Cook's theorem - Factbites

Cook's theorem - Factbites
Where results make sense
About us | Why use us? | Reviews | PR | Contact us

Topic: Cook's theorem

Note: these results are not from the primary (high quality) database.

In the News (Tue 29 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Business Software Review : Article 'Cook's theorem'
		The theorem, which is known as Cook or Cook-Levin theorem, was a breakthrough in computer science and is the foundation of computational complexity.
		In computational complexity theory, Cook's theorem, proved by Stephen Cook in his 1971 paper "The Complexity of Theorem Proving Procedures", states that the Boolean satisfiability problem is NP-complete.
		In fact, it was the first known NP -complete problem, as proved by Stephen Cook in 1971 (see Cook's theorem for the proof).
	www.business-software-review.org /DisplayArticle553727.html (662 words)

	Business Software Review : Article 'Cook's theorem'
		The theorem, which is known as Cook or Cook-Levin theorem, was a breakthrough in computer science and is the foundation of computational complexity.
		In computational complexity theory, Cook's theorem, proved by Stephen Cook in his 1971 paper "The Complexity of Theorem Proving Procedures", states that the Boolean satisfiability problem is NP-complete.
		In fact, it was the first known NP -complete problem, as proved by Stephen Cook in 1971 (see Cook's theorem for the proof).
	www.business-software-review.org /DisplayArticle553727.html (662 words)

	Business Software Review : Article 'Cook's theorem'
		The theorem, which is known as Cook or Cook-Levin theorem, was a breakthrough in computer science and is the foundation of computational complexity.
		In computational complexity theory, Cook's theorem, proved by Stephen Cook in his 1971 paper "The Complexity of Theorem Proving Procedures", states that the Boolean satisfiability problem is NP-complete.
		In fact, it was the first known NP -complete problem, as proved by Stephen Cook in 1971 (see Cook's theorem for the proof).
	www.business-software-review.org /DisplayArticle553727.html (662 words)

	Stephen Cook - Wikipedia, the free encyclopedia
		Cook formalised the notion of NP-completeness in a famous 1971 paper "The Complexity of Theorem Proving Procedures", which also contained Cook's theorem, a proof that the boolean satisfiability problem is NP-complete.
		Cook received the Turing Award in 1982 for his discovery.
		Stephen Arthur Cook is a noted computer scientist.
	en.wikipedia.org /wiki/Stephen_Cook (255 words)

	Fields Institute - Stephen Cook
		Cook was the 1982 recipient of the Turing award, a Killam Research Fellowship in 1982, and a Steacie Fellowship in 1977.
		Stephen Cook was born in Buffalo, New York.
		Cook's principal research area is computational complexity, with excursions into programming language semantics, parallel computation and especially the interaction between logic and complexity theory.
	www.fields.utoronto.ca /programs/scientific/99-00/stephen_cook (225 words)

	CS 611, v3.0: Exams Archives
		Know how to show that something is NP-complete and appreciate the beauty of the Cook-Levin theorem, its proof and consequences.
		Be comfortable with the s-m-n theorem, the recursion theorem and Rice's theorem.
		Then it proves some useful theorems, like Rice's theorem, the SMN theorem and the recursion theorem, then it uses those theorems in proofs of other theorems.
	lal.cs.byu.edu /cs611/archives/exams (1226 words)

	Computational Complexity: Favorite Theorems: Abstract Complexity
		McCreight and Meyer also give an honesty theorem showing that computable t there is (in a weak sense) a time-constructible t' such that languages computable with resource bound t are equal to languages computable with resource bound t'.
		After the P versus NP problem was popularized by Cook and Karp in 1971, the focus of complexity went to polynomial-time (which also was machine independent) and away from abstract complexity.
		Trakhtenbrot independently proved the gap theorem for abstract complexity measures.
	weblog.fortnow.com /2005/08/favorite-theorems-abstract-complexity.html (442 words)

	Combined Bibliography
		Cook, Stephen A. (1971) "The complexity of theorem-proving procedures," Proc.
		Cook, Walter A., S.J. Case Grammar: Development of the Matrix Model, Georgetown University Press, Washington, DC.
		Cook, Walter A., S.J. Case Grammar Theory, Georgetown University Press, Washington, DC.
	www.jfsowa.com /bib.htm (442 words)

