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	co-np (Site not responding. Last check: 2007-11-07)
		Since all problems in NP can be reduced to this problem it follows that for all problems in NP we can construct a non-deterministic Turing machine that decides the complement of the problem in polynomial time, i.e., NP is a subset of co-NP.
		From this it follows that the set of complements of the problems in NP is a subset of the set of complements of the problems in co-NP, i.e., co-NP is a subset of NP.
		Since we already knew that NP is a subset of co-NP it follows that they are the same.
	www.yourencyclopedia.net /Co-NP.html (393 words)

	NP-complete - Wikipedia, the free encyclopedia
		To prove that a NP problem A is in fact a NP-complete problem we must show that an already known NP-complete problem reduces to A.
		This implies that NP = co-NP as is shown in the proof in the article on co-NP.
		Although the question of NP = co-NP is an open question it is considered unlikely and therefore it is also unlikely that the two definitions of NP-completeness are equivalent.
	en.wikipedia.org /wiki/NP-complete (1439 words)

	Co-NP - Wikipedia, the free encyclopedia
		In computational complexity theory, co-NP is a complexity class, the complement of the complexity class NP.
		NP and co-NP are also thought to be unequal.
		If a problem can be shown to be in both NP and co-NP, that is generally accepted as strong evidence that the problem is probably not NP-complete (since otherwise NP = co-NP).
	en.wikipedia.org /wiki/Co-NP (354 words)

	[No title]
		NP is like: "I don't know how to find it, but I'll know it when I see it" --> Traveling Salesman problem (TSP): Given graph G, find shortest tour that visits all the vertices exactly once.
		First of all it's in NP since a proof is just a satisfying assignment, and we can check by just running time circuit in time O(m) which is poly in size of input.
		Since Q' is in NP, there is by definition a polynomial-time verification algorithm A that takes an instance x of Q' and a proof y, and outputs 1 if y is a legal proof that x is a YES instance.
	www.cs.cmu.edu /afs/cs.cmu.edu/academic/class/15451-s99/www/lectures/lect0415 (1105 words)

	[No title]
		Specifically, Lillo-Martin argues that ASL allows Topic NP Deletion, i.e., for the topic of a sentence to be "deleted under identity with a topic of a preceding sentence" [Hua84], and that ASL plain verbs may have an EC subject/object as the result of topic movement.
		The point of central importance is that the deletion of an NP that co-refers with the topic of a previous sentence (or discourse topic) is not permissible in English, though it often is in ASL.
		To identify the referent of a missing NP, we treat the omitted NP (whose position in the sentence will be identified by syntactic analysis) as an anaphor which, like Sidner's treatment of full definite NP's and personal pronouns, co-specifies with an element recorded by the focusing algorithm.
	www.asel.udel.edu /nli/pubs/1992/Suri92.txt (11350 words)

	Solutions to practice questions for CSCI 6420 exam 2
		That is, NP is a subset of DP and DP is a subset of PSPACE.
		If P and NP are different then there does not exist a polynomial time algorithm to solve the vertex cover problem, since the vertex cover problem is NP-complete.
		It is not known whether or not Co-NP and NP are the same classes of problems.
	www.cs.ecu.edu /~karl/6420/spr04/solution2.html (1486 words)

	comp7713 NP-Completeness (Site not responding. Last check: 2007-11-07)
		NP is the set of problems for which there is polynomial-time verification algorithm.
		There are four possibilities for relationship among P, NP and co-NP, see Figure 36.2, P. 928 of the textbook.
		If the complexity of reduction algorithm itself is larger than that of the reduced problem, then it will dominate the complexity of the whole algorithm, and becomes less useful.
	www.msci.memphis.edu /~giri/7713/f99/jizhou2.htm (927 words)

	Co-NP - Wikipedia
		In complexity theory, Co-NP is the complement of the class NP.
		For every decision problem in NP, Co-NP contains the same decision problem with the YES and NO answers swapped.
		Equivalently, for every language in NP, Co-NP contains the complement of that language.
	nostalgia.wikipedia.org /wiki/Co-NP (151 words)

