Using Randomization and Learning to Solve Hard Real-World Instances of Satisfiability

Baptista, Luís; Silva, João P. Marques

doi:10.1007/3-540-45349-0_36

Cited by 45 publications

(48 citation statements)

References 7 publications

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“…We note that this result can be viewed as a generalization of the completeness condition used in search restarts, which consists of increasing the backtrack cutoff value after search restart [1].…”

Section: Propositionmentioning

confidence: 92%

See 1 more Smart Citation

Heuristic-Based Backtracking Relaxation for Propositional Satisfiability

Bhalla¹,

Lynce²,

Sousa³

et al. 2005

Sat 2005

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Abstract. In recent years backtrack search algorithms for propositional satisfiability (SAT) have been the subject of dramatic improvements. These improvements allowed SAT solvers to successfully solve instances with thousands or tens of thousands of variables. However, many new challenging problem instances are still too hard for current SAT solvers. As a result, further improvements to SAT technology are expected to have key consequences in solving hard realworld instances. This paper introduces a new idea: choosing the backtrack variable using a heuristic approach with the goal of diversifying the regions of the space that are explored during the search. The proposed heuristics are inspired by the heuristics proposed in recent years for the decision branching step of SAT solvers, namely, VSIDS and its improvements. Completeness conditions are established, which guarantee completeness for the new algorithm, as well as for any other incomplete backtracking algorithm. Experimental results on hundreds of instances derived from real-world problems show that the new technique is able to speed SAT solvers, while aborting fewer instances. These results clearly motivate the integration of heuristic backtracking in SAT solvers.

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Section: Propositionmentioning

confidence: 92%

“…The search is repeatedly restarted whenever a cutoff value is reached. In [1], search restarts were jointly used with learning for solving hard real-world instances of SAT. This latter algorithm is complete because the backtrack cutoff value increases after each restart.…”

Section: Related Workmentioning

confidence: 99%

Heuristic-Based Backtracking Relaxation for Propositional Satisfiability

Bhalla¹,

Lynce²,

Sousa³

et al. 2005

Sat 2005

Self Cite

View full text Add to dashboard Cite

show abstract

“…The algorithm proposed is not complete, since the restart cutoff point is kept constant. But in [2] search restarts were combined with learning for solving hard, real-world instances of SAT. This latter algorithm is complete, since the backtrack cutoff value increases after each restart.…”

Section: Methodsmentioning

confidence: 99%

Local Search for Unsatisfiability

Prestwich

Lynce

2006

Lecture Notes in Computer Science

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Abstract. Local search is widely applied to satisfiable SAT problems, and on some classes outperforms backtrack search. An intriguing challenge posed by Selman, Kautz and McAllester in 1997 is to use it instead to prove unsatisfiability. We investigate two distinct approaches. Firstly we apply standard local search to a reformulation of the problem, such that a solution to the reformulation corresponds to a refutation of the original problem. Secondly we design a greedy randomised resolution algorithm that will eventually discover proofs of any size while using bounded memory. We show experimentally that both approaches can refute some problems more quickly than backtrack search.

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“…Conflict clause minimization was introduced by Eén and Sörensson [ES04] in their solver Minisat. Randomized restarts were introduced by Gomes et al [GSK98] and further developed by Baptista and Marques-Silva [BMS00]. The watch literals scheme by Moskewicz et al was introduced in their solver zChaff [MMZ + 01], and is now a standard method used by most SAT solvers for efficient constraint propagation.…”

Section: Related Workmentioning

confidence: 99%

Formalization and Implementation of Modern SAT Solvers

Marić

2009

J Autom Reasoning

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Most, if not all, state-of-the-art complete SAT solvers are complex variations of the DPLL procedure described in the early 1960's. Published descriptions of these modern algorithms and related data structures are given either as high-level (rule-based) transition systems or, informally, as (pseudo) programming language code. The former, although often accompanied with (informal) correctness proofs, are usually very abstract and do not specify many details crucial for efficient implementation. The latter usually do not involve any correctness argument and the given code is often hard to understand and modify. This paper aims at bridging this gap: we present SAT solving algorithms that are formally proved correct, but at the same time they contain information required for efficient implementation. We use a tutorial, top-down, approach and develop a SAT solver, starting from a simple design that is subsequently extended, step-by-step, with the requisite series of features. Heuristic parts of the solver are abstracted away, since they usually do not affect solver correctness (although they are very important for efficiency). All algorithms are given in pseudo-code. The code is accompanied with correctness conditions, given in Hoare logic style. Correctness proofs are formalized within the Isabelle theorem proving system and are available in the extended version of this paper. The given pseudo-code served as a basis for our SAT solver argo-sat.

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Using Randomization and Learning to Solve Hard Real-World Instances of Satisfiability

Cited by 45 publications

References 7 publications

Heuristic-Based Backtracking Relaxation for Propositional Satisfiability

Heuristic-Based Backtracking Relaxation for Propositional Satisfiability

Local Search for Unsatisfiability

Formalization and Implementation of Modern SAT Solvers

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