	Computability Complexity Logic Book
		Theorem of 481 Cook, theorem of Henschen & Wos, polynomial equivalence of Horn- and network-complexity, theorem of Stockmeyer.
		Grzegorczyk hierarchy theorem Equivalence of 197 the characterisation by growth-rate (limited recursion, excursus on Ackermann branches), recursion- and loop- depth, computing-time complexity from Kleene normal form with polynomially bounded or R3-coding functions.
		Theorem of 378 Skolem, compactness theorem, non-characterisability of the concept of infiniteness, non-standard models of number theory.
	www.di.unipi.it /~boerger/cclbookcontents.html (788 words)

	To be or not with PCP
		NP was defined and Cook’s theorem was stated:
		Is the main theorem; what is more is fume.
		In pursuit of this goal, PCP was defined.
	www.cs.berkeley.edu /~satishr/to-be-or-not-with-pcp.html (680 words)

	Complexity course outline Spring 1999
		Completeness; Circuit Value is P-complete (two proofs) Cook's Theorem (2 proofs)
		relations between deterministic and nondeterministic complexity classes, Savitch's theorem; the configuration graph, the reachability method, Immerman's theorem.
		Time and Space Hierarchy theorems, Gap theorem (w/o proof), relations between deterministic and nondeterministic complexity classes (incomplete);
	www.math.tau.ac.il /~rshamir/complexity/99/outline.html (386 words)

	Seymour is Solved!!!
		Four Color Theorem by Neil Robertson, Daniel Sanders, Paul Seymour, and Robin Thomas.
		The Four Color Theorem states that any map can be colored using four colors in such a way that adjacent regions (i.e.
		It took less than four hours of CPU time to complete the proof of the Four Color Theorem.
	www-unix.mcs.anl.gov /metaneos/seymour (485 words)

	Combined Bibliography
		Cook, Stephen A. (1971) "The complexity of theorem-proving procedures," Proc.
		Cook, Walter A., S.J. Case Grammar: Development of the Matrix Model, Georgetown University Press, Washington, DC.
		Cook, Walter A., S.J. Case Grammar Theory, Georgetown University Press, Washington, DC.
	www.jfsowa.com /bib.htm (485 words)

	lect05.tex
		Then our entire formula is in ${\rm NTIME}(n^{1 + \epsilon})$; from Cook's Strong Theorem we know that this reduces to a satisfiability problem in \lang{SAT} of length $n^{1 + \epsilon} \log n$, which is in ${\rm TIME}((n^{1 + \epsilon} \log n) ^ {1 + \epsilon})$.
		In the proof of Savitch's Theorem, we continually divided the computation in half, and examined each half to see if it was a valid computation.
		The contradiction will come from the Time Hierarchy Theorem (we could also derive it, with some more work, from the Space Hierarchy Theorem).
	theory.lcs.mit.edu /~madhu/ST03/scribe/lect05.tex (1290 words)

	Computational Complexity: Favorite Theorems: Abstract Complexity
		McCreight and Meyer also give an honesty theorem showing that computable t there is (in a weak sense) a time-constructible t' such that languages computable with resource bound t are equal to languages computable with resource bound t'.
		After the P versus NP problem was popularized by Cook and Karp in 1971, the focus of complexity went to polynomial-time (which also was machine independent) and away from abstract complexity.
		Trakhtenbrot independently proved the gap theorem for abstract complexity measures.
	weblog.fortnow.com /2005/08/favorite-theorems-abstract-complexity.html (442 words)

	Computability Complexity Logic Book
		Theorem of 481 Cook, theorem of Henschen & Wos, polynomial equivalence of Horn- and network-complexity, theorem of Stockmeyer.
		Theorem of 155 Rabin-Blum-Meyer on functions of arbitrarily large program- or computing-time complexity, Blum's program-shortening theorem, gap theorem, union theorem.
		Theorem of 378 Skolem, compactness theorem, non-characterisability of the concept of infiniteness, non-standard models of number theory.
	www.di.unipi.it /~boerger/cclbookcontents.html (442 words)