	Co-NP - Wikipedia
		La clase de complejidad P es un subconjunto tanto de NP como de co-NP y se piensa que la inclusión es estricta en ambos casos.
		Se piensa también que NP y co-NP son diferentes.
		De ser cierto esto, ningún problema de NP-completo podría estar en co-NP y ningún problema de co-NP-completo podría estar en NP.
	es.wikipedia.org /wiki/Co-NP (135 words)

	G12FCO -- Formal Computation, lecture 13
		If co-NP /= NP [as we expect], then there is quite a lot of known structure in the universe of problems.
		If NP /= P, then there is no efficient way to solve your problem, except by having the luck to guess a solution.
		If, against expectations, it turns out that NP = P, then we will know that there is a polynomial-time solution to your problem, and it is extremely likely that the proof will show us some way to construct it.
	www.maths.nott.ac.uk /personal/anw/G12FCO/lect13.html (1556 words)

	P, NP, CO-NP, NP-complete, NP-hard (Site not responding. Last check: 2007-11-07)
		NP is the set of decision problems solvable in polynomial time on a nondeterministic Turing machine.
		The complexity class NP-complete is the set of problems that are the hardest problems in NP, in the sense that they are the ones most likely not to be in P. If you can find a way to solve an NP-complete problem quickly, then you can use that algorithm to solve all NP problems quickly.
		If you could reduce an NP problem to an NP-hard problem and then solve it in polynomial time, you could solve all NP problems.
	www.cc.gatech.edu /~howardz/micellaneous/gre_cs_sub/np_complete.htm (210 words)

	MGH-Institute of Health Professions (Site not responding. Last check: 2007-11-07)
		Clinical practicum with application of family theories to practice in the assessment, diagnosis, and management of individuals and families with common and complex, acute and chronic illnesses.
		NP 861 Advanced Assessment and Management of Common Psychiatric Symptoms.
		Management of acute and chronic problems for selected patient populations will be explored, with emphasis on the integration of social and cultural factors in treatment plans.
	www.mghihp.edu /faculty/nursing_courses5.html (577 words)

	Theory Seminar 12 Nov 2002: Matt Yurkewycz (Site not responding. Last check: 2007-11-07)
		A major result in Descriptive Complexity reveals that NP is equal to the set of formulas expressible in second order existential logic.
		Monadic NP is a subset of second order existential logic whose second order existential quantifiers range over unary relations.
		This talk will focus on the game-theoretic technique of Ehrenfeucht and Fraisse, which is a method of ascertaining what is and is not expressible in logics such as Monadic NP.
	www.cs.umass.edu /~barring/thysem/nov12.html (111 words)

	Realty Times: Heartburn in Heartland: New Broker Models VS Full-service Brokers
		NP Dodge Co, among the largest real estate firms in Omaha, has notified a few smaller companies that their agents will be paid less on sales commissions than the co-op fee listed in the MLS.
		NP Dodge says it's because the companies offer less than full service, causing the NP Dodge agents to have to work harder.
		Said Joe Marcarelli, an Alliance co-owner, "NP Dodge's actions indicate it's upset at the small companies' success." "He said, according to the author, that the big firms, with well-furnished offices at key locations, can't afford to discount commissions and compete with the new companies offering alternative ways to sell real estate.
	realtytimes.com /printrtpages/20040907_heartburn.htm (1190 words)

	[No title]
		Assume NP = P. Then SAT is in P. Therefore there exists a value k such that SAT is in TIME(nk).
		Because every language in NP is polynomial-time reducible to SAT, we know that P is a subset of TIME(nk).
		Therefore our assumption that NP = P must be false.¡ø $o$v j 0$ + 8ªb5±i6,8ó óó óó/ðÄó ó óóóóóPÿÿÿbêrßõp»"bè; é(àà ò@/Èê0Òº( ÿ0;ÿ[ÿ0 0 000åÿÿ$([\{bÿáÿº¦00 ÿÿû0ÿÿÿÿ00ý0þ0000ü0 ÿ0=ÿ]ÿ 00 000°0 2 3 !àÿÿA0C0E0G0I0c00000¡0£0¥0§0©0Ã0ã0å0ç0î0õ0ö0!%),.:;?]}aÿcÿdÿeÿgÿhÿiÿjÿkÿlÿmÿnÿoÿpÿÿÿÕ·DTimes New Roman$¶b$¶b0²bÞ0T²bT²bß0·DSymbolew Roman$¶b$¶b0²bÞ0T²bT²bß0«ÿ@ @@``© @£nÿý?" dd@ÿÿïÿÿÿÿÿÿ @@``@ð8ð°Tt ð`¿ÀÁÄË1ÍÎÐÑ×ÿ?@ñÿÿÿÿ÷ðóÐÿ úgþý42d2d`²bß0X²b $ Ðüÿÿ¸ÿÿÿpûppû@?Ù Ú%ðó¨Homework 8 Solutions¨Problem 1.
	www.cs.unm.edu /~gemmell/C500/hw8.ppt (977 words)

