SAT v CSP

Walsh, Toby

doi:10.1007/3-540-45349-0_32

Cited by 163 publications

(108 citation statements)

References 3 publications

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“…Each tuple t k ∈ C j forbids a simultaneous assignment of the two variables in |D j1 × D j1 | (Cartesian product). There are several ways to encode a CSP problem into clauses [16]. This paper just considers the direct encoding but any other could be considered.…”

Section: Modeling Problems As Group Maxsatmentioning

confidence: 99%

An Empirical Study of Encodings for Group MaxSAT

Heras

Morgado

Marques-Silva

2012

Advances in Artificial Intelligence

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Abstract. Weighted Partial MaxSAT (WPMS) is a well-known optimization variant of Boolean Satisfiability (SAT) that finds a wide range of practical applications.WPMS divides the formula in two sets of clauses: The hard clauses that must be satisfied and the soft clauses that can be unsatisfied with a penalty given by their associated weight. However, some applications may require each constraint to be modeled as a set or group of clauses. The resulting formalism is referred to as Group MaxSAT. This paper overviews Group MaxSAT, and shows how several optimization problems can be modeled as Group MaxSAT. Several encodings from Group MaxSAT to standard MaxSAT are formalized and refined. A comprehensive empirical study compares the performance of several MaxSAT solvers with the proposed encodings. The results indicate that, depending on the underlying MaxSAT solver and problem domain, the solver may perform better with a given encoding than with the others.

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Section: Modeling Problems As Group Maxsatmentioning

confidence: 99%

An Empirical Study of Encodings for Group MaxSAT

Heras

Morgado

Marques-Silva

2012

Advances in Artificial Intelligence

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“…A widely used translation of graph coloring problems into SAT is known as the direct encoding [15]. Given a graph G = (V, E) and a set of colors C, the direct encoding uses (Boolean) color variables x v,i with v ∈ V and i ∈ C. If x v,i is assigned to true, it means that vertex v has color i.…”

Section: Direct Encodingmentioning

confidence: 99%

“…The main problem we solve is how to efficiently encode the graph coloring constraints of [12] into SAT. A naive direct encoding [15] of these constraints would lead to O(k 2 |V | 2 ) clauses, where k is the size of the identified DFA, and V is the set of labeled examples. Such a direct encoding is in fact identical to the unary encoding from [13], which can be considered the current state-of-the-art in translations of DFA identification to SAT.…”

Section: Introductionmentioning

confidence: 99%

Exact DFA Identification Using SAT Solvers

Heule

Verwer

2010

Grammatical Inference: Theoretical Results and Applications

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Abstract. We present an exact algorithm for identification of deterministic finite automata (DFA) which is based on satisfiability (SAT) solvers. Despite the size of the low level SAT representation, our approach is competitive with alternative techniques. Our contributions are fourfold: First, we propose a compact translation of DFA identification into SAT. Second, we reduce the SAT search space by adding lower bound information using a fast max-clique approximation algorithm. Third, we include many redundant clauses to provide the SAT solver with some additional knowledge about the problem. Fourth, we show how to use the flexibility of our translation in order to apply it to very hard problems. Experiments on a well-known suite of random DFA identification problems show that SAT solvers can efficiently tackle all instances. Moreover, our algorithm outperforms state-of-the-art techniques on several hard problems.

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“…In general, there are different ways to produce a SAT instance from a given CSP, usually called encodings [24,18]. Very popular encodings assign a logical variable to each possible element of a CSP domain, i.e., for each CSP variable i and each value v in its domain, there is a logical variable x i,v that is true iff variable i takes value v. The reason for such a domain representation is that it lets the SAT solver achieve pruning in a similar way to a CSP solver applied to the original CSP.…”

Section: Introductionmentioning

confidence: 99%

“…When the SAT solver infers that a logical variable x i,v is false, it means that the corresponding CSP variable i cannot take value v: the value v has been pruned. The most popular CSP-SAT encoding was called direct encoding by Walsh [24]; the DPLL applied to the SAT encoded CSP mimics the Forward Checking on the original CSP [10,24]. Gent [11] proposes the support encoding, that has the same representation of domains, but a different representation of constraints.…”

Section: Introductionmentioning

confidence: 99%

The Log-Support Encoding of CSP into SAT

Gavanelli

Principles and Practice of Constraint Programming – CP 2007

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Abstract. It is known that Constraint Satisfaction Problems (CSP) can be converted into Boolean Satisfiability problems (SAT); however how to encode a CSP into a SAT problem such that a SAT solver will efficiently find a solution is still an open question. Various encodings have been proposed in the literature. Some of them use a logical variable for each element in each domain: among these very successful are the direct and the support encodings. It is known that a SAT solver based on the DPLL procedure obtains a propagation similar to Forward Checking on a directencoded CSP, and to Maintaining Arc-Consistency on a support-encoded CSP.Other methods, such as the log-encoding, are more compact, and use a logarithmic number of logical variables to encode domains. However, they lack the propagation power of the direct and support encodings, so many SAT solvers perform better on direct/support encodings than in the log-encoding, as witnessed by many works in the literature. In this paper, we propose a new encoding that combines the log and support encodings. The new encoding, called log-support, has a logarithmic number of variables, and uses support clauses to obtain improved propagation. Experiments on Job-Shop scheduling problems and randomlygenerated problems show the effectiveness of the proposed approach, with respect to other popular approaches.

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SAT v CSP

Cited by 163 publications

References 3 publications

An Empirical Study of Encodings for Group MaxSAT

An Empirical Study of Encodings for Group MaxSAT

Exact DFA Identification Using SAT Solvers

The Log-Support Encoding of CSP into SAT

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