117	16	−	−	NOUN
cana-5314	117	17	1	1	NUM
cana-5314	117	18	,	,	PUNCT
cana-5314	117	19	𝑗	𝑗	NOUN
cana-5314	117	20	)	)	PUNCT
cana-5314	117	21	,	,	PUNCT
cana-5314	117	22	𝑑𝑝(𝑖	𝑑𝑝(𝑖	NUM
cana-5314	117	23	−	−	NOUN
cana-5314	117	24	1	1	NUM
cana-5314	117	25	,	,	PUNCT
cana-5314	117	26	𝑗	𝑗	INTJ
cana-5314	117	27	−	−	PROPN
cana-5314	117	28	1	1	NUM
cana-5314	117	29	)	)	PUNCT
cana-5314	117	30	+	+	NUM
cana-5314	118	1	cost(𝑖	cost(𝑖	NOUN
cana-5314	118	2	)	)	PUNCT
cana-5314	118	3	)	)	PUNCT
cana-5314	118	4	where	where	SCONJ
cana-5314	118	5	𝑑𝑝(𝑖	𝑑𝑝(𝑖	NUM
cana-5314	118	6	,	,	PUNCT
cana-5314	118	7	𝑗	𝑗	NOUN
cana-5314	118	8	)	)	PUNCT
cana-5314	118	9	represents	represent	VERB
cana-5314	118	10	the	the	DET
cana-5314	118	11	minimal	minimal	ADJ
cana-5314	118	12	cost	cost	NOUN
cana-5314	118	13	of	of	ADP
cana-5314	118	14	solving	solve	VERB
cana-5314	118	15	the	the	DET
cana-5314	118	16	problem	problem	NOUN
cana-5314	118	17	at	at	ADP
cana-5314	118	18	step	step	NOUN
cana-5314	118	19	𝑖	𝑖	NUM
cana-5314	118	20	with	with	ADP
cana-5314	118	21	state	state	NOUN
cana-5314	118	22	𝑗	𝑗	PROPN
cana-5314	118	23	,	,	PUNCT
cana-5314	118	24	and	and	CCONJ
cana-5314	118	25	cost(𝑖	cost(𝑖	NOUN
cana-5314	118	26	)	)	PUNCT
cana-5314	118	27	is	be	AUX
cana-5314	118	28	the	the	DET
cana-5314	118	29	cost	cost	NOUN
cana-5314	118	30	at	at	ADP
cana-5314	118	31	step	step	NOUN
cana-5314	118	32	𝑖.	𝑖.	NOUN
cana-5314	118	33	figure	figure	NOUN
cana-5314	118	34	1	1	NUM
cana-5314	118	35	:	:	PUNCT
cana-5314	118	36	flowchart	flowchart	NOUN
cana-5314	118	37	of	of	ADP
cana-5314	118	38	methodology	methodology	NOUN
cana-5314	118	39	for	for	ADP
cana-5314	118	40	evaluating	evaluate	VERB
cana-5314	118	41	p	p	NOUN
cana-5314	118	42	vs	vs	ADP
cana-5314	118	43	np	np	NOUN
cana-5314	118	44	through	through	ADP
cana-5314	118	45	algorithmic	algorithmic	ADJ
cana-5314	118	46	analysis	analysis	NOUN
cana-5314	118	47	communications	communication	NOUN
cana-5314	118	48	on	on	ADP
cana-5314	118	49	applied	apply	VERB
cana-5314	118	50	nonlinear	nonlinear	ADJ
cana-5314	118	51	analysis	analysis	NOUN
cana-5314	118	52	issn	issn	NOUN
cana-5314	118	53	:	:	PUNCT
cana-5314	118	54	1074	1074	NUM
cana-5314	118	55	-	-	PUNCT
cana-5314	118	56	133x	133x	NUM
cana-5314	118	57	vol	vol	NOUN
cana-5314	118	58	31	31	NUM
cana-5314	118	59	no	no	NOUN
cana-5314	118	60	.	.	PUNCT
cana-5314	119	1	8s	8s	PROPN
cana-5314	119	2	(	(	PUNCT
cana-5314	119	3	2024	2024	NUM
cana-5314	119	4	)	)	PUNCT
cana-5314	119	5	952	952	NUM
cana-5314	119	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5314	119	7	this	this	DET
cana-5314	119	8	methodology	methodology	NOUN
cana-5314	119	9	sets	set	VERB
cana-5314	119	10	the	the	DET
cana-5314	119	11	stage	stage	NOUN
cana-5314	119	12	for	for	ADP
cana-5314	119	13	deeper	deep	ADJ
cana-5314	119	14	exploration	exploration	NOUN
cana-5314	119	15	into	into	ADP
cana-5314	119	16	the	the	DET
cana-5314	119	17	p	p	NOUN
cana-5314	119	18	versus	versus	ADP
cana-5314	119	19	np	np	PRON
cana-5314	119	20	problem	problem	NOUN
cana-5314	119	21	,	,	PUNCT
cana-5314	119	22	providing	provide	VERB
cana-5314	119	23	a	a	DET
cana-5314	119	24	structured	structured	ADJ
cana-5314	119	25	approach	approach	NOUN
cana-5314	119	26	for	for	ADP
cana-5314	119	27	both	both	CCONJ
cana-5314	119	28	theoretical	theoretical	ADJ
cana-5314	119	29	exploration	exploration	NOUN
cana-5314	119	30	and	and	CCONJ
cana-5314	119	31	empirical	empirical	ADJ
cana-5314	119	32	testing	testing	NOUN
cana-5314	119	33	.	.	PUNCT
cana-5314	120	1	by	by	ADP
cana-5314	120	2	utilizing	utilize	VERB
cana-5314	120	3	both	both	DET
cana-5314	120	4	existing	exist	VERB
cana-5314	120	5	models	model	NOUN
cana-5314	120	6	and	and	CCONJ
cana-5314	120	7	introducing	introduce	VERB
cana-5314	120	8	new	new	ADJ
cana-5314	120	9	computational	computational	ADJ
cana-5314	120	10	frameworks	framework	NOUN
cana-5314	120	11	,	,	PUNCT
cana-5314	120	12	the	the	DET
cana-5314	120	13	research	research	NOUN
cana-5314	120	14	aims	aim	VERB
cana-5314	120	15	to	to	PART
cana-5314	120	16	shed	shed	VERB
cana-5314	120	17	light	light	NOUN
cana-5314	120	18	on	on	ADP
cana-5314	120	19	the	the	DET
cana-5314	120	20	central	central	ADJ
cana-5314	120	21	question	question	NOUN
cana-5314	120	22	in	in	ADP
cana-5314	120	23	computational	computational	ADJ
cana-5314	120	24	complexity	complexity	NOUN
cana-5314	120	25	theory	theory	NOUN
cana-5314	120	26	.	.	PUNCT
cana-5314	121	1	iv	iv	X
cana-5314	121	2	.	.	PROPN
cana-5314	121	3	result	result	PROPN
cana-5314	121	4	&	&	CCONJ
cana-5314	121	5	discussions	discussion	NOUN
cana-5314	121	6	our	our	PRON
cana-5314	121	7	methodology	methodology	NOUN
cana-5314	121	8	produces	produce	VERB
cana-5314	121	9	result	result	NOUN
cana-5314	121	10	about	about	ADP
cana-5314	121	11	computational	computational	ADJ
cana-5314	121	12	complexity	complexity	NOUN
cana-5314	121	13	theory	theory	NOUN
cana-5314	121	14	which	which	PRON
cana-5314	121	15	investigate	investigate	VERB
cana-5314	121	16	potential	potential	ADJ
cana-5314	121	17	p	p	NOUN
cana-5314	121	18	and	and	CCONJ
cana-5314	121	19	np	np	ADP
cana-5314	121	20	relationships	relationship	NOUN
cana-5314	121	21	.	.	PUNCT
cana-5314	122	1	the	the	DET
cana-5314	122	2	research	research	NOUN
cana-5314	122	3	employed	employ	VERB
cana-5314	122	4	data	datum	NOUN
cana-5314	122	5	simulations	simulation	NOUN
cana-5314	122	6	together	together	ADV
cana-5314	122	7	with	with	ADP
cana-5314	122	8	theoretical	theoretical	ADJ
cana-5314	122	9	concepts	concept	NOUN
cana-5314	122	10	for	for	ADP
cana-5314	122	11	evaluating	evaluate	VERB
cana-5314	122	12	its	its	PRON
cana-5314	122	13	performance	performance	NOUN
cana-5314	122	14	.	.	PUNCT
cana-5314	123	1	an	an	DET
cana-5314	123	2	analysis	analysis	NOUN
cana-5314	123	3	of	of	ADP
cana-5314	123	4	experimental	experimental	ADJ
cana-5314	123	5	findings	finding	NOUN
cana-5314	123	6	follows	follow	VERB
cana-5314	123	7	in	in	ADP
cana-5314	123	8	this	this	DET
cana-5314	123	9	section	section	NOUN
cana-5314	123	10	while	while	SCONJ
cana-5314	123	11	performance	performance	NOUN
cana-5314	123	12	results	result	NOUN
cana-5314	123	13	get	get	AUX
cana-5314	123	14	evaluated	evaluate	VERB
cana-5314	123	15	and	and	CCONJ
cana-5314	123	16	the	the	DET
cana-5314	123	17	current	current	ADJ
cana-5314	123	18	p	p	NOUN
cana-5314	123	19	versus	versus	ADP
cana-5314	123	20	np	np	PRON
cana-5314	123	21	debate	debate	NOUN
cana-5314	123	22	gets	get	AUX
cana-5314	123	23	investigated	investigate	VERB
cana-5314	123	24	[	[	PUNCT
cana-5314	123	25	6	6	NUM
cana-5314	123	26	]	]	PUNCT
cana-5314	123	27	.	.	PUNCT
cana-5314	124	1	we	we	PRON
cana-5314	124	2	examined	examine	VERB
cana-5314	124	3	np	np	ADJ
cana-5314	124	4	-	-	ADJ
cana-5314	124	5	complete	complete	ADJ
cana-5314	124	6	computational	computational	ADJ
cana-5314	124	7	challenges	challenge	NOUN
cana-5314	124	8	through	through	ADP
cana-5314	124	9	dynamic	dynamic	ADJ
cana-5314	124	10	programming	programming	NOUN
cana-5314	124	11	using	use	VERB
cana-5314	124	12	the	the	DET
cana-5314	124	13	tsp	tsp	NOUN
cana-5314	124	14	and	and	CCONJ
cana-5314	124	15	knapsack	knapsack	NOUN
cana-5314	124	16	problem	problem	NOUN
cana-5314	124	17	as	as	ADP
cana-5314	124	18	main	main	ADJ
cana-5314	124	19	research	research	NOUN
cana-5314	124	20	targets	target	NOUN
cana-5314	124	21	.	.	PUNCT
cana-5314	125	1	the	the	DET
cana-5314	125	2	recognized	recognize	VERB
cana-5314	125	3	problems	problem	NOUN
cana-5314	125	4	from	from	ADP
cana-5314	125	5	computational	computational	ADJ
cana-5314	125	6	theory	theory	NOUN
cana-5314	125	7	create	create	VERB
cana-5314	125	8	perfect	perfect	ADJ
cana-5314	125	9	conditions	condition	NOUN
cana-5314	125	10	to	to	PART
cana-5314	125	11	evaluate	evaluate	VERB
cana-5314	125	12	new	new	ADJ
cana-5314	125	13	algorithms	algorithm	NOUN
cana-5314	125	14	.	.	PUNCT
cana-5314	126	1	dynamic	dynamic	ADJ
cana-5314	126	2	programming	programming	NOUN
cana-5314	126	3	created	create	VERB
cana-5314	126	4	substantial	substantial	ADJ
cana-5314	126	5	improvements	improvement	NOUN
cana-5314	126	6	to	to	ADP
cana-5314	126	7	time	time	NOUN
cana-5314	126	8	complexity	complexity	NOUN
cana-5314	126	9	but	but	CCONJ
cana-5314	126	10	the	the	DET
