A machine program for theorem-proving

Davis, Martin; Logemann, George; Loveland, Donald W.

doi:10.1145/368273.368557

Cited by 2,239 publications

(719 citation statements)

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“…However, their proposed algorithm had impractically large memory requirements. Davis, Logemann and Loveland [8] proposed an algorithm that used search instead of resolution. This algorithm is often referred to as the DPLL algorithm.…”

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%

“…The well known Davis-Logemann-Loveland (DLL) [8] algorithm forms the framework for many successful complete SAT solvers. DLL is sometimes referred to as DPLL for historical reasons.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: The Dpll Algorithm With Learningmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Zchaff2004: An Efficient SAT Solver

Mahajan

Malik

2005

Theory and Applications of Satisfiability Testing

111

View full text Add to dashboard Cite

show abstract

“…This basic mechanism is then exploited to decide a formula f , by adding one clause at a time and solving |f | incremental sub-problems. The proposed algorithm is an adaptation of the basic DPLL procedure [9] that retains the position in the search tree (the path form the root to the last node examined) when a model for f is encountered. Then, if the assignment also satisfies f ∪ {Γ }, nothing has to be done.…”

Section: Related Workmentioning

confidence: 99%

Incremental Compilation-to-SAT Procedures

Benedetti

Bernardini

2005

Theory and Applications of Satisfiability Testing

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Abstract. We focus on incremental compilation-to-SAT procedures (iCTS), a promising way to push the standard CTS approaches beyond their limits. We propose the first comprehensive framework that encompasses all the aspects of an incremental decision procedure, from the encoding to the incremental solver. We apply our guidelines to a real-world CTS approach (Bounded Model Checking) and show how to modify both the generation mechanism of a real BMC tool (NuSMV) and the solving engine of a public-domain SAT solver (SIM). Related approaches and experimental results are discussed as well.

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“…By a random (n, m, k)-CNF expression we mean a CNF expression of m clauses, each chosen uniformly at random and with replacement from among the set of 2 k n k elementary disjunctions of k literals on a set of n Boolean variables and their complements. Simple variants of the well known Davis-PutnamLogemann-Loveland algorithm (DPLL) [32] which never reassign a value to a variable once it is set can solve large random (n, m, k)-CNF expressions with probability tending to 1 if they are generated with m/n < c k 2 k /k, where c k is a constant plus a term of complexity o(k). Since variables are assigned at most one time, those variants run in polynomial time.…”

Section: Introductionmentioning

confidence: 99%