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In computer science, the Sharp Satisfiability Problem (sometimes called Sharp-SAT or #SAT) is the problem of counting the number of interpretations that satisfies a given Boolean formula, introduced by Valiant in 1979. In other words, it asks in how many ways the variables of a given Boolean formula can be consistently replaced by the values TRUE or FALSE in such a way that the formula evaluates to TRUE. For example, the formula is satisfiable by three distinct boolean value assignments of the variables, namely, for any of the assignments ( = TRUE, = FALSE), ( = FALSE, = FALSE), ( = TRUE, = TRUE), we have = TRUE.

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rdf:type	yago:WikicatComputationalProblems yago:WikicatSatisfiabilityProblems yago:Abstraction100002137 yago:Attribute100024264 yago:Condition113920835 yago:Difficulty114408086 yago:Problem114410605 disease yago:State100024720
rdfs:label	Sharp-SAT (en) Sharp-SAT (pt)
rdfs:comment	Na teoria da complexidade computacional, #SAT, ou Sharp-SAT é um problema de função relacionado com o problema da satisfabilidade booleana. (pt) In computer science, the Sharp Satisfiability Problem (sometimes called Sharp-SAT or #SAT) is the problem of counting the number of interpretations that satisfies a given Boolean formula, introduced by Valiant in 1979. In other words, it asks in how many ways the variables of a given Boolean formula can be consistently replaced by the values TRUE or FALSE in such a way that the formula evaluates to TRUE. For example, the formula is satisfiable by three distinct boolean value assignments of the variables, namely, for any of the assignments ( = TRUE, = FALSE), ( = FALSE, = FALSE), ( = TRUE, = TRUE), we have = TRUE. (en)
dcterms:subject	Combinatorics Satisfiability problems Computational problems
Wikipage page ID	25590565 (xsd:integer)
Wikipage revision ID	1032111377 (xsd:integer)
Link from a Wikipage to another Wikipage	Enumerative combinatorics Validity (logic) Interpretation (logic) ♯P ♯P-complete Conjunctive normal form Computational complexity theory Computer science Horn-satisfiability Combinatorics Non-deterministic Turing machine Binary Decision Diagram Satisfiability problems Counting problem (complexity) Artificial intelligence Computational problems 2SAT 3SAT Boolean satisfiability problem Cook-Levin theorem Satisfiability Sharp-P-complete Statistical physics Boolean logic Formula (mathematical logic) dbr:Planar_3SAT
sameAs	Sharp-SAT Sharp-SAT Sharp-SAT Sharp-SAT Sharp-SAT
dbp:wikiPageUsesTemplate	dbt:Correct_title dbt:Refimprove dbt:Reflist
reason	hash (en)
title	#SAT (en)
has abstract	In computer science, the Sharp Satisfiability Problem (sometimes called Sharp-SAT or #SAT) is the problem of counting the number of interpretations that satisfies a given Boolean formula, introduced by Valiant in 1979. In other words, it asks in how many ways the variables of a given Boolean formula can be consistently replaced by the values TRUE or FALSE in such a way that the formula evaluates to TRUE. For example, the formula is satisfiable by three distinct boolean value assignments of the variables, namely, for any of the assignments ( = TRUE, = FALSE), ( = FALSE, = FALSE), ( = TRUE, = TRUE), we have = TRUE. #SAT is different from Boolean satisfiability problem (SAT), which asks if there exists a solution of Boolean formula. Instead, #SAT asks to enumerate all the solutions to a Boolean Formula. #SAT is harder than SAT in the sense that, once the total number of solutions to a Boolean formula is known, SAT can be decided in constant time. However, the converse is not true, because knowing a Boolean formula has a solution does not help us to count all the solutions, as there are an exponential number of possibilities. #SAT is a well-known example of the class of counting problems, known as #P-complete (read as sharp P complete). In other words, every instance of a problem in the complexity class #P can be reduced to an instance of the #SAT problem. This is an important result because many difficult counting problems arise in Enumerative Combinatorics, Statistical physics, Network Reliability, and Artificial intelligence without any known formula. If a problem is shown to be hard, then it provides a complexity theoretic explanation for the lack of nice looking formulas. (en) Na teoria da complexidade computacional, #SAT, ou Sharp-SAT é um problema de função relacionado com o problema da satisfabilidade booleana. (pt)
gold:hypernym	Problem
prov:wasDerivedFrom	wikipedia-en:Sharp-SAT?oldid=1032111377&ns=0
page length (characters) of wiki page	6546 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Sharp-SAT
is Link from a Wikipage to another Wikipage of	♯P-complete ♯P-completeness of 01-permanent Boolean satisfiability problem IP (complexity) Riemann mapping theorem Sharpsat
is Wikipage redirect of	Sharpsat
is foaf:primaryTopic of	wikipedia-en:Sharp-SAT

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