	[No title]
		PRIMALITY in NP =============== Remember we talked about how FACTORING (does N have a factor between 2 and k) is in both NP and Co-NP.
		NP: A is in NP if there is a polynomial-time algorithm V(I,w) such that: If "I" is in YES_A, then there exists w such that V(I,w) = 1.
		Co-NP: other way around from NP: swap YES and NO. RP (randomized polynomial time): A is in RP if exists poly-time V s.t.: If "I" is in YES_A, then for at least half of w, V(I,w) = 1.
	www.cs.cmu.edu /afs/cs.cmu.edu/academic/class/15451-f01/www/lectures/lect1120 (1120 words)

	CSCI 3110 - Analysis of Algorithms I (Site not responding. Last check: 2007-11-07)
		Thus, if G is a graph, and w is claimed to be a solution of the Hamiltonian problem for the graph, then the verification algorithm checks to see if w is indeed a solution, and answers yes or no correctly.
		Definition: NP is the set of encoded problems for each of which there exists a polynomial time verification algorithm.
		Now, suppose that there is a problem L which is in NP, and not in P.
	www.mscs.dal.ca /~keast/t_and_a/3110/week12/notes17.html (909 words)

	RP - free-definition
		P is a subset of RP, which is a subset of NP.
		It is also not known whether RP is a subset of the intersection of NP and Co-NP.
		The definition of RP is based on probabilistic Turing machines.
	www.netlexikon.akademie.de /RP.html (352 words)

	1999 (Site not responding. Last check: 2007-11-07)
		Garden of the Gods, CO This was a cool place - kind of like a enormous rock garden type thing.
		Black Canyon of the Gunnison NP, CO We took a mini railroad thing to see the Royal Gorge and Black Canyon of the Gunnison.
		Sun Crater NP, AZ I liked this park, because it felt like we were in a giant crater.
	www.wideopenwest.com /~tefuhrman/Melissa/1999.htm (586 words)

	Co-NP-NP (Site not responding. Last check: 2007-11-07)
		NP y los co-NP-NP también se piensan para ser desiguales.
		Puesto que todos los problemas en NP se pueden reducir a este problema sigue que eso para todos los problemas en NP podemos construir una máquina no determinista de Turing que decida al complemento del problema en tiempo polinómico, es decir, NP es un subconjunto de co-NP-NP.
		Puesto que sabíamos ya que NP es un subconjunto de co-NP-NP sigue que él es igual.
	www.yotor.net /wiki/es/co/CoNPNP.htm (368 words)

	Co-NP (Site not responding. Last check: 2007-11-07)
		In the latest development in the restructuring of the retail petroleum sector here, the National Petroleum Marketing Co. (NP), which controls the gasoline station network and all petroleum retailing, says the sector will undergo phased privatization...
		Co., NP, PA Materiel Control Inc., NP Mid-States Engineering & Manufacturing...
		MAGAZINES Hewlett-Packard Journal 8/1/1998 Foster, Harry D. equivalence points in an attempt to minimize an OBDD is itself a co- NP-complete problem.[2,3] However, for most cases it is only necessary...
	enciclopedia.cc /Co-NP (388 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		Alternately, NP is the class of languages whose positive instance can be proved (or verified) to be in the language in polynomial time.
		Q: According to second definition, is the Punch-Card Puzzle in NP?¡\? 9ßóC#¨Puzzle ExampleShort Proof¡¨ªA: Yes.
		Thus proof is a linear size proof, and puzzle is in NP.
	www.cs.columbia.edu /~zeph/3261/L22/L22.ppt (550 words)