cana-5314	126	11	solution	solution	NOUN
cana-5314	126	12	duration	duration	NOUN
cana-5314	126	13	for	for	ADP
cana-5314	126	14	large	large	ADJ
cana-5314	126	15	datasets	dataset	NOUN
cana-5314	126	16	demonstrated	demonstrate	VERB
cana-5314	126	17	exponential	exponential	ADJ
cana-5314	126	18	growth	growth	NOUN
cana-5314	126	19	patterns	pattern	NOUN
cana-5314	126	20	.	.	PUNCT
cana-5314	127	1	the	the	DET
cana-5314	127	2	algorithm	algorithm	NOUN
cana-5314	127	3	operated	operate	VERB
cana-5314	127	4	with	with	ADP
cana-5314	127	5	polynomial	polynomial	ADJ
cana-5314	127	6	efficiency	efficiency	NOUN
cana-5314	127	7	during	during	ADP
cana-5314	127	8	modest	modest	ADJ
cana-5314	127	9	problem	problem	NOUN
cana-5314	127	10	executions	execution	NOUN
cana-5314	127	11	although	although	SCONJ
cana-5314	127	12	its	its	PRON
cana-5314	127	13	performance	performance	NOUN
cana-5314	127	14	severely	severely	ADV
cana-5314	127	15	declined	decline	VERB
cana-5314	127	16	when	when	SCONJ
cana-5314	127	17	problems	problem	NOUN
cana-5314	127	18	grew	grow	VERB
cana-5314	127	19	larger	large	ADJ
cana-5314	127	20	.	.	PUNCT
cana-5314	128	1	the	the	DET
cana-5314	128	2	findings	finding	NOUN
cana-5314	128	3	were	be	AUX
cana-5314	128	4	confirmed	confirm	VERB
cana-5314	128	5	by	by	ADP
cana-5314	128	6	establishing	establish	VERB
cana-5314	128	7	execution	execution	NOUN
cana-5314	128	8	times	time	NOUN
cana-5314	128	9	versus	versus	ADP
cana-5314	128	10	variable	variable	ADJ
cana-5314	128	11	numbers	number	NOUN
cana-5314	128	12	and	and	CCONJ
cana-5314	128	13	analyzing	analyze	VERB
cana-5314	128	14	them	they	PRON
cana-5314	128	15	relative	relative	ADJ
cana-5314	128	16	to	to	ADP
cana-5314	128	17	theoretical	theoretical	ADJ
cana-5314	128	18	predictions	prediction	NOUN
cana-5314	128	19	reported	report	VERB
cana-5314	128	20	earlier	early	ADV
cana-5314	128	21	[	[	X
cana-5314	128	22	7	7	NUM
cana-5314	128	23	]	]	PUNCT
cana-5314	128	24	.	.	PUNCT
cana-5314	129	1	the	the	DET
cana-5314	129	2	main	main	ADJ
cana-5314	129	3	outcome	outcome	NOUN
cana-5314	129	4	from	from	ADP
cana-5314	129	5	our	our	PRON
cana-5314	129	6	testing	testing	NOUN
cana-5314	129	7	revealed	reveal	VERB
cana-5314	129	8	how	how	SCONJ
cana-5314	129	9	np	np	X
cana-5314	129	10	-	-	PUNCT
cana-5314	129	11	complete	complete	ADJ
cana-5314	129	12	problems	problem	NOUN
cana-5314	129	13	resist	resist	VERB
cana-5314	129	14	polynomial	polynomial	ADJ
cana-5314	129	15	-	-	PUNCT
cana-5314	129	16	time	time	NOUN
cana-5314	129	17	solvers	solver	NOUN
cana-5314	129	18	beyond	beyond	ADP
cana-5314	129	19	specific	specific	ADJ
cana-5314	129	20	difficulty	difficulty	NOUN
cana-5314	129	21	thresholds	threshold	NOUN
cana-5314	129	22	.	.	PUNCT
cana-5314	130	1	dynamic	dynamic	ADJ
cana-5314	130	2	programming	programming	NOUN
cana-5314	130	3	in	in	ADP
cana-5314	130	4	the	the	DET
cana-5314	130	5	tsp	tsp	NOUN
cana-5314	130	6	first	first	ADV
cana-5314	130	7	achieved	achieve	VERB
cana-5314	130	8	faster	fast	ADJ
cana-5314	130	9	computation	computation	NOUN
cana-5314	130	10	but	but	CCONJ
cana-5314	130	11	expanding	expand	VERB
cana-5314	130	12	city	city	NOUN
cana-5314	130	13	numbers	number	NOUN
cana-5314	130	14	caused	cause	VERB
cana-5314	130	15	the	the	DET
cana-5314	130	16	path	path	NOUN
cana-5314	130	17	optimization	optimization	NOUN
cana-5314	130	18	time	time	NOUN
cana-5314	130	19	to	to	PART
cana-5314	130	20	explode	explode	VERB
cana-5314	130	21	exponentially	exponentially	ADV
cana-5314	130	22	.	.	PUNCT
cana-5314	131	1	the	the	DET
cana-5314	131	2	table	table	NOUN
cana-5314	131	3	shows	show	VERB
cana-5314	131	4	how	how	SCONJ
cana-5314	131	5	dynamic	dynamic	ADJ
cana-5314	131	6	programming	programming	NOUN
cana-5314	131	7	performances	performance	NOUN
cana-5314	131	8	better	well	ADV
cana-5314	131	9	than	than	ADP
cana-5314	131	10	traditional	traditional	ADJ
cana-5314	131	11	brute	brute	ADJ
cana-5314	131	12	-	-	PUNCT
cana-5314	131	13	force	force	NOUN
cana-5314	131	14	solutions	solution	NOUN
cana-5314	131	15	but	but	CCONJ
cana-5314	131	16	adopts	adopt	VERB
cana-5314	131	17	a	a	DET
cana-5314	131	18	scalability	scalability	NOUN
cana-5314	131	19	challenge	challenge	NOUN
cana-5314	131	20	when	when	SCONJ
cana-5314	131	21	facing	face	VERB
cana-5314	131	22	larger	large	ADJ
cana-5314	131	23	problem	problem	NOUN
cana-5314	131	24	sizes	size	NOUN
cana-5314	131	25	.	.	PUNCT
cana-5314	132	1	table	table	NOUN
cana-5314	132	2	1	1	NUM
cana-5314	132	3	:	:	PUNCT
cana-5314	132	4	comparison	comparison	NOUN
cana-5314	132	5	of	of	ADP
cana-5314	132	6	brute	brute	ADJ
cana-5314	132	7	-	-	PUNCT
cana-5314	132	8	force	force	NOUN
cana-5314	132	9	and	and	CCONJ
cana-5314	132	10	dynamic	dynamic	ADJ
cana-5314	132	11	programming	programming	NOUN
cana-5314	132	12	approaches	approach	NOUN
cana-5314	132	13	for	for	ADP
cana-5314	132	14	tsp	tsp	NOUN
cana-5314	132	15	problem	problem	NOUN
cana-5314	132	16	size	size	NOUN
cana-5314	132	17	(	(	PUNCT
cana-5314	132	18	cities	city	NOUN
cana-5314	132	19	)	)	PUNCT
cana-5314	132	20	brute	brute	ADJ
cana-5314	132	21	-	-	PUNCT
cana-5314	132	22	force	force	NOUN
cana-5314	132	23	time	time	NOUN
cana-5314	132	24	(	(	PUNCT
cana-5314	132	25	seconds	second	NOUN
cana-5314	132	26	)	)	PUNCT
cana-5314	132	27	dynamic	dynamic	ADJ
cana-5314	132	28	programming	programming	NOUN
cana-5314	132	29	time	time	NOUN
cana-5314	132	30	(	(	PUNCT
cana-5314	132	31	seconds	second	NOUN
cana-5314	132	32	)	)	PUNCT
cana-5314	132	33	10	10	NUM
cana-5314	132	34	5.2	5.2	NUM
cana-5314	132	35	3.8	3.8	NUM
cana-5314	132	36	20	20	NUM
cana-5314	132	37	40.5	40.5	NUM
cana-5314	132	38	28.3	28.3	NUM
cana-5314	132	39	50	50	NUM
cana-5314	132	40	225.0	225.0	NUM
cana-5314	132	41	132.0	132.0	NUM
cana-5314	132	42	100	100	NUM
cana-5314	132	43	980.0	980.0	NUM
cana-5314	132	44	550.0	550.0	NUM
cana-5314	132	45	the	the	DET
cana-5314	132	46	analysis	analysis	NOUN
cana-5314	132	47	reveals	reveal	VERB
cana-5314	132	48	np	np	ADJ
cana-5314	132	49	-	-	PUNCT
cana-5314	132	50	complete	complete	ADJ
cana-5314	132	51	problems	problem	NOUN
cana-5314	132	52	have	have	VERB
cana-5314	132	53	fundamental	fundamental	ADJ
cana-5314	132	54	time	time	NOUN
cana-5314	132	55	complexity	complexity	NOUN
cana-5314	132	56	characteristics	characteristic	NOUN
cana-5314	132	57	because	because	SCONJ
cana-5314	132	58	problems	problem	NOUN
cana-5314	132	59	of	of	ADP
cana-5314	132	60	increased	increase	VERB
cana-5314	132	61	size	size	NOUN
cana-5314	132	62	prove	prove	VERB
cana-5314	132	63	resistant	resistant	ADJ
cana-5314	132	64	to	to	ADP
cana-5314	132	65	performance	performance	NOUN
cana-5314	132	66	communications	communication	NOUN
cana-5314	132	67	on	on	ADP
cana-5314	132	68	applied	apply	VERB
cana-5314	132	69	nonlinear	nonlinear	ADJ
cana-5314	132	70	analysis	analysis	NOUN
cana-5314	132	71	issn	issn	NOUN
cana-5314	132	72	:	:	PUNCT
cana-5314	132	73	1074	1074	NUM
cana-5314	132	74	-	-	PUNCT
cana-5314	132	75	133x	133x	NUM
cana-5314	132	76	vol	vol	NOUN
cana-5314	132	77	31	31	NUM
cana-5314	132	78	no	no	NOUN
cana-5314	132	79	.	.	PUNCT
cana-5314	133	1	8s	8s	PROPN
cana-5314	133	2	(	(	PUNCT
cana-5314	133	3	2024	2024	NUM
cana-5314	133	4	)	)	PUNCT
cana-5314	133	5	953	953	NUM
cana-5314	133	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5314	133	7	improvements	improvement	NOUN
cana-5314	133	8	of	of	ADP
cana-5314	133	9	optimized	optimize	VERB
cana-5314	133	10	procedures	procedure	NOUN
cana-5314	133	11	.	.	PUNCT
cana-5314	134	1	the	the	DET
cana-5314	134	2	speed	speed	NOUN
cana-5314	134	3	-	-	PUNCT
cana-5314	134	4	up	up	NOUN
cana-5314	134	5	from	from	ADP
cana-5314	134	6	np	np	NOUN
cana-5314	134	7	-	-	PUNCT
cana-5314	134	8	complete	complete	ADJ
cana-5314	134	9	problems	problem	NOUN
cana-5314	134	10	running	run	VERB
cana-5314	134	11	at	at	ADP
cana-5314	134	12	exponential	exponential	ADJ
cana-5314	134	13	rates	rate	NOUN
cana-5314	134	14	continues	continue	VERB
cana-5314	134	15	to	to	PART
cana-5314	134	16	make	make	VERB
cana-5314	134	17	finding	find	VERB
cana-5314	134	18	polynomial	polynomial	ADJ
cana-5314	134	19	-	-	PUNCT
cana-5314	134	20	time	time	NOUN
cana-5314	134	21	solutions	solution	NOUN
cana-5314	134	22	impossible	impossible	ADJ
cana-5314	134	23	.	.	PUNCT
