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145
The Quest for Efficient Boolean Satisfiability Solvers
, 2002
"... has seen much interest in not just the theoretical computer science community, but also in areas where practical solutions to this problem enable significant practical applications. Since the first development of the basic search based algorithm proposed by Davis, Putnam, Logemann and Loveland (DPLL ..."
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Cited by 149 (3 self)
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has seen much interest in not just the theoretical computer science community, but also in areas where practical solutions to this problem enable significant practical applications. Since the first development of the basic search based algorithm proposed by Davis, Putnam, Logemann and Loveland (DPLL) about forty years ago, this area has seen active research effort with many interesting contributions that have culminated in stateoftheart SAT solvers today being able to handle problem instances with thousands, and in same cases even millions, of variables. In this paper we examine some of the main ideas along this passage that have led to our current capabilities. Given the depth of the literature in this field, it is impossible to do this in any comprehensive way; rather we focus on techniques with consistent demonstrated efficiency in available solvers. For the most part, we focus on techniques within the basic DPLL search framework, but also briefly describe other approaches and look at some possible future research directions. 1.
New methods for 3SAT decision and worstcase analysis
 THEORETICAL COMPUTER SCIENCE
, 1999
"... We prove the worstcase upper bound 1:5045 n for the time complexity of 3SAT decision, where n is the number of variables in the input formula, introducing new methods for the analysis as well as new algorithmic techniques. We add new 2 and 3clauses, called "blocked clauses", generali ..."
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Cited by 73 (14 self)
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We prove the worstcase upper bound 1:5045 n for the time complexity of 3SAT decision, where n is the number of variables in the input formula, introducing new methods for the analysis as well as new algorithmic techniques. We add new 2 and 3clauses, called "blocked clauses", generalizing the extension rule of "Extended Resolution." Our methods for estimating the size of trees lead to a refined measure of formula complexity of 3clausesets and can be applied also to arbitrary trees. Keywords: 3SAT, worstcase upper bounds, analysis of algorithms, Extended Resolution, blocked clauses, generalized autarkness. 1 Introduction In this paper we study the exponential part of time complexity for 3SAT decision and prove the worstcase upper bound 1:5044:: n for n the number of variables in the input formula, using new algorithmic methods as well as new methods for the analysis. These methods also deepen the already existing approaches in a systematically manner. The following results...
Stochastic Boolean Satisfiability
 Journal of Automated Reasoning
, 2000
"... . Satisfiability problems and probabilistic models are core topics of artificial intelligence and computer science. This paper looks at the rich intersection between these two areas, opening the door for the use of satisfiability approaches in probabilistic domains. The paper examines a generic stoc ..."
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Cited by 63 (9 self)
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. Satisfiability problems and probabilistic models are core topics of artificial intelligence and computer science. This paper looks at the rich intersection between these two areas, opening the door for the use of satisfiability approaches in probabilistic domains. The paper examines a generic stochastic satisfiability problem, SSat, which can function for probabilistic domains as Sat does for deterministic domains. It shows the connection between SSat and well studied problems in belief network inference and planning under uncertainty, and defines algorithms, both systematic and stochastic, for solving SSat instances. These algorithms are validated on random SSat formulae generated under the fixedclause model. In spite of the large complexity gap between SSat (PSPACE) and Sat (NP), the paper suggests that much of what we've learned about Sat transfers to the probabilistic domain. 1. Introduction There has been a recent focus in artificial intelligence (AI) on solving problems exh...
The efficiency of resolution and DavisPutnam procedures
 SIAM Journal on Computing
, 1999
"... We consider several problems related to the use of resolutionbased methods for determining whether a given boolean formula in conjunctive normal form is satisfiable. First, building on work of Clegg, Edmonds and Impagliazzo, we give an algorithm for satisfiability that when given an unsatisfiabl ..."
