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EFFICIENT ALGORITHMS FOR CLAUSELEARNING SAT SOLVERS
, 2004
"... Boolean satisfiability (SAT) is NPcomplete. No known algorithm for SAT is of polynomial time complexity. Yet, many of the SAT instances generated as a means of solving realworld electronic design automation problems are simple enough, structurally, that modern solvers can decide them efficiently. ..."
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Cited by 58 (0 self)
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Boolean satisfiability (SAT) is NPcomplete. No known algorithm for SAT is of polynomial time complexity. Yet, many of the SAT instances generated as a means of solving realworld electronic design automation problems are simple enough, structurally, that modern solvers can decide them efficiently. Consequently, SAT solvers are widely used in industry for logic verification. The most robust solver algorithms are poorly understood and only vaguely described in the literature of the field. We refine these algorithms, and present them clearly. We introduce several new techniques for Boolean constraint propagation that substantially improve solver efficiency. We explain why literal count decision strategies succeed, and on that basis, we introduce a new decision strategy that outperforms the state of the art. The culmination of this work is the most powerful SAT solver publically available.
Diversification and determinism in local search for satisfiability
 In Proceedings of the Eighth International Conference on Theory and Applications of Satisfiability Testing (SAT05), volume 3569 of Lecture Notes in Computer Science (LNCS
, 2005
"... Abstract. The choice of the variable to flip in the Walksat family procedures is always random in that it is selected from a randomly chosen unsatisfied clause c. This choice in Novelty or RNovelty heuristics also contains some determinism in that the variable to flip is always limited to the two b ..."
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Cited by 36 (6 self)
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Abstract. The choice of the variable to flip in the Walksat family procedures is always random in that it is selected from a randomly chosen unsatisfied clause c. This choice in Novelty or RNovelty heuristics also contains some determinism in that the variable to flip is always limited to the two best variables in c. Inthis paper, we first propose a diversification parameter for Novelty (or RNovelty) heuristic to break the determinism in Novelty and show its performance compared with the random walk parameter in Novelty+. Then we exploit promising decreasing paths in a deterministic fashion in local search using a gradientbased approach. In other words, when promising decreasing paths exist, the variable to flip is no longer selected from a randomly chosen unsatisfied clause but in a deterministic fashion to surely decrease the number of unsatisfied clauses. Experimental results show that the proposed diversification and the determinism allow to significantly improve Novelty (and Walksat). 1
Propositional Satisfiability and Constraint Programming: a Comparative Survey
 ACM Computing Surveys
, 2006
"... Propositional Satisfiability (SAT) and Constraint Programming (CP) have developed as two relatively independent threads of research, crossfertilising occasionally. These two approaches to problem solving have a lot in common, as evidenced by similar ideas underlying the branch and prune algorithms ..."
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Cited by 32 (4 self)
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Propositional Satisfiability (SAT) and Constraint Programming (CP) have developed as two relatively independent threads of research, crossfertilising occasionally. These two approaches to problem solving have a lot in common, as evidenced by similar ideas underlying the branch and prune algorithms that are most successful at solving both kinds of problems. They also exhibit differences in the way they are used to state and solve problems, since SAT’s approach is in general a blackbox approach, while CP aims at being tunable and programmable. This survey overviews the two areas in a comparative way, emphasising the similarities and differences between the two and the points where we feel that one technology can benefit from ideas or experience acquired
Complete local search for propositional satisfiability
 In proceedings of AAAI
, 2004
"... Algorithms based on following local gradient information are surprisingly effective for certain classes of constraint satisfaction problems. Unfortunately, previous local search algorithms are notoriously incomplete: They are not guaranteed to find a feasible solution if one exists and they cannot b ..."
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Cited by 24 (0 self)
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Algorithms based on following local gradient information are surprisingly effective for certain classes of constraint satisfaction problems. Unfortunately, previous local search algorithms are notoriously incomplete: They are not guaranteed to find a feasible solution if one exists and they cannot be used to determine unsatisfiability. We present an algorithmic framework for complete local search and discuss in detail an instantiation for the propositional satisfiability problem (SAT). The fundamental idea is to use constraint learning in combination with a novel objective function that converges during search to a surface without local minima. Although the algorithm has worstcase exponential space complexity, we present empirical results on challenging SAT competition benchmarks that suggest that our implementation can perform as well as stateoftheart solvers based on more mature techniques. Our framework suggests a range of possible algorithms lying between treebased search and local search.
Satisfiability Solvers
, 2008
"... The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worstcase exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a generalpurpose tool in areas as diverse as software and h ..."
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Cited by 24 (0 self)
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The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worstcase exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a generalpurpose tool in areas as diverse as software and hardware verification [29–31, 228], automatic test pattern generation [138, 221], planning [129, 197], scheduling [103], and even challenging problems from algebra [238]. Annual SAT competitions have led to the development of dozens of clever implementations of such solvers [e.g. 13,
GrADSAT: A Parallel SAT Solver for the Grid
, 2003
"... We present GrADSAT, a parallel satisfiability solver aimed at solving hard SAT instances using a large number of widely distributed commodity computational resources. The GrADSAT parallel algorithm uses intelligent backtracking, sharing of learned clauses and clause reduction. The distributed implem ..."