cana-5314	135	1	under	under	ADP
cana-5314	135	2	normal	normal	ADJ
cana-5314	135	3	circumstances	circumstance	NOUN
cana-5314	135	4	dynamic	dynamic	ADJ
cana-5314	135	5	programming	programming	NOUN
cana-5314	135	6	failed	fail	VERB
cana-5314	135	7	to	to	PART
cana-5314	135	8	yield	yield	VERB
cana-5314	135	9	a	a	DET
cana-5314	135	10	polynomial	polynomial	ADJ
cana-5314	135	11	-	-	PUNCT
cana-5314	135	12	time	time	NOUN
cana-5314	135	13	solution	solution	NOUN
cana-5314	135	14	for	for	ADP
cana-5314	135	15	larger	large	ADJ
cana-5314	135	16	problems	problem	NOUN
cana-5314	135	17	which	which	PRON
cana-5314	135	18	supports	support	VERB
cana-5314	135	19	the	the	DET
cana-5314	135	20	hypothesis	hypothesis	NOUN
cana-5314	135	21	that	that	PRON
cana-5314	135	22	np	np	NOUN
cana-5314	135	23	-	-	PUNCT
cana-5314	135	24	complete	complete	ADJ
cana-5314	135	25	problems	problem	NOUN
cana-5314	135	26	exist	exist	VERB
cana-5314	135	27	beyond	beyond	ADP
cana-5314	135	28	the	the	DET
cana-5314	135	29	p	p	NOUN
cana-5314	135	30	class	class	NOUN
cana-5314	135	31	because	because	SCONJ
cana-5314	135	32	algorithmic	algorithmic	ADJ
cana-5314	135	33	theory	theory	NOUN
cana-5314	135	34	has	have	AUX
cana-5314	135	35	not	not	PART
cana-5314	135	36	delivered	deliver	VERB
cana-5314	135	37	major	major	ADJ
cana-5314	135	38	advancements	advancement	NOUN
cana-5314	135	39	.	.	PUNCT
cana-5314	136	1	an	an	DET
cana-5314	136	2	experiment	experiment	NOUN
cana-5314	136	3	was	be	AUX
cana-5314	136	4	conducted	conduct	VERB
cana-5314	136	5	to	to	PART
cana-5314	136	6	compare	compare	VERB
cana-5314	136	7	the	the	DET
cana-5314	136	8	knapsack	knapsack	NOUN
cana-5314	136	9	problem	problem	NOUN
cana-5314	136	10	performances	performance	NOUN
cana-5314	136	11	between	between	ADP
cana-5314	136	12	a	a	DET
cana-5314	136	13	greedy	greedy	ADJ
cana-5314	136	14	algorithm	algorithm	NOUN
cana-5314	136	15	and	and	CCONJ
cana-5314	136	16	dynamic	dynamic	ADJ
cana-5314	136	17	programming	programming	NOUN
cana-5314	136	18	method	method	NOUN
cana-5314	136	19	.	.	PUNCT
cana-5314	137	1	the	the	DET
cana-5314	137	2	dynamic	dynamic	ADJ
cana-5314	137	3	programming	programming	NOUN
cana-5314	137	4	method	method	NOUN
cana-5314	137	5	delivered	deliver	VERB
cana-5314	137	6	optimal	optimal	ADJ
cana-5314	137	7	solutions	solution	NOUN
cana-5314	137	8	in	in	ADP
cana-5314	137	9	every	every	DET
cana-5314	137	10	case	case	NOUN
cana-5314	137	11	yet	yet	ADV
cana-5314	137	12	it	it	PRON
cana-5314	137	13	needed	need	VERB
cana-5314	137	14	growing	grow	VERB
cana-5314	137	15	amounts	amount	NOUN
cana-5314	137	16	of	of	ADP
cana-5314	137	17	computational	computational	ADJ
cana-5314	137	18	power	power	NOUN
cana-5314	137	19	while	while	SCONJ
cana-5314	137	20	problem	problem	NOUN
cana-5314	137	21	size	size	NOUN
cana-5314	137	22	increased	increase	VERB
cana-5314	137	23	.	.	PUNCT
cana-5314	138	1	we	we	PRON
cana-5314	138	2	analyzed	analyze	VERB
cana-5314	138	3	the	the	DET
cana-5314	138	4	total	total	ADJ
cana-5314	138	5	processing	processing	NOUN
cana-5314	138	6	duration	duration	NOUN
cana-5314	138	7	for	for	ADP
cana-5314	138	8	various	various	ADJ
cana-5314	138	9	problem	problem	NOUN
cana-5314	138	10	scales	scale	VERB
cana-5314	138	11	through	through	ADP
cana-5314	138	12	a	a	DET
cana-5314	138	13	diagram	diagram	NOUN
cana-5314	138	14	which	which	PRON
cana-5314	138	15	displayed	display	VERB
cana-5314	138	16	the	the	DET
cana-5314	138	17	time	time	NOUN
cana-5314	138	18	comparison	comparison	NOUN
cana-5314	138	19	between	between	ADP
cana-5314	138	20	the	the	DET
cana-5314	138	21	algorithms	algorithm	NOUN
cana-5314	138	22	.	.	PUNCT
cana-5314	139	1	the	the	DET
cana-5314	139	2	illustration	illustration	NOUN
cana-5314	139	3	demonstrates	demonstrate	VERB
cana-5314	139	4	that	that	SCONJ
cana-5314	139	5	dynamic	dynamic	ADJ
cana-5314	139	6	programming	programming	NOUN
cana-5314	139	7	demonstrates	demonstrate	VERB
cana-5314	139	8	superior	superior	ADJ
cana-5314	139	9	efficiency	efficiency	NOUN
cana-5314	139	10	over	over	ADP
cana-5314	139	11	greedy	greedy	ADJ
cana-5314	139	12	algorithm	algorithm	NOUN
cana-5314	139	13	as	as	SCONJ
cana-5314	139	14	problem	problem	NOUN
cana-5314	139	15	dimensions	dimension	NOUN
cana-5314	139	16	escalate	escalate	VERB
cana-5314	139	17	.	.	PUNCT
cana-5314	140	1	figure	figure	NOUN
cana-5314	140	2	2	2	NUM
cana-5314	140	3	:	:	PUNCT
cana-5314	140	4	computational	computational	ADJ
cana-5314	140	5	time	time	NOUN
cana-5314	140	6	comparison	comparison	NOUN
cana-5314	140	7	for	for	ADP
cana-5314	140	8	tsp	tsp	NOUN
cana-5314	140	9	the	the	DET
cana-5314	140	10	experiment	experiment	NOUN
cana-5314	140	11	findings	finding	NOUN
cana-5314	140	12	demonstrate	demonstrate	VERB
cana-5314	140	13	key	key	ADJ
cana-5314	140	14	aspects	aspect	NOUN
cana-5314	140	15	about	about	ADP
cana-5314	140	16	the	the	DET
cana-5314	140	17	computational	computational	ADJ
cana-5314	140	18	difficulties	difficulty	NOUN
cana-5314	140	19	found	find	VERB
cana-5314	140	20	in	in	ADP
cana-5314	140	21	np	np	NOUN
cana-5314	140	22	-	-	PUNCT
cana-5314	140	23	complete	complete	ADJ
cana-5314	140	24	problems	problem	NOUN
cana-5314	140	25	.	.	PUNCT
cana-5314	141	1	the	the	DET
cana-5314	141	2	examination	examination	NOUN
cana-5314	141	3	demonstrates	demonstrate	VERB
cana-5314	141	4	that	that	SCONJ
cana-5314	141	5	dynamic	dynamic	ADJ
cana-5314	141	6	programming	programming	NOUN
cana-5314	141	7	xoffseters	xoffseter	NOUN
cana-5314	141	8	brute	brute	ADJ
cana-5314	141	9	-	-	PUNCT
cana-5314	141	10	force	force	NOUN
cana-5314	141	11	approaches	approach	NOUN
cana-5314	141	12	yet	yet	ADV
cana-5314	141	13	fails	fail	VERB
cana-5314	141	14	to	to	PART
cana-5314	141	15	generate	generate	VERB
cana-5314	141	16	polynomial	polynomial	ADJ
cana-5314	141	17	-	-	PUNCT
cana-5314	141	18	time	time	NOUN
cana-5314	141	19	solutions	solution	NOUN
cana-5314	141	20	for	for	ADP
cana-5314	141	21	npcomplete	npcomplete	ADJ
cana-5314	141	22	problems	problem	NOUN
cana-5314	141	23	.	.	PUNCT
cana-5314	142	1	the	the	DET
cana-5314	142	2	prevailing	prevail	VERB
cana-5314	142	3	evidence	evidence	NOUN
cana-5314	142	4	shows	show	VERB
cana-5314	142	5	that	that	SCONJ
cana-5314	142	6	p	p	NOUN
cana-5314	142	7	is	be	AUX
cana-5314	142	8	different	different	ADJ
cana-5314	142	9	from	from	ADP
cana-5314	142	10	np	np	PROPN
cana-5314	142	11	.	.	PUNCT
cana-5314	143	1	the	the	DET
cana-5314	143	2	rapid	rapid	ADJ
cana-5314	143	3	execution	execution	NOUN
cana-5314	143	4	of	of	ADP
cana-5314	143	5	greedy	greedy	ADJ
cana-5314	143	6	approaches	approach	NOUN
cana-5314	143	7	leads	lead	VERB
cana-5314	143	8	to	to	ADP
cana-5314	143	9	undesirable	undesirable	ADJ
cana-5314	143	10	suboptimal	suboptimal	ADJ
cana-5314	143	11	results	result	NOUN
cana-5314	143	12	that	that	SCONJ
cana-5314	143	13	creation	creation	NOUN
cana-5314	143	14	of	of	ADP
cana-5314	143	15	reliable	reliable	ADJ
cana-5314	143	16	real	real	ADJ
cana-5314	143	17	-	-	PUNCT
cana-5314	143	18	world	world	NOUN
cana-5314	143	19	solutions	solution	NOUN
cana-5314	143	20	becomes	become	VERB
cana-5314	143	21	challenging	challenging	ADJ
cana-5314	143	22	.	.	PUNCT
cana-5314	144	1	our	our	PRON
cana-5314	144	2	research	research	NOUN
cana-5314	144	3	focused	focus	VERB
cana-5314	144	4	on	on	ADP
cana-5314	144	5	the	the	DET
cana-5314	144	6	boolean	boolean	ADJ
cana-5314	144	7	satisfiability	satisfiability	NOUN
cana-5314	144	8	problem	problem	NOUN
cana-5314	144	9	sat	sit	VERB
cana-5314	144	10	through	through	ADP
cana-5314	144	11	a	a	DET
cana-5314	144	12	review	review	NOUN
cana-5314	144	13	of	of	ADP
cana-5314	144	14	reduction	reduction	NOUN
cana-5314	144	15	methods	method	NOUN
cana-5314	144	16	that	that	PRON
cana-5314	144	17	intended	intend	VERB
cana-5314	144	18	to	to	PART
cana-5314	144	19	make	make	VERB
cana-5314	144	20	the	the	DET
cana-5314	144	21	problem	problem	NOUN
cana-5314	144	22	more	more	ADV
cana-5314	144	23	manageable	manageable	ADJ
cana-5314	144	24	.	.	PUNCT
cana-5314	145	1	the	the	DET
cana-5314	145	2	experimental	experimental	ADJ
cana-5314	145	3	design	design	NOUN
cana-5314	145	4	used	use	VERB
cana-5314	145	5	known	know	VERB
cana-5314	145	6	polynomial	polynomial	ADJ
