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...lity (logics)|satisfiability]] and [[finite satisfiability (logics)|finite satisfiability]], are [[decidability (computer science)|decidable]].<ref>E. Grädel, P.G. K ...onal complexity theory|computational complexity]] for their satisfiability problems. ...

...iability''' ('''NAE3SAT''') is an [[NP-complete]] variant of the [[Boolean satisfiability problem]], often used in proofs of NP-completeness.{{r|moqo}} ...hich combines three variables or negations of variables. However, unlike 3-satisfiability, which requires each clause to have at least one true Boolean value, NAE3SA ...

...ath>x+1=x</math> is not satisfiable over the integers. The dual concept to satisfiability is [[Validity (logic)|validity]]; a formula is ''valid'' if every assignmen ...ional [[axiom]]s. The [[satisfiability modulo theories]] problem considers satisfiability of a formula with respect to a [[Theory (mathematical logic)|formal theory] ...

...tational complexity theory]] that is a maximization version of the Boolean satisfiability problem [[3SAT]]. In MAXEkSAT, each clause has exactly ''k'' literals, each ...to remove its dependence on randomness. There are problems related to the satisfiability of conjunctive normal form Boolean formulas. ...

...larkson.edu/~alexis/PCMI/Notes/lectureB07.pdf|title=Lecture 7: NP-Complete Problems|date=July 5, 2000|author=David Mix Barrington and Alexis Maciel}}</ref> In ...e notes] from his course ''Quantum Computing Since Democritus''.</ref> The satisfiability of a circuit containing <math>m</math> arbitrary binary gates can be decide ...

...he Theory of NP-Completeness|Garey & Johnson's]] classical [[NP-complete]] problems.<ref name="GareyJohnson"/> The problem is sometimes called [[Property B|hyp == Connection to other problems == ...

{{short description|On the complexity classes of problems about satisfying a subset of boolean relations}} ...liamson|date=Mar 2000|title=The Approximability of Constraint Satisfaction Problems|journal=SIAM J. Comput.|publisher=SIAM|volume=30 | number=6 |pages=1863–192 ...

...ristic (computer_science)|heuristics]]) that solves types of the [[Boolean satisfiability problem]] despite there being [[P versus NP problem|no known efficient algo The Boolean satisfiability (or SAT) problem can be stated formally as: ...

{{Short description|Software for solving satisfiability problems}} '''Z3''', also known as the '''Z3 Theorem Prover''', is a [[satisfiability modulo theories]] (SMT) solver developed by [[Microsoft]].<ref>{{Cite web | ...

...mporal Logic]] (MTL). This fragment is often preferred to MTL because some problems that are [[Undecidable problem|undecidable]] for MTL become [[Decidable pro === Problems that MITL avoids === ...

...highly complex) cases, and those, expressed as [[Boolean satisfiability]] problems, were examined using a [[SAT solver]]. Creating the proof took about 4 CPU- ...omputer Science|volume=9710|pages=228–245|title=Theory and Applications of Satisfiability Testing – SAT 2016: 19th International Conference, Bordeaux, France, July 5 ...

...f counting the number of [[Interpretation (logic)|interpretations]] that [[Satisfiability|satisfy]] a given [[Boolean logic|Boolean]] [[Formula (mathematical logic)| <nowiki>#</nowiki>SAT is different from [[Boolean satisfiability problem]] (SAT), which asks if there exists ''a solution'' of Boolean formu ...

...t complexity|non-uniform]] analogue of the class [[NP (complexity)|NP]] of problems solvable in [[polynomial time]] by a [[non-deterministic Turing machine]]. NP/poly is defined as the class of problems solvable in polynomial time by a non-deterministic Turing machine that has ...

...clause learning''' ('''CDCL''') is an algorithm for solving the [[Boolean satisfiability problem]] (SAT). Given a Boolean formula, the SAT problem asks for an assi ...hor2=Karem A. Sakallah | title=GRASP: A Search Algorithm for Propositional Satisfiability | journal=IEEE Transactions on Computers | volume=48 | number=5 | pages=506 ...

...to this problem, which is the property we are interested in with decision problems. == Related problems == ...

{{Short description|Boolean satisfiability problem restricted to a planar incidence graph}} ...logic)|evaluates to TRUE]]. If this is the case, the formula is called ''[[Satisfiability|satisfiable]]''. On the other hand, if no such assignment exists, the funct ...

...e used to classify [[Boolean satisfiability problem|Boolean satisfiability problems]]. ...

..." /> In other words, it is a consequence of the [[QMA]] complexity of qPCP problems.<ref name=":1">{{Cite web |date=2020-11-03 |title=Circuit lower bounds for ...s that [[satisfiability]] problems like [[Boolean satisfiability problem#3-satisfiability|3SAT]] are [[NP (complexity)|NP-hard]] when estimating the maximal number o ...

...-instance basis. It is motivated by the observation that on many practical problems, different algorithms have different performance characteristics. That is, === Boolean satisfiability problem (and other hard combinatorial problems)=== ...

...time algorithm then they all do, and that many known algorithms for these problems have optimal or near-optimal time {{nowrap|complexity.{{r|ip99}}}} ...T}} can be solved in {{nowrap|time <math>O(2^{\delta n})</math>.}} Because problems with larger <math>k</math> cannot be easier, these numbers are ordered as { ...