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Cited by 24 (7 self)
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We present GrADSAT, a parallel satisfiability solver aimed at solving hard SAT instances using a large number of widely distributed commodity computational resources. The GrADSAT parallel algorithm uses intelligent backtracking, sharing of learned clauses and clause reduction. The distributed implementation allows for dynamic resource acquisition. We show how the large number of computational resources and communication overhead influence the implementation strategy. GrADSAT is compared against the best sequential solver using a wide variety of problem instances. The results show that GrADSAT delivers speedup on most instances. Furthermore it is capable of solving problem instance which were never solved before.
Fiftyfive solvers in Vancouver: The SAT 2004 competition
 In Proceedings of the Seventh International Conference on Theory and Applications of Satisfiability Testing (SAT’04
, 2004
"... Abstract. For the third consecutive year, a SAT competition was organized as a joint event with the SAT conference. With 55 solvers from 25 author groups, the competition was a clear success. One of the noticeable facts from the 2004 competition is the superiority of incomplete solvers on satisfiabl ..."
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Cited by 22 (2 self)
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Abstract. For the third consecutive year, a SAT competition was organized as a joint event with the SAT conference. With 55 solvers from 25 author groups, the competition was a clear success. One of the noticeable facts from the 2004 competition is the superiority of incomplete solvers on satisfiable random kSAT benchmarks. It can also be pointed out that the complete solvers awarded this year, namely Zchaff, jerusat1.3, satzoo1.02, kncfsand marcheq, participated in the SAT 2003 competition (or at least former versions of those solvers). This paper is not reporting exhaustive competition results, already available in details online, but rather focuses on some remarkable results derived from the competition dataset. The SAT 2004 competition is ending a 3year takeoff period that attracted new SAT researchers and provided many new benchmarks and solvers to the community. The good participation rate of this year (despite the addition of the antiblackbox rule) establishes the competition as an awaited yearly event. Some new directions for a new way of thinking about the competition are discussed at the end of the paper. 1
The SAT2002 Competition
, 2002
"... SAT Competition 2002 held in MarchMay 2002 in conjunction with SAT 2002 (the Fifth International Symposium on the Theory and Applications of Satisfiability Testing). About 30 solvers and 2300 benchmarks took part in the competition, which required more than 2 CPU years to complete the evaluation ..."
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Cited by 21 (2 self)
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SAT Competition 2002 held in MarchMay 2002 in conjunction with SAT 2002 (the Fifth International Symposium on the Theory and Applications of Satisfiability Testing). About 30 solvers and 2300 benchmarks took part in the competition, which required more than 2 CPU years to complete the evaluation. In this report
Ten challenges redux: Recent progress in propositional reasoning and search
 In Proceedings of CP ’03
, 2003
"... Abstract. In 1997 we presented ten challenges for research on satisfiability testing [1]. In this paper we review recent progress towards each of these challenges, including our own work on the power of clause learning and randomized restart policies. 1 ..."
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Cited by 16 (1 self)
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Abstract. In 1997 we presented ten challenges for research on satisfiability testing [1]. In this paper we review recent progress towards each of these challenges, including our own work on the power of clause learning and randomized restart policies. 1
Disorder inequality: A combinatorial approach to nearest neighbor search
 In WSDM’08
"... We say that an algorithm for nearest neighbor search is combinatorial if only direct comparisons between two pairwise similarity values are allowed. Combinatorial algorithms for nearest neighbor search have two important advantages: (1) they do not map similarity values to artificial distance values ..."
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Cited by 16 (4 self)
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We say that an algorithm for nearest neighbor search is combinatorial if only direct comparisons between two pairwise similarity values are allowed. Combinatorial algorithms for nearest neighbor search have two important advantages: (1) they do not map similarity values to artificial distance values and do not use the triangle inequality for the latter, and (2) they work for arbitrarily complicated data representations and similarity functions. In this paper we introduce a special property of the similarity function on a set S that leads to efficient combinatorial algorithms for S. The disorder constant D(S) of a set S is defined to ensure the following inequality: if x is the a’th most similar object to z and y is the b’th most similar object to z, then x is among the D(S) · (a + b) most similar objects to y. Assuming that disorder is small we present the first two known combinatorial algorithms for nearest neighbors whose query time has logarithmic dependence on the size of S. The first one, called Ranwalk, is a randomized zeroerror algorithm that always returns the exact nearest neighbor. It uses space quadratic in the input size in preprocessing, but is very efficient in query processing. The second algorithm, called Arwalk, uses nearlinear space. It uses random choices in preprocessing, but the query processing is essentially deterministic. For an arbitrary query q, there is only a small probability that the chosen data structure does not support q. Finally, we show that for the Reuters corpus average disorder is indeed quite small and that Ranwalk efficiently computes the nearest neighbor in most cases.