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{{Short description|Set of computational problems stated by Richard Karp (1973)}} .... This was one of the first demonstrations that many natural computational problems occurring throughout [[computer science]] are [[computationally intractable ...

{{Short description|Local search algorithm solving boolean satisfiability}} ...orithm]]s to solve [[Boolean_satisfiability_problem|Boolean satisfiability problems]]. ...

...") form a [[complexity class]] in [[computational complexity theory]]. The problems in this complexity class are defined by having the following two properties *The problem is in [[♯P|#P]], the class of problems that can be defined as counting the number of accepting paths of a [[polyno ...

==Named problems== *[[Satisfiability problem]] ...

...al [[Horn clause]]s is [[Boolean satisfiability|satisfiable]] or not. Horn-satisfiability and Horn clauses are named after [[Alfred Horn]].<ref name="Horn51">{{cite Horn satisfiability is actually one of the "hardest" or "most expressive" problems which is known to be computable in polynomial time, in the sense that it is ...

...dicating better solutions. Domination analysis is most commonly applied to problems for which the total number of possible solutions is known and for which exa === Max Satisfiability === ...

[[Category:Satisfiability problems]] [[Category:PSPACE-complete problems]] ...

...implementation challenges to determine practical algorithm performance on problems of interest. There have been eleven DIMACS challenges so far. ...lem|Max Clique]], [[Graph coloring problem|Graph Coloring]], and [[Boolean satisfiability problem|SAT]] ...

...s to the variables of the formula. It is a generalization of the [[Boolean satisfiability problem]], which asks whether there exists a truth assignment that makes al ...problem), since its solution easily leads to the solution of the [[boolean satisfiability problem]], which is [[NP-complete]]. ...

...mplete problem quickly, then that algorithm can be used to solve all co-NP problems quickly. ...ome problems in both [[NP (complexity)|NP]] and [[co-NP]], for example all problems in [[P (complexity)|P]] or [[integer factorization]]. However, it is not kn ...

...graph with loops that are not too short. The cavity method can solve many problems also solvable using the [[replica trick]] but has the advantage of being mo ...lving [[optimization problem]]s such as [[Boolean satisfiability problem|k-satisfiability]] and [[graph coloring]]. It has yielded not only ground states energy pred ...

{{Short description|Complexity class of approximable problems}} ...''constant-factor approximation algorithms''' for short). In simple terms, problems in this class have efficient [[algorithm]]s that can find an answer within ...

That is, '''co-NP''' is the set of decision problems where there exists a polynomial {{tmath|p(n)}} and a polynomial-time bounde ==Complementary problems== ...

* [[Boolean satisfiability problem]] (SAT, 2-SAT, 3-SAT) * [[SAT solver]], an algorithm for solving Boolean satisfiability problems ...

...e output is more complex than that of a [[decision problem]]. For function problems, the output is not simply 'yes' or 'no'. ...'FSAT''' for short. The problem, which is closely related to the [[Boolean satisfiability problem|'''SAT''']] decision problem, can be formulated as follows: ...

...ion|When a finite set S of relations yields polynomial-time or NP-complete problems}} ...oolean domain yields [[P (complexity)|polynomial-time]] or [[NP-complete]] problems when the relations of ''S'' are used to constrain some of the [[proposition ...

...ption|Boolean satisfiability is NP-complete and therefore that NP-complete problems exist}} ...n [[polynomial time]] by a [[deterministic Turing machine]] to the Boolean satisfiability problem. ...

...established a relationship between the constraint satisfaction problem and problems in other areas such as [[finite model theory]] and [[database]]s. ...straint satisfaction problems. Such other problems include [[propositional satisfiability]] and [[Three-colorable graph|three-colorability]]. ...

...mplexity]] subfield of [[computer science]]. It generalises the [[Boolean satisfiability problem]] (SAT) which is a [[decision problem]] considered in [[computation ...>(''x''_i1,...,''x''_iq) using 2^q [[Boolean satisfiability problem|SAT]] clauses. Clauses of length ''q'' are converted to length 3 b ...

...cally checkable proof]]s. Recall that '''NP''' can be seen as the class of problems where an all-powerful prover gives a purported proof that a string is in th ...at NEXPTIME-complete problems are not in NP; it has been proven that these problems cannot be verified in [[polynomial time]], by the [[time hierarchy theorem] ...