cana-5314	145	7	-	-	PUNCT
cana-5314	145	8	time	time	NOUN
cana-5314	145	9	reductions	reduction	NOUN
cana-5314	145	10	as	as	ADP
cana-5314	145	11	transformation	transformation	NOUN
cana-5314	145	12	methods	method	NOUN
cana-5314	145	13	to	to	PART
cana-5314	145	14	monitor	monitor	VERB
cana-5314	145	15	how	how	SCONJ
cana-5314	145	16	sat	sat	AUX
cana-5314	145	17	instances	instance	NOUN
cana-5314	145	18	evolved	evolve	VERB
cana-5314	145	19	into	into	ADP
cana-5314	145	20	different	different	ADJ
cana-5314	145	21	problems	problem	NOUN
cana-5314	145	22	.	.	PUNCT
cana-5314	146	1	even	even	ADV
cana-5314	146	2	though	though	SCONJ
cana-5314	146	3	reductions	reduction	NOUN
cana-5314	146	4	help	help	VERB
cana-5314	146	5	control	control	NOUN
cana-5314	146	6	sat	sit	VERB
cana-5314	146	7	's	's	PART
cana-5314	146	8	complexity	complexity	NOUN
cana-5314	146	9	they	they	PRON
cana-5314	146	10	do	do	AUX
cana-5314	146	11	not	not	PART
cana-5314	146	12	prevent	prevent	VERB
cana-5314	146	13	the	the	DET
cana-5314	146	14	problem	problem	NOUN
cana-5314	146	15	from	from	ADP
cana-5314	146	16	becoming	become	VERB
cana-5314	146	17	exponentially	exponentially	ADV
cana-5314	146	18	more	more	ADV
cana-5314	146	19	challenging	challenging	ADJ
cana-5314	146	20	as	as	ADP
cana-5314	146	21	5.2	5.2	NUM
cana-5314	146	22	40.5	40.5	NUM
cana-5314	146	23	225	225	NUM
cana-5314	146	24	3.8	3.8	NUM
cana-5314	146	25	28.3	28.3	NUM
cana-5314	146	26	132	132	NUM
cana-5314	146	27	0	0	NUM
cana-5314	146	28	50	50	NUM
cana-5314	146	29	100	100	NUM
cana-5314	146	30	150	150	NUM
cana-5314	146	31	200	200	NUM
cana-5314	146	32	250	250	NUM
cana-5314	146	33	10	10	NUM
cana-5314	146	34	20	20	NUM
cana-5314	146	35	50	50	NUM
cana-5314	146	36	computational	computational	ADJ
cana-5314	146	37	time	time	NOUN
cana-5314	146	38	comparison	comparison	NOUN
cana-5314	146	39	for	for	ADP
cana-5314	146	40	tsp	tsp	NOUN
cana-5314	146	41	dynamic	dynamic	ADJ
cana-5314	146	42	programming	programming	NOUN
cana-5314	146	43	time	time	NOUN
cana-5314	146	44	(	(	PUNCT
cana-5314	146	45	seconds	second	NOUN
cana-5314	146	46	)	)	PUNCT
cana-5314	146	47	brute	brute	ADJ
cana-5314	146	48	-	-	PUNCT
cana-5314	146	49	force	force	NOUN
cana-5314	146	50	time	time	NOUN
cana-5314	146	51	(	(	PUNCT
cana-5314	146	52	seconds	second	NOUN
cana-5314	146	53	)	)	PUNCT
cana-5314	146	54	communications	communication	NOUN
cana-5314	146	55	on	on	ADP
cana-5314	146	56	applied	apply	VERB
cana-5314	146	57	nonlinear	nonlinear	ADJ
cana-5314	146	58	analysis	analysis	NOUN
cana-5314	146	59	issn	issn	NOUN
cana-5314	146	60	:	:	PUNCT
cana-5314	146	61	1074	1074	NUM
cana-5314	146	62	-	-	PUNCT
cana-5314	146	63	133x	133x	NUM
cana-5314	146	64	vol	vol	NOUN
cana-5314	146	65	31	31	NUM
cana-5314	146	66	no	no	NOUN
cana-5314	146	67	.	.	PUNCT
cana-5314	147	1	8s	8s	PROPN
cana-5314	147	2	(	(	PUNCT
cana-5314	147	3	2024	2024	NUM
cana-5314	147	4	)	)	PUNCT
cana-5314	147	5	954	954	NUM
cana-5314	147	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-5314	147	7	problem	problem	NOUN
cana-5314	147	8	size	size	NOUN
cana-5314	147	9	grows	grow	VERB
cana-5314	147	10	.	.	PUNCT
cana-5314	148	1	the	the	DET
cana-5314	148	2	experimental	experimental	ADJ
cana-5314	148	3	results	result	NOUN
cana-5314	148	4	served	serve	VERB
cana-5314	148	5	as	as	ADP
cana-5314	148	6	compelling	compelling	ADJ
cana-5314	148	7	evidence	evidence	NOUN
cana-5314	148	8	that	that	PRON
cana-5314	148	9	sat	sit	VERB
cana-5314	148	10	belongs	belong	VERB
cana-5314	148	11	to	to	ADP
cana-5314	148	12	the	the	DET
cana-5314	148	13	category	category	NOUN
cana-5314	148	14	of	of	ADP
cana-5314	148	15	problems	problem	NOUN
cana-5314	148	16	that	that	PRON
cana-5314	148	17	remain	remain	VERB
cana-5314	148	18	untouchable	untouchable	ADJ
cana-5314	148	19	by	by	ADP
cana-5314	148	20	p	p	PRON
cana-5314	148	21	together	together	ADV
cana-5314	148	22	with	with	ADP
cana-5314	148	23	all	all	DET
cana-5314	148	24	other	other	ADJ
cana-5314	148	25	np	np	ADJ
cana-5314	148	26	-	-	PUNCT
cana-5314	148	27	complete	complete	ADJ
cana-5314	148	28	problems	problem	NOUN
cana-5314	148	29	.	.	PUNCT
cana-5314	149	1	figure	figure	VERB
cana-5314	149	2	3	3	NUM
cana-5314	149	3	:	:	PUNCT
cana-5314	149	4	computational	computational	ADJ
cana-5314	149	5	time	time	NOUN
cana-5314	149	6	for	for	ADP
cana-5314	149	7	sat	sit	VERB
cana-5314	149	8	problem	problem	NOUN
cana-5314	149	9	reductions	reduction	NOUN
cana-5314	149	10	experimental	experimental	ADJ
cana-5314	149	11	evidence	evidence	NOUN
cana-5314	149	12	indicates	indicate	VERB
cana-5314	149	13	that	that	SCONJ
cana-5314	149	14	tsp	tsp	NOUN
cana-5314	149	15	,	,	PUNCT
cana-5314	149	16	knapsack	knapsack	NOUN
cana-5314	149	17	and	and	CCONJ
cana-5314	149	18	sat	sit	VERB
cana-5314	149	19	problems	problem	NOUN
cana-5314	149	20	alongside	alongside	ADP
cana-5314	149	21	other	other	ADJ
cana-5314	149	22	np	np	PROPN
cana-5314	149	23	-	-	PUNCT
cana-5314	149	24	complete	complete	ADJ
cana-5314	149	25	problems	problem	NOUN
cana-5314	149	26	can	can	AUX
cana-5314	149	27	not	not	PART
cana-5314	149	28	be	be	AUX
cana-5314	149	29	solved	solve	VERB
cana-5314	149	30	within	within	ADP
cana-5314	149	31	polynomial	polynomial	ADJ
cana-5314	149	32	time	time	NOUN
cana-5314	149	33	.	.	PUNCT
cana-5314	150	1	research	research	NOUN
cana-5314	150	2	results	result	NOUN
cana-5314	150	3	confirm	confirm	VERB
cana-5314	150	4	the	the	DET
cana-5314	150	5	hypothesis	hypothesis	NOUN
cana-5314	150	6	which	which	PRON
cana-5314	150	7	states	state	VERB
cana-5314	150	8	p	p	NOUN
cana-5314	150	9	is	be	AUX
cana-5314	150	10	not	not	PART
cana-5314	150	11	equal	equal	ADJ
cana-5314	150	12	to	to	ADP
cana-5314	150	13	np	np	PRON
cana-5314	150	14	thus	thus	ADV
cana-5314	150	15	demonstrating	demonstrate	VERB
cana-5314	150	16	the	the	DET
cana-5314	150	17	difficulty	difficulty	NOUN
cana-5314	150	18	computational	computational	ADJ
cana-5314	150	19	complexity	complexity	NOUN
cana-5314	150	20	theory	theory	NOUN
cana-5314	150	21	faces	face	VERB
cana-5314	150	22	when	when	SCONJ
cana-5314	150	23	trying	try	VERB
cana-5314	150	24	to	to	PART
cana-5314	150	25	classify	classify	VERB
cana-5314	150	26	and	and	CCONJ
cana-5314	150	27	solve	solve	VERB
cana-5314	150	28	np	np	ADV
cana-5314	150	29	-	-	PUNCT
cana-5314	150	30	complete	complete	ADJ
cana-5314	150	31	problems	problem	NOUN
cana-5314	150	32	.	.	PUNCT
cana-5314	151	1	studies	study	NOUN
cana-5314	151	2	on	on	ADP
cana-5314	151	3	both	both	CCONJ
cana-5314	151	4	dynamic	dynamic	ADJ
cana-5314	151	5	programming	programming	NOUN
cana-5314	151	6	and	and	CCONJ
cana-5314	151	7	greedy	greedy	ADJ
cana-5314	151	8	algorithms	algorithm	NOUN
cana-5314	151	9	prove	prove	VERB
cana-5314	151	10	the	the	DET
cana-5314	151	11	complexity	complexity	NOUN
cana-5314	151	12	of	of	ADP
cana-5314	151	13	achieving	achieve	VERB
cana-5314	151	14	efficient	efficient	ADJ
cana-5314	151	15	solutions	solution	NOUN
cana-5314	151	16	for	for	ADP
cana-5314	151	17	large	large	ADJ
cana-5314	151	18	np	np	ADJ
cana-5314	151	19	-	-	PUNCT
cana-5314	151	20	complete	complete	ADJ
cana-5314	151	21	problems	problem	NOUN
cana-5314	151	22	even	even	ADV
cana-5314	151	23	when	when	SCONJ
cana-5314	151	24	polynomial	polynomial	ADJ
cana-5314	151	25	-	-	PUNCT
cana-5314	151	26	time	time	NOUN
cana-5314	151	27	answers	answer	NOUN
cana-5314	151	28	remain	remain	VERB
cana-5314	151	29	out	out	ADP
cana-5314	151	30	of	of	ADP
cana-5314	151	31	reach	reach	NOUN
cana-5314	151	32	.	.	PUNCT
cana-5314	152	1	the	the	DET
cana-5314	152	2	conclusions	conclusion	NOUN
cana-5314	152	3	from	from	ADP
cana-5314	152	4	our	our	PRON
cana-5314	152	5	computational	computational	ADJ
cana-5314	152	6	tests	test	NOUN
cana-5314	152	7	possess	possess	VERB
cana-5314	152	8	distinct	distinct	ADJ
cana-5314	152	9	value	value	NOUN
cana-5314	152	10	for	for	ADP
cana-5314	152	11	domains	domain	NOUN
cana-5314	152	12	dependent	dependent	ADJ
cana-5314	152	13	on	on	ADP
cana-5314	152	14	np	np	ADJ
cana-5314	152	15	-	-	PUNCT
cana-5314	152	16	complete	complete	ADJ
cana-5314	152	17	problems	problem	NOUN
cana-5314	152	18	including	include	VERB
cana-5314	152	19	cryptography	cryptography	NOUN
cana-5314	152	20	and	and	CCONJ
cana-5314	152	21	optimization	optimization	NOUN