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Cited by 62 (1 self)
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We consider several problems related to the use of resolutionbased methods for determining whether a given boolean formula in conjunctive normal form is satisfiable. First, building on work of Clegg, Edmonds and Impagliazzo, we give an algorithm for satisfiability that when given an unsatisfiable formula of F finds a resolution proof of F , and the runtime of our algorithm is nontrivial as a function of the size of the shortest resolution proof of F . Next we investigate a class of backtrack search algorithms, commonly known as DavisPutnam procedures and provide the first averagecase complexity analysis for their behavior on random formulas. In particular, for a simple algorithm in this class, called ordered DLL we prove that the running time of the algorithm on a randomly generated kCNF formula with n variables and m clauses is 2 Q(n(n/m) 1/(k2) ) with probability 1  o(1). Finally, we give new lower bounds on res(F), the size of the smallest resolution refutation ...
Zchaff2004: An efficient sat solver
 Lecture Notes in Computer Science
, 2005
"... Abstract. The Boolean Satisfiability Problem (SAT) is a well known NPComplete 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 w ..."
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Cited by 60 (1 self)
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Abstract. The Boolean Satisfiability Problem (SAT) is a well known NPComplete 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. 1
A Distributed Algorithm to Evaluate Quantified Boolean Formulae
, 2000
"... In this paper, we present PQSOLVE, a distributed theoremprover for Quantified Boolean Formulae. First, we introduce our sequential algorithm QSOLVE, which uses new heuristics and improves the use of known heuristics to prune the search tree. As a result, QSOLVE is more efficient than the QSAT ..."
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Cited by 57 (1 self)
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In this paper, we present PQSOLVE, a distributed theoremprover for Quantified Boolean Formulae. First, we introduce our sequential algorithm QSOLVE, which uses new heuristics and improves the use of known heuristics to prune the search tree. As a result, QSOLVE is more efficient than the QSATsolvers previously known. We have parallelized QSOLVE. The resulting distributed QSATsolver PQSOLVE uses parallel search techniques, which we have developed for distributed game tree search. PQSOLVE runs efficiently on distributed systems, i. e. parallel systems without any shared memory. We briefly present experiments that show a speedup of about 114 on 128 processors. To the best of our knowledge we are the first to introduce an efficient parallel QSATsolver.
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 50 (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,
On the Complexity of Unsatisfiability Proofs for Random kCNF Formulas
 In 30th Annual ACM Symposium on the Theory of Computing
, 1997
"... We study the complexity of proving unsatisfiability for random kCNF formulas with clause density D = m=n where m is number of clauses and n is the number of variables. We prove the first nontrivial general upper bound, giving algorithms that, in particular, for k = 3 produce refutations almost cer ..."
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Cited by 48 (1 self)
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We study the complexity of proving unsatisfiability for random kCNF formulas with clause density D = m=n where m is number of clauses and n is the number of variables. We prove the first nontrivial general upper bound, giving algorithms that, in particular, for k = 3 produce refutations almost certainly in time 2 O(n=D) . This is polynomial when m n 2 =logn. We show that our upper bounds are tight for certain natural classes of DavisPutnam algorithms. We show further that random 3CNF formulas of clause density D almost certainly have no resolution refutation of size smaller than 2 W(n=D 4+e ) , which implies the same lower bound on any DavisPutnam algorithm. We also give a much simpler argument based on a novel form of selfreduction that yields a slightly weaker 2 W(n=D 5+e ) lower bound. 1 Introduction The random kCNF model has been widely studied for several good reasons. First, it is an intrinsically natural model, analogous to the random graph model, that shed...
Bounded synthesis
, 2007
"... The bounded synthesis problem is to construct an implementation that satisfies a given temporal specification and a given bound on the number of states. We present a solution to the bounded synthesis problem for lineartime temporal logic (LTL), based on a novel emptinesspreserving translation from ..."
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Cited by 41 (9 self)
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The bounded synthesis problem is to construct an implementation that satisfies a given temporal specification and a given bound on the number of states. We present a solution to the bounded synthesis problem for lineartime temporal logic (LTL), based on a novel emptinesspreserving translation from LTL to safety tree automata. For distributed architectures, where standard unbounded synthesis is in general undecidable, we show that bounded synthesis can be reduced to a SAT problem. As a result, we obtain an effective algorithm for the bounded synthesis from LTL specifications in arbitrary architectures. By iteratively increasing the bound, our construction can also be used as a semidecision procedure for the unbounded synthesis problem.
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 38 (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