	Theory of Computation
		B5: A language is said to be in co-NP if it's complement is in NP.
		Prove that P is a subset of co-NP b.
		We mentioned in class that PRIMES is in P. Use this fact to show that FACTOR is in both NP and co-NP.
	www.cs.ecu.edu /~hochberg/spring2003/csci6420.html (525 words)

	CS154 Assignment 7 Solutions (Site not responding. Last check: 2007-11-07)
		Then every problem P in NP is in co-NP; just transform -P to -Q in polynomial time and then use the nondeterministic polynomial-time algorithm for -Q to solve -P in nondeterministic polynomial time.
		Since Q is in co-NP, -Q is in NP, and thus so is -P.
		That shows co-NP is contained in NP, and we now have NP = co-NP.
	www-db.stanford.edu /~ullman/ialc/win00/hw7sols.html (391 words)

	ECCC Report TR93-027 and related Papers (Site not responding. Last check: 2007-11-07)
		Abstract: It this paper we prove that coNP is identical to NP, if deterministic polynomial reductions allow result switching, otherwise P != NP.
		If the theory were to disallow this, then it is easily shown that P != NP via a simple proof that co-NP != NP.
		You may contribute to the discussion of this ECCC Report; see the detailed instructions.
	www.eccc.uni-trier.de /eccc-reports/1993/TR93-027 (115 words)

	Proof Complexity
		NP consists of those languages that have short, easily-verifiable proofs of membership.
		The `holy grail' of proof complexity is to prove that no short, easily-verifiable proofs of tautology (or equivalently any other co-NP-complete language) exist.
		This would have the consequence of separating NP from co-NP and, as a result, separate P from NP.
	www.cs.washington.edu /homes/beame/projects/proofcomplexity.html (756 words)

	Oregon Blue Book Multnomah County
		The remaining area includes picturesque rural land, from pastoral farms on Sauvie Island to the rugged Columbia River Gorge and the western slopes of Mt. Hood.
		County Officials: Commissioners—Serena Cruz (NP) 2007; Maria Rojo Desteffey (NP) 2009, Diane Linn (NP) 2007, Lisa Naito (NP) 2008, Lonnie Roberts (NP) 2008; Dist. Atty.
		Robert Ellis; Recorder Cindy Swick; Sheriff Bernie Giusto (NP) 2007; Surv.
	bluebook.state.or.us /local/counties/counties26.htm (226 words)

	InternetCamcorderBatteries.co.uk NP F10 (Site not responding. Last check: 2007-11-07)
		Camcorder Batteries > Camcorder Batteries > Sony Camcorder Batteries > NP F10
		SSF11 Energizer Camcorder Battery for SONY NP F10
		This battery is unsuitable for digital still cameras due to its thickness please click here for a suitable battery.
	www.internetcamcorderbatteries.co.uk /acatalog/SONYNPF10battery.html (62 words)

	ShopMemoryCard.co.uk NP F950 (Site not responding. Last check: 2007-11-07)
		NP550 Energizer Camcorder Battery for SONY NP F950
		NP750 Energizer Camcorder Battery for SONY NP F950
		NP950 Energizer Camcorder Battery for SONY NP F950
	www.shopmemorycard.co.uk /acatalog/SONYNPF950battery.html (166 words)

	Realtors - NP Dodge Co. Iowa Pottawattamie County
		Realtors - NP Dodge Co. Iowa Pottawattamie County
		Realtors - NP Dodge Co. - 1730 Madison Ave - Council Bluffs, IA 51503 - 712-328-5008 -
		Brian & Roxanne “Rocky” Shepard — “Selling Iowa One Yard At A Time” Husband and wife team working with buyers and sellers of all types of real estate, servicing Council Bluffs, Treynor, Glenwood, Missouri Valley, Crescent, Underwood, Neola, Carson, and all of Southwest Iowa.
	valuecom.com /acclaim/Iowa/Real_Estate_Services/Realtors___NP_Dodge_Co.html (135 words)

	NP Coed Volleyball League Brampton Ontario Canada (Site not responding. Last check: 2007-11-07)
		The six teams are created from individual or team entries based on a pre-season draft pick.
		This season each member will pay $TBA to join the NP Club.
		If any of their 48 spots are open, a try-out evening will be offered to New Players
	members.aol.com /vballnews/NP_League.html (177 words)

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