cana-5314	152	22	.	.	PUNCT
cana-5314	153	1	the	the	DET
cana-5314	153	2	exploration	exploration	NOUN
cana-5314	153	3	of	of	ADP
cana-5314	153	4	these	these	DET
cana-5314	153	5	problems	problem	NOUN
cana-5314	153	6	requires	require	VERB
cana-5314	153	7	breakthroughs	breakthrough	NOUN
cana-5314	153	8	to	to	PART
cana-5314	153	9	determine	determine	VERB
cana-5314	153	10	p	p	NOUN
cana-5314	153	11	equals	equal	VERB
cana-5314	153	12	np	np	PRON
cana-5314	153	13	status	status	NOUN
cana-5314	153	14	or	or	CCONJ
cana-5314	153	15	to	to	PART
cana-5314	153	16	develop	develop	VERB
cana-5314	153	17	more	more	ADV
cana-5314	153	18	effective	effective	ADJ
cana-5314	153	19	methods	method	NOUN
cana-5314	153	20	that	that	PRON
cana-5314	153	21	solve	solve	VERB
cana-5314	153	22	np	np	NOUN
cana-5314	153	23	-	-	PUNCT
cana-5314	153	24	complete	complete	ADJ
cana-5314	153	25	problems	problem	NOUN
cana-5314	153	26	.	.	PUNCT
cana-5314	154	1	this	this	DET
cana-5314	154	2	experimental	experimental	ADJ
cana-5314	154	3	study	study	NOUN
cana-5314	154	4	helps	help	VERB
cana-5314	154	5	advance	advance	VERB
cana-5314	154	6	ongoing	ongoing	ADJ
cana-5314	154	7	research	research	NOUN
cana-5314	154	8	about	about	ADP
cana-5314	154	9	computational	computational	ADJ
cana-5314	154	10	complexity	complexity	NOUN
cana-5314	154	11	by	by	ADP
cana-5314	154	12	creating	create	VERB
cana-5314	154	13	a	a	DET
cana-5314	154	14	basis	basis	NOUN
cana-5314	154	15	for	for	ADP
cana-5314	154	16	potential	potential	ADJ
cana-5314	154	17	solutions	solution	NOUN
cana-5314	154	18	which	which	PRON
cana-5314	154	19	could	could	AUX
cana-5314	154	20	eventually	eventually	ADV
cana-5314	154	21	determine	determine	VERB
cana-5314	154	22	p	p	PROPN
cana-5314	154	23	versus	versus	ADP
cana-5314	154	24	np	np	PROPN
cana-5314	154	25	.	.	PROPN
cana-5314	154	26	table	table	NOUN
cana-5314	155	1	2	2	NUM
cana-5314	155	2	:	:	PUNCT
cana-5314	155	3	computational	computational	ADJ
cana-5314	155	4	time	time	NOUN
cana-5314	155	5	for	for	SCONJ
cana-5314	155	6	sat	sit	VERB
cana-5314	155	7	problem	problem	NOUN
cana-5314	155	8	reductions	reduction	NOUN
cana-5314	155	9	sat	sit	VERB
cana-5314	155	10	problem	problem	NOUN
cana-5314	155	11	size	size	NOUN
cana-5314	155	12	(	(	PUNCT
cana-5314	155	13	variables	variable	NOUN
cana-5314	155	14	)	)	PUNCT
cana-5314	155	15	reduction	reduction	NOUN
cana-5314	155	16	time	time	NOUN
cana-5314	155	17	(	(	PUNCT
cana-5314	155	18	seconds	second	NOUN
cana-5314	155	19	)	)	PUNCT
cana-5314	155	20	total	total	ADJ
cana-5314	155	21	time	time	NOUN
cana-5314	155	22	(	(	PUNCT
cana-5314	155	23	seconds	second	NOUN
cana-5314	155	24	)	)	PUNCT
cana-5314	155	25	10	10	NUM
cana-5314	155	26	0.2	0.2	NUM
cana-5314	155	27	1.0	1.0	NUM
cana-5314	155	28	20	20	NUM
cana-5314	155	29	0.5	0.5	NUM
cana-5314	155	30	3.2	3.2	NUM
cana-5314	155	31	50	50	NUM
cana-5314	155	32	3.0	3.0	NUM
cana-5314	155	33	12.8	12.8	NUM
cana-5314	155	34	100	100	NUM
cana-5314	155	35	15.0	15.0	NUM
cana-5314	155	36	52.5	52.5	NUM
cana-5314	155	37	0.2	0.2	NUM
cana-5314	155	38	0.5	0.5	NUM
cana-5314	155	39	3	3	NUM
cana-5314	155	40	1	1	NUM
cana-5314	155	41	3.2	3.2	NUM
cana-5314	155	42	12.8	12.8	NUM
cana-5314	155	43	0	0	NUM
cana-5314	155	44	2	2	NUM
cana-5314	155	45	4	4	NUM
cana-5314	155	46	6	6	NUM
cana-5314	155	47	8	8	NUM
cana-5314	155	48	10	10	NUM
cana-5314	155	49	12	12	NUM
cana-5314	155	50	14	14	NUM
cana-5314	155	51	10	10	NUM
cana-5314	155	52	20	20	NUM
cana-5314	155	53	50	50	NUM
cana-5314	155	54	computational	computational	ADJ
cana-5314	155	55	time	time	NOUN
cana-5314	155	56	for	for	SCONJ
cana-5314	155	57	sat	sit	VERB
cana-5314	155	58	problem	problem	NOUN
cana-5314	155	59	reductions	reduction	NOUN
cana-5314	155	60	reduction	reduction	NOUN
cana-5314	155	61	time	time	NOUN
cana-5314	155	62	(	(	PUNCT
cana-5314	155	63	seconds	second	NOUN
cana-5314	155	64	)	)	PUNCT
cana-5314	155	65	total	total	ADJ
cana-5314	155	66	time	time	NOUN
cana-5314	155	67	(	(	PUNCT
cana-5314	155	68	seconds	second	NOUN
cana-5314	155	69	)	)	PUNCT
cana-5314	155	70	communications	communication	NOUN
cana-5314	155	71	on	on	ADP
cana-5314	155	72	applied	apply	VERB
cana-5314	155	73	nonlinear	nonlinear	ADJ
cana-5314	155	74	analysis	analysis	NOUN
cana-5314	155	75	issn	issn	NOUN
cana-5314	155	76	:	:	PUNCT
cana-5314	155	77	1074	1074	NUM
cana-5314	155	78	-	-	PUNCT
cana-5314	155	79	133x	133x	NUM
cana-5314	155	80	vol	vol	NOUN
cana-5314	155	81	31	31	NUM
cana-5314	155	82	no	no	NOUN
cana-5314	155	83	.	.	PUNCT
cana-5314	156	1	8s	8s	PROPN
cana-5314	156	2	(	(	PUNCT
cana-5314	156	3	2024	2024	NUM
cana-5314	156	4	)	)	PUNCT
cana-5314	156	5	955	955	NUM
cana-5314	156	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5314	156	7	the	the	DET
cana-5314	156	8	experimental	experimental	ADJ
cana-5314	156	9	data	datum	NOUN
cana-5314	156	10	strengthens	strengthen	VERB
cana-5314	156	11	the	the	DET
cana-5314	156	12	understanding	understanding	NOUN
cana-5314	156	13	that	that	PRON
cana-5314	156	14	np	np	ADJ
cana-5314	156	15	-	-	PUNCT
cana-5314	156	16	complete	complete	ADJ
cana-5314	156	17	problems	problem	NOUN
cana-5314	156	18	possess	possess	VERB
cana-5314	156	19	fundamental	fundamental	ADJ
cana-5314	156	20	characteristics	characteristic	NOUN
cana-5314	156	21	which	which	PRON
cana-5314	156	22	prevent	prevent	VERB
cana-5314	156	23	them	they	PRON
cana-5314	156	24	from	from	ADP
cana-5314	156	25	having	have	VERB
cana-5314	156	26	polynomial	polynomial	ADJ
cana-5314	156	27	runtime	runtime	NOUN
cana-5314	156	28	solutions	solution	NOUN
cana-5314	156	29	.	.	PUNCT
cana-5314	157	1	p	p	X
cana-5314	157	2	=	=	PUNCT
cana-5314	157	3	np	np	PROPN
cana-5314	157	4	stands	stand	VERB
cana-5314	157	5	as	as	ADP
cana-5314	157	6	one	one	NUM
cana-5314	157	7	of	of	ADP
cana-5314	157	8	the	the	DET
cana-5314	157	9	most	most	ADV
cana-5314	157	10	complex	complex	ADJ
cana-5314	157	11	theoretical	theoretical	ADJ
cana-5314	157	12	challenges	challenge	NOUN
cana-5314	157	13	today	today	NOUN
cana-5314	157	14	while	while	SCONJ
cana-5314	157	15	leaving	leave	VERB
cana-5314	157	16	ample	ample	ADJ
cana-5314	157	17	space	space	NOUN
cana-5314	157	18	for	for	ADP
cana-5314	157	19	improvement	improvement	NOUN
cana-5314	157	20	in	in	ADP
cana-5314	157	21	resolving	resolve	VERB
cana-5314	157	22	the	the	DET
cana-5314	157	23	question	question	NOUN
cana-5314	157	24	.	.	PUNCT
cana-5314	158	1	v.	v.	ADP
cana-5314	158	2	conclusion	conclusion	NOUN
cana-5314	158	3	computer	computer	NOUN
cana-5314	158	4	science	science	NOUN
cana-5314	158	5	's	's	PART
cana-5314	158	6	main	main	ADJ
cana-5314	158	7	unresolved	unresolved	ADJ
cana-5314	158	8	issue	issue	NOUN
cana-5314	158	9	retains	retain	VERB
cana-5314	158	10	the	the	DET
cana-5314	158	11	p	p	NOUN
cana-5314	158	12	vs.	vs.	ADP
cana-5314	158	13	np	np	INTJ
cana-5314	158	14	problem	problem	NOUN
cana-5314	158	15	as	as	SCONJ
cana-5314	158	16	it	it	PRON
cana-5314	158	17	defines	define	VERB
cana-5314	158	18	the	the	DET
cana-5314	158	19	boundary	boundary	NOUN
cana-5314	158	20	between	between	ADP
cana-5314	158	21	efficient	efficient	ADJ
cana-5314	158	22	computation	computation	NOUN
cana-5314	158	23	and	and	CCONJ
cana-5314	158	24	unsolvable	unsolvable	ADJ
cana-5314	158	25	problems	problem	NOUN
cana-5314	158	26	.	.	PUNCT
cana-5314	159	1	the	the	DET
cana-5314	159	2	problem	problem	NOUN
cana-5314	159	3	's	's	PART
cana-5314	159	4	analysis	analysis	NOUN
cana-5314	159	5	affects	affect	VERB
cana-5314	159	6	security	security	NOUN
cana-5314	159	7	practices	practice	NOUN
cana-5314	159	8	together	together	ADV
cana-5314	159	9	with	with	ADP
cana-5314	159	10	optimization	optimization	NOUN
cana-5314	159	11	processes	process	NOUN
cana-5314	159	12	and	and	CCONJ
cana-5314	159	13	theoretical	theoretical	ADJ
cana-5314	159	14	computer	computer	NOUN
cana-5314	159	15	science	science	NOUN
cana-5314	159	16	along	along	ADP
cana-5314	159	17	with	with	ADP
cana-5314	159	18	philosophical	philosophical	ADJ
cana-5314	159	19	considerations	consideration	NOUN
cana-5314	159	20	.	.	PUNCT
cana-5314	160	1	this	this	DET
cana-5314	160	2	research	research	NOUN
cana-5314	160	3	first	first	ADV
cana-5314	160	4	conducted	conduct	VERB
cana-5314	160	5	an	an	DET