	Kids Be Safe : Article 'Polynomial-time reduction'
		This means that if the Boolean satisfiability problem could be solved in polynomial time by a deterministic Turing machine, then all problems in NP could be solved in polynomial time, and so the complexity class NP would be equal to the complexity class P. Cook's theorem was the first proof of NP-completeness for any problem.
		Gödel's incompleteness theorem says that no system as powerful as the Peano axioms can be both consistent and complete.
		We have shown that any problem in NP can be reduced in polynomial time to an instance of the Boolean satisfiability problem.
	www.kidsbesafe.org /DisplayArticle81055.html (5656 words)

	Doctoral Degree - CS Dept
		NP-Completeness and Cook's theorem, other NP-complete problems and proofs.
		Time and space bounded computation, time and space hierarchy theorems, complexity classes P, NP, Co-NP, L, NL, polynomial time hierarchy and basic known/unknown results, relativization and oracle computations.
		Complexity Theory: Blum's axioms, gap theorem, speedup theorem, basic theorems about abstract complexity measures.
	www.cs.pitt.edu /education/grad/prelim/theory (266 words)

	Computability and Complexity -- Fall 2004
		The P versus NP problem (and Cook's Theorem), reductions and completeness.
		The reachability method (Savitch's theorem, and the Immerman-Szelepscenyi theorem).
		Computability: finite automata, rewriting systems, Turing machines (linear speedup, robustness, and the Universal Turing machine).
	www.dcss.mcmaster.ca /~soltys/cas705-f04/index.html (1168 words)

	Complexity course outline Spring 1999
		Completeness; Circuit Value is P-complete (two proofs) Cook's Theorem (2 proofs)
		relations between deterministic and nondeterministic complexity classes, Savitch's theorem; the configuration graph, the reachability method, Immerman's theorem.
		Time and Space Hierarchy theorems, Gap theorem (w/o proof), relations between deterministic and nondeterministic complexity classes (incomplete);
	www.cs.tau.ac.il /~rshamir/complexity/99/outline.html (386 words)

	Complexity course outline Spring 1999
		Completeness; Circuit Value is P-complete (two proofs) Cook's Theorem (2 proofs)
		Time and Space Hierarchy theorems, Gap theorem (w/o proof), relations between deterministic and nondeterministic complexity classes (incomplete);
		relations between deterministic and nondeterministic complexity classes, Savitch's theorem; the configuration graph, the reachability method, Immerman's theorem.
	www.math.tau.ac.il /~rshamir/complexity/99/outline.html (386 words)

	CS 380/480 Course Syllabus
		Rice's Theorem, Cook's Theorem and the Chomsky Hierarchy
		Regular Languages, Finite Automata and the Myhill-Nerode Theorem
	www.cs.utk.edu /~langston/courses/cs380/syllabus.html (101 words)

	CS 172, Fall 2004: Syllabus
		More examples; proof of Cook's Theorem [ Sipser 7.4 & 7.5]
		P, NP and co-NP; PSPACE and NPSPACE; Savitch's Theorem [ Sipser 8.1-8.2]
		The Myhill-Nerode theorem; minimization of DFAs [Note on web page]
	www.cs.berkeley.edu /~sinclair/cs172/syll.html (211 words)

	UCSB General Catalog - Mathematics
		Tractable and intractable problems; the class NP and NP-completeness; Cook's Theorem; resource-bounded reducibilities; and NP-complete problems in graph theory and combinatorics.
		Curves and surfaces in three-dimensional Euclidean space, first and second fundamental forms, Gaussian and mean curvature, geodesics, Gauss-Bonnet theorem, and non-euclidean geometry.
		Prerequisites: Mathematics 118A-B-C. Existence and stability of solutions, Floquet theory, Poincare-Bendixson theorem, invariant manifolds, existence and stability of periodic solutions, bifurcation theory and normal forms, hyperbolic structure and chaos, Feigenbaum period-doubling cascade, Ruelle-Takens cascade.
	www.catalog.ucsb.edu /2003cat/LS/math.htm (7318 words)

