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101
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 122 (2 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", generalizing the e ..."
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Cited by 66 (12 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...
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 55 (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 ...
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 53 (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.
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 51 (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...
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 49 (2 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...
Zchaff2004: An efficient SAT solver
 IN SAT (SELECTED PAPERS
, 2004
"... 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 ..."
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Cited by 39 (1 self)
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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 verification, planning, routing, etc. 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.
Approximate Solution Of Weighted MAXSAT Problems Using GRASP
, 1997
"... Computing the optimal solution to an instance of the weighted maximum satisfiability problem (MAXSAT) is difficult even when each clause contains at most two literals. In this paper, we describe a greedy randomized adaptive search procedure (GRASP) for computing approximate solutions of weighted MA ..."
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Cited by 33 (11 self)
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Computing the optimal solution to an instance of the weighted maximum satisfiability problem (MAXSAT) is difficult even when each clause contains at most two literals. In this paper, we describe a greedy randomized adaptive search procedure (GRASP) for computing approximate solutions of weighted MAXSAT problems. The heuristic is tested on a large set of test instances. Computational experience indicates the suitability of GRASP for this class of problems.
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 SATâ€™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
Reactive Search, a historybased heuristic for MAXSAT
 ACM Journal of Experimental Algorithmics
, 1996
"... The Reactive Search (RS) method proposes the integration of a simple historybased feedback scheme into local search for the online determination of free parameters. In this paper a new RS algorithm is proposed for the approximated solution of the Maximum Satisfiability problem: a component base ..."
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Cited by 29 (1 self)
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The Reactive Search (RS) method proposes the integration of a simple historybased feedback scheme into local search for the online determination of free parameters. In this paper a new RS algorithm is proposed for the approximated solution of the Maximum Satisfiability problem: a component based on local search with temporary prohibitions is complemented with a reactive scheme that determines ("learns") the appropriate value of the prohibition parameter by monitoring the Hamming distance along the search trajectory (algorithm HRTS). In addition, the nonoblivious functions recently introduced in the framework of approximation algorithms are used to discover a better local optimum in the initial part of the search.