cana-5314	160	6	overview	overview	NOUN
cana-5314	160	7	of	of	ADP
cana-5314	160	8	problem	problem	NOUN
cana-5314	160	9	development	development	NOUN
cana-5314	160	10	before	before	ADP
cana-5314	160	11	evaluating	evaluate	VERB
cana-5314	160	12	scholarly	scholarly	ADJ
cana-5314	160	13	work	work	NOUN
cana-5314	160	14	and	and	CCONJ
cana-5314	160	15	examining	examine	VERB
cana-5314	160	16	important	important	ADJ
cana-5314	160	17	theoretical	theoretical	ADJ
cana-5314	160	18	approaches	approach	NOUN
cana-5314	160	19	.	.	PUNCT
cana-5314	161	1	endless	endless	ADJ
cana-5314	161	2	research	research	NOUN
cana-5314	161	3	supports	support	VERB
cana-5314	161	4	the	the	DET
cana-5314	161	5	belief	belief	NOUN
cana-5314	161	6	that	that	SCONJ
cana-5314	161	7	p	p	NOUN
cana-5314	161	8	does	do	AUX
cana-5314	161	9	not	not	PART
cana-5314	161	10	equal	equal	VERB
cana-5314	161	11	np	np	INTJ
cana-5314	161	12	through	through	ADP
cana-5314	161	13	both	both	CCONJ
cana-5314	161	14	empirical	empirical	ADJ
cana-5314	161	15	and	and	CCONJ
cana-5314	161	16	theoretical	theoretical	ADJ
cana-5314	161	17	studies	study	NOUN
cana-5314	161	18	even	even	ADV
cana-5314	161	19	though	though	SCONJ
cana-5314	161	20	p≠np	p≠np	NOUN
cana-5314	161	21	remains	remain	VERB
cana-5314	161	22	unproven	unproven	ADJ
cana-5314	161	23	.	.	PUNCT
cana-5314	162	1	additional	additional	ADJ
cana-5314	162	2	research	research	NOUN
cana-5314	162	3	might	might	AUX
cana-5314	162	4	achieve	achieve	VERB
cana-5314	162	5	its	its	PRON
cana-5314	162	6	goals	goal	NOUN
cana-5314	162	7	by	by	ADP
cana-5314	162	8	studying	study	VERB
cana-5314	162	9	nonconventional	nonconventional	ADJ
cana-5314	162	10	computation	computation	NOUN
cana-5314	162	11	models	model	NOUN
cana-5314	162	12	and	and	CCONJ
cana-5314	162	13	proof	proof	NOUN
cana-5314	162	14	theory	theory	NOUN
cana-5314	162	15	developments	development	NOUN
cana-5314	162	16	as	as	ADV
cana-5314	162	17	well	well	ADV
cana-5314	162	18	as	as	ADP
cana-5314	162	19	implementing	implement	VERB
cana-5314	162	20	quantum	quantum	NOUN
cana-5314	162	21	computing	computing	NOUN
cana-5314	162	22	approaches	approach	NOUN
cana-5314	162	23	to	to	PART
cana-5314	162	24	discover	discover	VERB
cana-5314	162	25	new	new	ADJ
cana-5314	162	26	findings	finding	NOUN
cana-5314	162	27	.	.	PUNCT
cana-5314	163	1	references	reference	NOUN
cana-5314	163	2	[	[	X
cana-5314	163	3	1	1	NUM
cana-5314	163	4	]	]	PUNCT
cana-5314	163	5	m.	m.	NOUN
cana-5314	163	6	o.	o.	PROPN
cana-5314	163	7	ball	ball	PROPN
cana-5314	163	8	,	,	PUNCT
cana-5314	163	9	“	"	PUNCT
cana-5314	163	10	computational	computational	ADJ
cana-5314	163	11	complexity	complexity	NOUN
cana-5314	163	12	of	of	ADP
cana-5314	163	13	network	network	NOUN
cana-5314	163	14	reliability	reliability	NOUN
cana-5314	163	15	analysis	analysis	NOUN
cana-5314	163	16	:	:	PUNCT
cana-5314	163	17	an	an	DET
cana-5314	163	18	overview	overview	NOUN
cana-5314	163	19	,	,	PUNCT
cana-5314	163	20	”	"	PUNCT
cana-5314	163	21	ieee	ieee	NOUN
cana-5314	163	22	transactions	transaction	NOUN
cana-5314	163	23	on	on	ADP
cana-5314	163	24	reliability	reliability	NOUN
cana-5314	163	25	,	,	PUNCT
cana-5314	163	26	vol	vol	NOUN
cana-5314	163	27	.	.	PROPN
cana-5314	163	28	35	35	NUM
cana-5314	163	29	,	,	PUNCT
cana-5314	163	30	no	no	INTJ
cana-5314	163	31	.	.	NOUN
cana-5314	163	32	3	3	NUM
cana-5314	163	33	,	,	PUNCT
cana-5314	163	34	pp	pp	ADJ
cana-5314	163	35	.	.	PUNCT
cana-5314	164	1	230–239	230–239	NUM
cana-5314	164	2	,	,	PUNCT
cana-5314	164	3	jan	jan	PROPN
cana-5314	164	4	.	.	PROPN
cana-5314	164	5	1986	1986	NUM
cana-5314	164	6	,	,	PUNCT
cana-5314	164	7	doi	doi	NOUN
cana-5314	164	8	:	:	PUNCT
cana-5314	164	9	10.1109	10.1109	NUM
cana-5314	164	10	/	/	SYM
cana-5314	164	11	tr.1986.4335422	tr.1986.4335422	NOUN
cana-5314	164	12	.	.	PUNCT
cana-5314	165	1	[	[	X
cana-5314	165	2	2	2	X
cana-5314	165	3	]	]	PUNCT
cana-5314	165	4	t.	t.	PROPN
cana-5314	165	5	sahai	sahai	NOUN
cana-5314	165	6	,	,	PUNCT
cana-5314	165	7	“	"	PUNCT
cana-5314	165	8	dynamical	dynamical	ADJ
cana-5314	165	9	systems	system	NOUN
cana-5314	165	10	theory	theory	NOUN
cana-5314	165	11	and	and	CCONJ
cana-5314	165	12	algorithms	algorithm	NOUN
cana-5314	165	13	for	for	ADP
cana-5314	165	14	np	np	NOUN
cana-5314	165	15	-	-	PUNCT
cana-5314	165	16	hard	hard	ADJ
cana-5314	165	17	problems	problem	NOUN
cana-5314	165	18	,	,	PUNCT
cana-5314	165	19	”	"	PUNCT
cana-5314	165	20	in	in	ADP
cana-5314	165	21	studies	study	NOUN
cana-5314	165	22	in	in	ADP
cana-5314	165	23	systems	system	NOUN
cana-5314	165	24	,	,	PUNCT
cana-5314	165	25	decision	decision	NOUN
cana-5314	165	26	and	and	CCONJ
cana-5314	165	27	control	control	NOUN
cana-5314	165	28	,	,	PUNCT
cana-5314	165	29	2020	2020	NUM
cana-5314	165	30	,	,	PUNCT
cana-5314	165	31	pp	pp	ADV
cana-5314	165	32	.	.	PUNCT
cana-5314	166	1	183–206	183–206	NUM
cana-5314	166	2	.	.	PUNCT
cana-5314	167	1	doi	doi	NOUN
cana-5314	167	2	:	:	PUNCT
cana-5314	167	3	10.1007/978	10.1007/978	NUM
cana-5314	167	4	-	-	SYM
cana-5314	167	5	3	3	NUM
cana-5314	167	6	-	-	PUNCT
cana-5314	167	7	03051264	03051264	NUM
cana-5314	167	8	-	-	PUNCT
cana-5314	167	9	4_8	4_8	NUM
cana-5314	167	10	.	.	PUNCT
cana-5314	168	1	[	[	X
cana-5314	168	2	3	3	X
cana-5314	168	3	]	]	X
cana-5314	168	4	d.	d.	PROPN
cana-5314	168	5	gamarnik	gamarnik	PROPN
cana-5314	168	6	,	,	PUNCT
cana-5314	168	7	c.	c.	PROPN
cana-5314	168	8	moore	moore	PROPN
cana-5314	168	9	,	,	PUNCT
cana-5314	168	10	and	and	CCONJ
cana-5314	168	11	l.	l.	PROPN
cana-5314	168	12	zdeborová	zdeborová	PROPN
cana-5314	168	13	,	,	PUNCT
cana-5314	168	14	“	"	PUNCT
cana-5314	168	15	disordered	disordered	ADJ
cana-5314	168	16	systems	system	NOUN
cana-5314	168	17	insights	insight	NOUN
cana-5314	168	18	on	on	ADP
cana-5314	168	19	computational	computational	ADJ
cana-5314	168	20	hardness	hardness	NOUN
cana-5314	168	21	,	,	PUNCT
cana-5314	168	22	”	"	PUNCT
cana-5314	168	23	journal	journal	NOUN
cana-5314	168	24	of	of	ADP
cana-5314	168	25	statistical	statistical	ADJ
cana-5314	168	26	mechanics	mechanic	NOUN
cana-5314	168	27	theory	theory	NOUN
cana-5314	168	28	and	and	CCONJ
cana-5314	168	29	experiment	experiment	NOUN
cana-5314	168	30	,	,	PUNCT
cana-5314	168	31	vol	vol	NOUN
cana-5314	168	32	.	.	PROPN
cana-5314	168	33	2022	2022	NUM
cana-5314	168	34	,	,	PUNCT
cana-5314	168	35	no	no	INTJ
cana-5314	168	36	.	.	NOUN
cana-5314	168	37	11	11	NUM
cana-5314	168	38	,	,	PUNCT
cana-5314	168	39	p.	p.	NOUN
cana-5314	168	40	114015	114015	NUM
cana-5314	168	41	,	,	PUNCT
cana-5314	168	42	nov	nov	PROPN
cana-5314	168	43	.	.	PROPN
cana-5314	168	44	2022	2022	NUM
cana-5314	168	45	,	,	PUNCT
cana-5314	168	46	doi	doi	NOUN
cana-5314	168	47	:	:	PUNCT
cana-5314	168	48	10.1088/1742	10.1088/1742	NUM
cana-5314	168	49	-	-	SYM
cana-5314	168	50	5468	5468	NUM
cana-5314	168	51	/	/	SYM
cana-5314	168	52	ac9cc8	ac9cc8	ADJ
cana-5314	168	53	.	.	PUNCT
cana-5314	169	1	[	[	X
cana-5314	169	2	4	4	X
cana-5314	169	3	]	]	PUNCT
cana-5314	169	4	k.	k.	PROPN
cana-5314	169	5	a.	a.	PROPN
cana-5314	169	6	smith	smith	PROPN
cana-5314	169	7	-	-	PUNCT
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cana-5314	169	9	,	,	PUNCT
cana-5314	169	10	“	"	PUNCT
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cana-5314	169	17	-	-	PUNCT
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cana-5314	169	19	for	for	ADP
cana-5314	169	20	algorithm	algorithm	NOUN
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cana-5314	169	22	,	,	PUNCT
cana-5314	169	23	”	"	PUNCT
cana-5314	169	24	acm	acm	PROPN
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cana-5314	169	26	surveys	survey	NOUN
cana-5314	169	27	,	,	PUNCT
cana-5314	169	28	vol	vol	NOUN
cana-5314	169	29	.	.	PROPN
cana-5314	169	30	41	41	NUM
cana-5314	169	31	,	,	PUNCT
cana-5314	169	32	no	no	INTJ
cana-5314	169	33	.	.	NOUN
cana-5314	169	34	1	1	NUM
cana-5314	169	35	,	,	PUNCT
cana-5314	169	36	pp	pp	ADJ
cana-5314	169	37	.	.	PUNCT
cana-5314	170	1	1–25	1–25	ADJ
cana-5314	170	2	,	,	PUNCT
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cana-5314	170	4	.	.	PROPN
cana-5314	170	5	2009	2009	NUM
cana-5314	170	6	,	,	PUNCT
cana-5314	170	7	doi	doi	NOUN
cana-5314	170	8	:	:	PUNCT
cana-5314	170	9	10.1145/1456650.1456656	10.1145/1456650.1456656	NUM
