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ASSAT: Computing Answer Sets of a Logic Program by SAT Solvers
 Artificial Intelligence
, 2002
"... We propose a new translation from normal logic programs with constraints under the answer set semantics to propositional logic. Given a normal logic program, we show that by adding, for each loop in the program, a corresponding loop formula to the program’s completion, we obtain a onetoone corresp ..."
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Cited by 263 (7 self)
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We propose a new translation from normal logic programs with constraints under the answer set semantics to propositional logic. Given a normal logic program, we show that by adding, for each loop in the program, a corresponding loop formula to the program’s completion, we obtain a onetoone correspondence between the answer sets of the program and the models of the resulting propositional theory. In the worst case, there may be an exponential number of loops in a logic program. To address this problem, we propose an approach that adds loop formulas a few at a time, selectively. Based on these results, we implement a system called ASSAT(X), depending on the SAT solver X used, for computing one answer set of a normal logic program with constraints. We test the system on a variety of benchmarks including the graph coloring, the blocks world planning, and Hamiltonian Circuit domains. Our experimental results show that in these domains, for the task of generating one answer set of a normal logic program, our system has a clear edge over the stateofart answer set programming systems Smodels and DLV. 1 1
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 144 (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.
Contingent Planning Under Uncertainty via Stochastic Satisfiability
 Artificial Intelligence
, 1999
"... We describe two new probabilistic planning techniques cmaxplan and zanderthat generate contingent plans in probabilistic propositional domains. Both operate by transforming the planning problem into a stochastic satisfiability problem and solving that problem instead. cmaxplan encodes t ..."
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Cited by 70 (11 self)
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We describe two new probabilistic planning techniques cmaxplan and zanderthat generate contingent plans in probabilistic propositional domains. Both operate by transforming the planning problem into a stochastic satisfiability problem and solving that problem instead. cmaxplan encodes the problem as an EMajsat instance, while zander encodes the problem as an SSat instance. Although SSat problems are in a higher complexity class than EMajsat problems, the problem encodings produced by zander are substantially more compact and appear to be easier to solve than the corresponding EMajsat encodings. Preliminary results for zander indicate that it is competitive with existing planners on a variety of problems. Introduction When planning under uncertainty, any information about the state of the world is precious. A contingent plan is one that can make action choices contingent on such information. In this paper, we present an implemented framework for contingent pl...
UnitWalk: A new SAT solver that uses local search guided by unit clause elimination
, 2002
"... In this paper we present a new randomized algorithm for SAT, i.e., the satisfiability problem for Boolean formulas in conjunctive normal form. Despite its simplicity, this algorithm performs well on many common benchmarks ranging from graph coloring problems to microprocessor verification. ..."
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Cited by 69 (1 self)
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In this paper we present a new randomized algorithm for SAT, i.e., the satisfiability problem for Boolean formulas in conjunctive normal form. Despite its simplicity, this algorithm performs well on many common benchmarks ranging from graph coloring problems to microprocessor verification.
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
Approximating Minimal Unsatisfiable Subformulae by Means of Adaptive Core Search
 Discrete Applied Mathematics
, 2002
"... The paper is concerned with the relevant practical problem of selecting a small unsatisfiable subset of clauses inside an unsatisfiable CNF formula. Moreover, it deals with the algorithmic problem of improving an enumerative (DPLLstyle) approach to SAT, in order to overcome some structural defects ..."
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Cited by 29 (1 self)
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The paper is concerned with the relevant practical problem of selecting a small unsatisfiable subset of clauses inside an unsatisfiable CNF formula. Moreover, it deals with the algorithmic problem of improving an enumerative (DPLLstyle) approach to SAT, in order to overcome some structural defects of such approach. Within a complete solution framework, we are able to evaluate the di#culty of each clause, by analyzing the history of the search. Such clause hardness evaluation is used in order to rapidly select an unsatisfiable subformula (of the given CNF) which is a good approximation of a minimal unsatisfiable subformula (MUS). Unsatisfiability is proved by solving only such subformula. Very small unsatisfiable subformulae are detected inside famous Dimacs unsatisfiable problems and in real world problems. Comparison with the very e#cient solver SATO 3.2 used as a stateoftheart DPLL procedure (disabling learning of new clauses) shows the e#ectiveness of such enumeration guide.
Evaluating Search Heuristics and Optimization Techniques in Propositional Satisfiability
 In Proc. of IJCAR 2001, volume 2083 of LNCS
, 2001
"... This paper is devoted to the experimental evaluation of several stateofthe art search heuristics and optimization techniques in propositional satisfiability (SAT). The test set consists of random 3CNF formulas as well as real world instances from planning, scheduling, circuit analysis, bounded ..."
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Cited by 26 (12 self)
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This paper is devoted to the experimental evaluation of several stateofthe art search heuristics and optimization techniques in propositional satisfiability (SAT). The test set consists of random 3CNF formulas as well as real world instances from planning, scheduling, circuit analysis, bounded model checking, and security protocols. All the heuristics and techniques have been implemented in a new library for SAT, called SIM. The comparison is fair because in SIM the selected heuristics and techniques are realized on a common platform. The comparison is significative because SIM as a solver performs very well when compared to other stateoftheart solvers. 1
Combining the Scalability of Local Search with the Pruning Techniques of . . .
 Annals of Operations Research
, 2002
"... Systematic backtracking is used in many constraint solvers and combinatorial optimisation algorithms. It is complete and can be combined with powerful search pruning techniques such as branchandbound, constraint propagation and dynamic variable ordering. However, it often scales poorly to large pr ..."
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Cited by 19 (6 self)
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Systematic backtracking is used in many constraint solvers and combinatorial optimisation algorithms. It is complete and can be combined with powerful search pruning techniques such as branchandbound, constraint propagation and dynamic variable ordering. However, it often scales poorly to large problems. Local search is incomplete, and has the additional drawback that it cannot exploit pruning techniques, making it uncompetitive on some problems. Nevertheless its scalability makes it superior for many large applications. This paper describes a hybrid approach called Incomplete Dynamic Backtracking, a very flexible form of backtracking that sacrifices completeness to achieve the scalability of local search. It is combined with forward checking and dynamic variable ordering, and evaluated on three combinatorial problems: on the nqueens problem it outperforms the best local search algorithms; it finds large optimal Golomb rulers much more quickly than a constraintbased backtracker, and better rulers than a genetic algorithm; and on benchmark graphs it finds larger cliques than almost all other tested algorithms. We argue that this form of backtracking is actually local search in a space of consistent partial assignments, offering a generic way of combining standard pruning techniques with local search.