	User:Gdr/Articles - Wikipedia, the free encyclopedia
		Computational complexity theory: Alternating Turing machine Alternating automaton Cook's theorem DSPACE DTIME E ELEMENTARY ESPACE Exponential hierarchy FNP FP Function problem Linear speedup theorem List of complexity classes NE NESPACE NEXPSPACE NEXPTIME NSPACE NTIME PH Polynomial hierarchy Savitch's theorem Speedup theorem
		Mathematical games: Dots and Boxes Envelope paradox Game complexity Game tree Generalized game Gomoku How to solve the Knight's tour Sprague-Grundy theorem Sprouts Tic-tac-toe
	en.wikipedia.org /wiki/User:Gdr/Articles (325 words)

	Lecture Summaries for 308362B, Winter 2003
		Lecture 20: We completed the proof of Cook's Theorem and we proved the NP-completeness of 3-SAT.
		Proof of the Weak duality theorem and statement of the Strong duality Theorem.
		Here are some lecture notes on the Maximum Matching-Minimum Cover Theorem for bipartite graphs.)
	cgm.cs.mcgill.ca /~fountoul/lects.html (287 words)

	Computability Complexity Logic Book
		Theorem of 481 Cook, theorem of Henschen & Wos, polynomial equivalence of Horn- and network-complexity, theorem of Stockmeyer.
		Spectrum problem Spectrum characterisation of 497 the E3-computation time hierarchy (theorem of Roedding & Schwichtenberg, Jones & Selman, Christen), logical characterisation of NP by global existential second order predicate (theorem of Fagin), of p by PL1+LFP- with-order (theorem of Immerman & Vardi), of PTAPE by PL2+TC (theorem of Immerman).
		Studies in Logic and the Foundations of Mathematics, vol.
	www.di.unipi.it /~boerger/cclbookcontents.html (788 words)

	3SAT
		This is a special case of Cook's theorem, which says anything done by a (non-deterministic) Turing machine can be simulated by a suitably constructed instance of satisfiability, or by 3-SAT.
		> >> This is a special case of Cook's theorem, which says > >> anything done by a (non-deterministic) Turing machine can > >> be simulated by a suitably constructed instance of satisfiability, > >> or by 3-SAT.
		Converting factoring to 3-SAT can be done in polynomial time, because of the abovementioned theorem (note that factoring can be done on a Turing machine) Then, it's in fact not quite clear what you mean by "factoring".
	www.math.niu.edu /~rusin/known-math/01_incoming/3SAT (1261 words)

	User:Gdr/Articles - Wikipedia, the free encyclopedia
		Computational complexity theory: Alternating Turing machine Alternating automaton Cook's theorem DSPACE DTIME E ELEMENTARY ESPACE Exponential hierarchy FNP FP Function problem Linear speedup theorem List of complexity classes NE NESPACE NEXPSPACE NEXPTIME NSPACE NTIME PH Polynomial hierarchy Savitch's theorem Speedup theorem
	en.wikipedia.org /wiki/User:Gdr/Articles (325 words)

	User:Gdr/Articles - Wikipedia, the free encyclopedia
		Computational complexity theory: Alternating Turing machine Alternating automaton Cook's theorem DSPACE DTIME E ELEMENTARY ESPACE Exponential hierarchy FNP FP Function problem Linear speedup theorem List of complexity classes NE NESPACE NEXPSPACE NEXPTIME NSPACE NTIME PH Polynomial hierarchy Savitch's theorem Speedup theorem
		This page was last modified 23:33, 15 November 2005.
		Imperial Japanese Navy: Japanese aircraft carrier Akagi Japanese aircraft carrier Hiryu Japanese aircraft carrier Junyo Japanese aircraft carrier Kaga Japanese aircraft carrier Ryujo Japanese aircraft carrier Shoho Japanese aircraft carrier Shokaku Japanese aircraft carrier Soryu Japanese aircraft carrier Zuikaku Japanese battleship Nagato Japanese cruiser Chikuma Japanese cruiser Tone Japanese destroyer Ikazuchi
	en.wikipedia.org /wiki/User:Gdr/Articles (343 words)

Try your search on: Qwika (all wikis)

Topic: Cook's theorem

Ads by Google

Related Topics

In the News (Tue 29 Dec 09)