cana-5314	170	10	.	.	PUNCT
cana-5314	171	1	[	[	X
cana-5314	171	2	5	5	NUM
cana-5314	171	3	]	]	PUNCT
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cana-5314	171	6	,	,	PUNCT
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cana-5314	171	8	a.	a.	NOUN
cana-5314	171	9	aloulou	aloulou	PROPN
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cana-5314	171	11	and	and	CCONJ
cana-5314	171	12	m.	m.	PROPN
cana-5314	171	13	y.	y.	PROPN
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cana-5314	171	15	,	,	PUNCT
cana-5314	171	16	“	"	PUNCT
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cana-5314	171	19	scheduling	scheduling	NOUN
cana-5314	171	20	and	and	CCONJ
cana-5314	171	21	batch	batch	NOUN
cana-5314	171	22	delivery	delivery	NOUN
cana-5314	171	23	with	with	ADP
cana-5314	171	24	fixed	fix	VERB
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cana-5314	171	26	times	time	NOUN
cana-5314	171	27	and	and	CCONJ
cana-5314	171	28	inventory	inventory	NOUN
cana-5314	171	29	holding	hold	VERB
cana-5314	171	30	costs	cost	NOUN
cana-5314	171	31	,	,	PUNCT
cana-5314	171	32	”	"	PUNCT
cana-5314	171	33	international	international	ADJ
cana-5314	171	34	journal	journal	NOUN
cana-5314	171	35	of	of	ADP
cana-5314	171	36	production	production	NOUN
cana-5314	171	37	research	research	NOUN
cana-5314	171	38	,	,	PUNCT
cana-5314	171	39	vol	vol	NOUN
cana-5314	171	40	.	.	PROPN
cana-5314	172	1	55	55	NUM
cana-5314	172	2	,	,	PUNCT
cana-5314	172	3	no	no	INTJ
cana-5314	172	4	.	.	NOUN
cana-5314	172	5	20	20	NUM
cana-5314	172	6	,	,	PUNCT
cana-5314	172	7	pp	pp	ADJ
cana-5314	172	8	.	.	PUNCT
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cana-5314	173	2	,	,	PUNCT
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cana-5314	173	4	.	.	PROPN
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cana-5314	173	6	,	,	PUNCT
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cana-5314	173	8	:	:	PUNCT
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cana-5314	173	10	.	.	PUNCT
cana-5314	174	1	[	[	X
cana-5314	174	2	6	6	NUM
cana-5314	174	3	]	]	PUNCT
cana-5314	174	4	m.	m.	NOUN
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cana-5314	174	10	“	"	PUNCT
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cana-5314	174	12	for	for	ADP
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cana-5314	174	14	manufacturing	manufacturing	NOUN
cana-5314	174	15	:	:	PUNCT
cana-5314	174	16	a	a	DET
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cana-5314	174	18	,	,	PUNCT
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cana-5314	174	20	journal	journal	NOUN
cana-5314	174	21	of	of	ADP
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cana-5314	174	23	production	production	NOUN
cana-5314	174	24	,	,	PUNCT
cana-5314	174	25	vol	vol	NOUN
cana-5314	174	26	.	.	PROPN
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cana-5314	174	28	,	,	PUNCT
cana-5314	174	29	pp	pp	ADJ
cana-5314	174	30	.	.	PUNCT
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cana-5314	175	2	,	,	PUNCT
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cana-5314	175	4	.	.	PROPN
cana-5314	175	5	2018	2018	NUM
cana-5314	175	6	,	,	PUNCT
cana-5314	175	7	doi	doi	NOUN
cana-5314	175	8	:	:	PUNCT
cana-5314	175	9	10.1016	10.1016	NUM
cana-5314	175	10	/	/	SYM
cana-5314	175	11	j.jclepro.2018.09.100	j.jclepro.2018.09.100	PROPN
cana-5314	175	12	.	.	PUNCT
cana-5314	176	1	communications	communication	NOUN
cana-5314	176	2	on	on	ADP
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cana-5314	176	7	:	:	PUNCT
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cana-5314	176	9	-	-	PUNCT
cana-5314	176	10	133x	133x	NUM
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cana-5314	176	12	31	31	NUM
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cana-5314	176	14	.	.	PUNCT
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cana-5314	177	2	(	(	PUNCT
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cana-5314	177	4	)	)	PUNCT
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cana-5314	178	1	[	[	X
cana-5314	178	2	7	7	X
cana-5314	178	3	]	]	X
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cana-5314	178	8	a.	a.	PROPN
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cana-5314	178	14	processing	processing	NOUN
cana-5314	178	15	time	time	NOUN
cana-5314	178	16	dissimilarity	dissimilarity	NOUN
cana-5314	178	17	in	in	ADP
cana-5314	178	18	batch	batch	NOUN
cana-5314	178	19	-	-	PUNCT
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cana-5314	178	21	scheduling	scheduling	NOUN
cana-5314	178	22	of	of	ADP
cana-5314	178	23	flowshop	flowshop	ADJ
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cana-5314	178	25	,	,	PUNCT
cana-5314	178	26	”	"	PUNCT
cana-5314	178	27	international	international	ADJ
cana-5314	178	28	journal	journal	NOUN
cana-5314	178	29	of	of	ADP
cana-5314	178	30	production	production	NOUN
cana-5314	178	31	research	research	NOUN
cana-5314	178	32	,	,	PUNCT
cana-5314	178	33	vol	vol	NOUN
cana-5314	178	34	.	.	PROPN
cana-5314	179	1	59	59	NUM
cana-5314	179	2	,	,	PUNCT
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cana-5314	179	5	21	21	NUM
cana-5314	179	6	,	,	PUNCT
cana-5314	179	7	pp	pp	ADJ
cana-5314	179	8	.	.	PUNCT
cana-5314	180	1	6544–6563	6544–6563	NUM
cana-5314	180	2	,	,	PUNCT
cana-5314	180	3	sep	sep	PROPN
cana-5314	180	4	.	.	PROPN
cana-5314	181	1	2020	2020	NUM
cana-5314	181	2	,	,	PUNCT
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cana-5314	181	4	:	:	PUNCT
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cana-5314	182	1	[	[	X
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cana-5314	182	20	“	"	PUNCT
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cana-5314	182	23	-	-	PUNCT
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cana-5314	182	32	time	time	NOUN
cana-5314	182	33	window	window	NOUN
cana-5314	182	34	and	and	CCONJ
cana-5314	182	35	employee	employee	NOUN
cana-5314	182	36	timetable	timetable	NOUN
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cana-5314	182	38	,	,	PUNCT
cana-5314	182	39	”	"	PUNCT
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cana-5314	182	44	,	,	PUNCT
cana-5314	182	45	vol	vol	NOUN
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cana-5314	182	47	186	186	NUM
cana-5314	182	48	,	,	PUNCT
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cana-5314	183	3	]	]	X
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cana-5314	183	11	,	,	PUNCT
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cana-5314	183	13	a.	a.	PROPN
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cana-5314	183	15	,	,	PUNCT
cana-5314	183	16	“	"	PUNCT
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cana-5314	183	27	with	with	ADP
cana-5314	183	28	sequence	sequence	NOUN
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cana-5314	183	42	167	167	NUM
cana-5314	183	43	,	,	PUNCT
cana-5314	183	44	p.	p.	NOUN
cana-5314	183	45	114137	114137	NUM
cana-5314	183	46	,	,	PUNCT
cana-5314	183	47	oct	oct	PROPN
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cana-5314	184	1	[	[	X
cana-5314	184	2	10	10	NUM
cana-5314	184	3	]	]	X
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cana-5314	184	10	“	"	PUNCT
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cana-5314	184	13	line	line	NOUN
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cana-5314	184	15	problems	problem	NOUN
cana-5314	184	16	:	:	PUNCT
cana-5314	184	17	a	a	DET
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cana-5314	184	32	,	,	PUNCT
cana-5314	184	33	vol	vol	NOUN
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cana-5314	184	35	250	250	NUM
cana-5314	184	36	,	,	PUNCT
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cana-5314	184	41	.	.	PROPN
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cana-5314	184	43	,	,	PUNCT
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cana-5314	184	45	:	:	PUNCT
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cana-5314	184	47	/	/	SYM
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cana-5314	185	1	[	[	X
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cana-5314	185	9	,	,	PUNCT
cana-5314	185	10	n.	n.	PROPN
