A Computing Procedure for Quantification Theory

Davis, Martin; Putnam, Hilary

doi:10.1007/978-3-642-81952-0_9

Cited by 547 publications

(782 citation statements)

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“…Resolution itself is a rule of inference widely used in automated deduction [18][19][20]. In the present study, as in [12], we implement the Satz resolution process (see Algorithm 2) as follows: when two clauses of a CNF formula have the property that some variable x i occurs positively in one and negatively in the other, the resolvent of the clauses is a disjunction of all the literals occurring in the clauses except x i and x i .…”

Section: Resolution Based Preprocessingmentioning

confidence: 99%

Adaptive Clause Weight Redistribution

Ishtaiwi

Thornton

Anbulagan

et al. 2006

Principles and Practice of Constraint Programming - CP 2006

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Abstract. In recent years, dynamic local search (DLS) clause weighting algorithms have emerged as the local search state-of-the-art for solving propositional satisfiability problems. However, most DLS algorithms require the tuning of domain dependent parameters before their performance becomes competitive. If manual parameter tuning is impractical then various mechanisms have been developed that can automatically adjust a parameter value during the search. To date, the most effective adaptive clause weighting algorithm is RSAPS. However, RSAPS is unable to convincingly outperform the best non-weighting adaptive algorithm AdaptNovelty + , even though manually tuned clause weighting algorithms can routinely outperform the Novelty + heuristic on which AdaptNovelty + is based. In this study we introduce R+DDFW + , an enhanced version of the DDFW clause weighting algorithm developed in 2005, that not only adapts the total amount of weight according to the degree of stagnation in the search, but also incorporates the latest resolution-based preprocessing approach used by the winner of the 2005 SAT competition (R+AdaptNovelty + ). In an empirical study we show R+DDFW + improves on DDFW and outperforms the other leading adaptive (R+Adapt-Novelty + , R+RSAPS) and non-adaptive (R+G 2 WSAT) local search solvers over a range of random and structured benchmark problems.

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Section: Resolution Based Preprocessingmentioning

confidence: 99%

Adaptive Clause Weight Redistribution

Ishtaiwi

Thornton

Anbulagan

et al. 2006

Principles and Practice of Constraint Programming - CP 2006

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“…The original Davis-Putnam satisfiability procedure [9] uses unit propagation and elimination for Cheap; it looks for the absence of complementary literals to declare Sat; it detects unsatisfiability in the form of an empty set; and merges by generating one round of resolvents.…”

Section: Intersection Methodsmentioning

confidence: 99%

Boolean Rings for Intersection-Based Satisfiability

Dershowitz

Hsiang

Huang

et al. 2006

Logic for Programming, Artificial Intelligence, and Reasoning

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There is not a person in this courtroomwho has never told a lie, who has never done an immoral thing, and there is no man living who has never looked upon a woman without desire. 1 -Harper Lee: To Kill a MockingbirdAbstract. A potential advantage of using a Boolean-ring formalism for propositional formulae is the large measure of simplification it facilitates. We propose a combined linear and binomial representation for Booleanring polynomials with which one can easily apply Gaussian elimination and Horn-clause methods to advantage. We demonstrate that this framework, with its enhanced simplification, is especially amenable to intersection-based learning, as in recursive learning and the method of Stålmarck. Experiments support the idea that problem variables can be eliminated and search trees can be shrunk by incorporating learning in the form of Boolean-ring saturation.

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“…In 1960, Davis and Putnam [7] proposed an algorithm for solving SAT which was based on resolution. Their method used resolution for the existential abstrac-tion of variables from the original instance and produced a series of equivalent SAT decision problems with fewer variables.…”

Section: The Dpll Algorithm With Learningmentioning

confidence: 99%

“…Consequently, there are many practical algorithms based on various principles such as Resolution [7], Systematic Search [8], Stochastic Local Search [9], Binary Decision Diagrams [10], Stålmarck's [11] algorithm, and others. Gu et al [12] provide a review of many of the algorithms.…”

Section: Introductionmentioning

confidence: 99%

Zchaff2004: An Efficient SAT Solver

Mahajan

Malik

2005

Theory and Applications of Satisfiability Testing

111

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Abstract. The Boolean Satisfiability Problem (SAT) is a well known NP-Complete problem. While its complexity remains a source of many interesting questions for theoretical computer scientists, the problem has found many practical applications in recent years. The emergence of efficient SAT solvers which can handle large structured SAT instances has enabled the use of SAT solvers in diverse domains such as electronic design automation and artificial intelligence. These applications continue to motivate the development of faster and more robust SAT solvers. In this paper, we describe the popular SAT solver zchaff with a focus on recent developments.

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A Computing Procedure for Quantification Theory

Cited by 547 publications

References 1 publication

Adaptive Clause Weight Redistribution

Adaptive Clause Weight Redistribution

Boolean Rings for Intersection-Based Satisfiability

Zchaff2004: An Efficient SAT Solver

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