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cana-5314	185	14	g.	g.	PROPN
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cana-5314	185	17	“	"	PUNCT
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cana-5314	185	20	of	of	ADP
cana-5314	185	21	machines	machine	NOUN
cana-5314	185	22	processing	processing	NOUN
cana-5314	185	23	pipeline	pipeline	NOUN
cana-5314	185	24	parts	part	NOUN
cana-5314	185	25	,	,	PUNCT
cana-5314	185	26	”	"	PUNCT
cana-5314	185	27	the	the	DET
cana-5314	185	28	international	international	ADJ
cana-5314	185	29	journal	journal	NOUN
cana-5314	185	30	of	of	ADP
cana-5314	185	31	advanced	advanced	ADJ
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cana-5314	185	33	technology	technology	NOUN
cana-5314	185	34	,	,	PUNCT
cana-5314	185	35	vol	vol	NOUN
cana-5314	185	36	.	.	PROPN
cana-5314	185	37	63	63	NUM
cana-5314	185	38	,	,	PUNCT
cana-5314	185	39	no	no	INTJ
cana-5314	185	40	.	.	PUNCT
cana-5314	185	41	9–12	9–12	PROPN
cana-5314	185	42	,	,	PUNCT
cana-5314	185	43	pp	pp	ADP
cana-5314	185	44	.	.	PUNCT
cana-5314	186	1	963–973	963–973	NUM
cana-5314	186	2	,	,	PUNCT
cana-5314	186	3	feb	feb	PROPN
cana-5314	186	4	.	.	PROPN
cana-5314	186	5	2012	2012	NUM
cana-5314	186	6	,	,	PUNCT
cana-5314	186	7	doi	doi	NOUN
cana-5314	186	8	:	:	PUNCT
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cana-5314	186	10	/	/	SYM
cana-5314	186	11	s00170	s00170	PROPN
cana-5314	186	12	-	-	PUNCT
cana-5314	186	13	012	012	NUM
cana-5314	186	14	-	-	PUNCT
cana-5314	186	15	3981y	3981y	NUM
cana-5314	186	16	.	.	PUNCT
cana-5314	187	1	[	[	X
cana-5314	187	2	12	12	NUM
cana-5314	187	3	]	]	PUNCT
cana-5314	187	4	a.	a.	NOUN
cana-5314	187	5	behrendt	behrendt	PROPN
cana-5314	187	6	,	,	PUNCT
cana-5314	187	7	m.	m.	NOUN
cana-5314	187	8	savelsbergh	savelsbergh	PROPN
cana-5314	187	9	,	,	PUNCT
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cana-5314	187	11	h.	h.	PROPN
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cana-5314	187	13	,	,	PUNCT
cana-5314	187	14	“	"	PUNCT
cana-5314	187	15	a	a	DET
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cana-5314	187	17	machine	machine	NOUN
cana-5314	187	18	learning	learning	NOUN
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cana-5314	187	21	courier	courier	NOUN
cana-5314	187	22	scheduling	scheduling	NOUN
cana-5314	187	23	on	on	ADP
cana-5314	187	24	crowdsourced	crowdsourced	ADJ
cana-5314	187	25	delivery	delivery	NOUN
cana-5314	187	26	platforms	platform	NOUN
cana-5314	187	27	,	,	PUNCT
cana-5314	187	28	”	"	PUNCT
cana-5314	187	29	transportation	transportation	NOUN
cana-5314	187	30	science	science	NOUN
cana-5314	187	31	,	,	PUNCT
cana-5314	187	32	vol	vol	NOUN
cana-5314	187	33	.	.	PROPN
cana-5314	187	34	57	57	NUM
cana-5314	187	35	,	,	PUNCT
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cana-5314	187	37	.	.	NOUN
cana-5314	187	38	4	4	NUM
cana-5314	187	39	,	,	PUNCT
cana-5314	187	40	pp	pp	ADJ
cana-5314	187	41	.	.	PUNCT
cana-5314	188	1	889–907	889–907	NUM
cana-5314	188	2	,	,	PUNCT
cana-5314	188	3	jun	jun	PROPN
cana-5314	188	4	.	.	PROPN
cana-5314	188	5	2022	2022	NUM
cana-5314	188	6	,	,	PUNCT
cana-5314	188	7	doi	doi	NOUN
cana-5314	188	8	:	:	PUNCT
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cana-5314	188	10	/	/	SYM
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cana-5314	189	2	13	13	NUM
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cana-5314	189	4	d.	d.	PROPN
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cana-5314	189	6	et	et	PROPN
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cana-5314	189	8	.	.	PROPN
cana-5314	189	9	,	,	PUNCT
cana-5314	189	10	“	"	PUNCT
cana-5314	189	11	the	the	DET
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cana-5314	189	13	of	of	ADP
cana-5314	189	14	industry	industry	NOUN
cana-5314	189	15	4.0	4.0	NUM
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cana-5314	189	19	for	for	ADP
cana-5314	189	20	manufacturing	manufacturing	NOUN
cana-5314	189	21	companies	company	NOUN
cana-5314	189	22	during	during	ADP
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cana-5314	189	24	,	,	PUNCT
cana-5314	189	25	”	"	PUNCT
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cana-5314	189	27	journal	journal	NOUN
cana-5314	189	28	of	of	ADP
cana-5314	189	29	production	production	NOUN
cana-5314	189	30	economics	economic	NOUN
cana-5314	189	31	,	,	PUNCT
cana-5314	189	32	vol	vol	NOUN
cana-5314	189	33	.	.	PROPN
cana-5314	189	34	256	256	NUM
cana-5314	189	35	,	,	PUNCT
cana-5314	189	36	p.	p.	NOUN
cana-5314	189	37	108728	108728	NUM
cana-5314	189	38	,	,	PUNCT
cana-5314	189	39	nov	nov	PROPN
cana-5314	189	40	.	.	PROPN
cana-5314	189	41	2022	2022	NUM
cana-5314	189	42	,	,	PUNCT
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cana-5314	189	44	:	:	PUNCT
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cana-5314	189	46	/	/	SYM
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cana-5314	189	48	.	.	PUNCT
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cana-5314	190	3	]	]	PUNCT
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cana-5314	190	10	x.	x.	PROPN
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cana-5314	190	12	,	,	PUNCT
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cana-5314	190	16	,	,	PUNCT
cana-5314	190	17	“	"	PUNCT
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cana-5314	190	22	task	task	NOUN
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cana-5314	190	24	and	and	CCONJ
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cana-5314	190	29	-	-	PUNCT
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cana-5314	190	33	assembly	assembly	NOUN
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cana-5314	190	35	,	,	PUNCT
cana-5314	190	36	”	"	PUNCT
cana-5314	190	37	international	international	ADJ
cana-5314	190	38	journal	journal	NOUN
cana-5314	190	39	of	of	ADP
cana-5314	190	40	production	production	NOUN
cana-5314	190	41	research	research	NOUN
cana-5314	190	42	,	,	PUNCT
cana-5314	190	43	vol	vol	NOUN
cana-5314	190	44	.	.	PROPN
cana-5314	190	45	61	61	NUM
cana-5314	190	46	,	,	PUNCT
cana-5314	190	47	no	no	INTJ
cana-5314	190	48	.	.	NOUN
cana-5314	190	49	21	21	NUM
cana-5314	190	50	,	,	PUNCT
cana-5314	190	51	pp	pp	ADJ
cana-5314	190	52	.	.	PUNCT
cana-5314	191	1	7213–7232	7213–7232	NUM
cana-5314	191	2	,	,	PUNCT
cana-5314	191	3	nov	nov	PROPN
cana-5314	191	4	.	.	PROPN
cana-5314	191	5	2022	2022	NUM
cana-5314	191	6	,	,	PUNCT
cana-5314	191	7	doi	doi	NOUN
cana-5314	191	8	:	:	PUNCT
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cana-5314	191	10	.	.	PUNCT
cana-5314	192	1	[	[	X
cana-5314	192	2	15	15	NUM
cana-5314	192	3	]	]	X
cana-5314	192	4	n.	n.	NOUN
cana-5314	192	5	chapados	chapado	NOUN
cana-5314	192	6	,	,	PUNCT
cana-5314	192	7	m.	m.	NOUN
cana-5314	192	8	joliveau	joliveau	PROPN
cana-5314	192	9	,	,	PUNCT
cana-5314	192	10	p.	p.	PROPN
cana-5314	192	11	l’ecuyer	l’ecuyer	PROPN
cana-5314	192	12	,	,	PUNCT
cana-5314	192	13	and	and	CCONJ
cana-5314	192	14	l.-m	l.-m	PROPN
cana-5314	192	15	.	.	PUNCT
cana-5314	193	1	rousseau	rousseau	PROPN
cana-5314	193	2	,	,	PUNCT
cana-5314	193	3	“	"	PUNCT
cana-5314	193	4	retail	retail	ADJ
cana-5314	193	5	store	store	NOUN
cana-5314	193	6	scheduling	scheduling	NOUN
cana-5314	193	7	for	for	ADP
cana-5314	193	8	profit	profit	NOUN
cana-5314	193	9	,	,	PUNCT
cana-5314	193	10	”	"	PUNCT
cana-5314	193	11	european	european	ADJ
cana-5314	193	12	journal	journal	PROPN
cana-5314	193	13	of	of	ADP
cana-5314	193	14	operational	operational	ADJ
cana-5314	193	15	research	research	NOUN
cana-5314	193	16	,	,	PUNCT
cana-5314	193	17	vol	vol	NOUN
cana-5314	193	18	.	.	PROPN
cana-5314	194	1	239	239	NUM
cana-5314	194	2	,	,	PUNCT
cana-5314	194	3	no	no	INTJ
cana-5314	194	4	.	.	NOUN
cana-5314	194	5	3	3	NUM
cana-5314	194	6	,	,	PUNCT
cana-5314	194	7	pp	pp	ADJ
cana-5314	194	8	.	.	PUNCT
cana-5314	195	1	609–624	609–624	NUM
cana-5314	195	2	,	,	PUNCT
cana-5314	195	3	jun	jun	PROPN
cana-5314	195	4	.	.	PROPN
cana-5314	195	5	2014	2014	NUM
cana-5314	195	6	,	,	PUNCT
cana-5314	195	7	doi	doi	NOUN
cana-5314	195	8	:	:	PUNCT
cana-5314	195	9	10.1016	10.1016	NUM
cana-5314	195	10	/	/	SYM
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cana-5314	195	12	.	.	PUNCT