On Approaches to Explaining Infeasibility of Sets of Boolean Clauses

Grégoire, Éric; Mazure, Bertrand; Piette, Cédric

doi:10.1109/ictai.2008.39

Cited by 24 publications

(25 citation statements)

References 30 publications

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“…A key definition in MUS extraction algorithms is that of transition clause [18]. A transition clause c is such that, if added to a satisfiable subformula R, the resulting subformula is unsatisfiable.…”

Section: From Mus Extraction To Mes Extractionmentioning

confidence: 99%

“…MUSes find a wide range of practical applications, and have been extensively studied (see [18,14,27] for recent overviews, and [23,21,16,17] for connections with CSP). The problem of computing minimal (or irredundant) representations of CNF formulas (and related problems) has been the subject of extensive research (e.g.…”

Section: Related Workmentioning

confidence: 99%

“…While the direct approach is similar to the well-known deletion-based approach for the computation of Minimal Unsatisfiable Subformulas (MUSes), most of the techniques developed for the extraction of MUSes (e.g. see [18,14,27]) have not been extended to the computation of MESes.…”

Section: Introductionmentioning

confidence: 99%

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On Computing Minimal Equivalent Subformulas

Belov

Janota

Lynce

et al. 2012

Lecture Notes in Computer Science

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Abstract. A propositional formula in Conjunctive Normal Form (CNF) may contain redundant clauses -clauses whose removal from the formula does not affect the set of its models. Identification of redundant clauses is important because redundancy often leads to unnecessary computation, wasted storage, and may obscure the structure of the problem. A formula obtained by the removal of all redundant clauses from a given CNF formula F is called a Minimal Equivalent Subformula (MES) of F. This paper proposes a number of efficient algorithms and optimization techniques for the computation of MESes. Previous work on MES computation proposes a simple algorithm based on iterative application of the definition of a redundant clause, similar to the well-known deletionbased approach for the computation of Minimal Unsatisfiable Subformulas (MUSes). This paper observes that, in fact, most of the existing algorithms for the computation of MUSes can be adapted to the computation of MESes. However, some of the optimization techniques that are crucial for the performance of the state-of-the-art MUS extractors cannot be applied in the context of MES computation, and thus the resulting algorithms are often not efficient in practice. To address the problem of efficient computation of MESes, the paper develops a new class of algorithms that are based on the iterative analysis of subsets of clauses. The experimental results, obtained on representative problem instances, confirm the effectiveness of the proposed algorithms. The experimental results also reveal that many CNF instances obtained from the practical applications of SAT exhibit a large degree of redundancy.

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Section: From Mus Extraction To Mes Extractionmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

On Computing Minimal Equivalent Subformulas

Belov

Janota

Lynce

et al. 2012

Lecture Notes in Computer Science

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“…A survey of existing approaches to this problem can be found in (Grégoire, Mazure, and Piette 2008). The majority of these techniques rely on the concept of Minimal Unsatisfiable Subformula (MUS) in order to explain the source of infeasibility.…”

Section: Explanations In Propositional Satmentioning

confidence: 99%

“…Our notion of explanation is related to that of Minimal Unsatisfiable Subformula (MUS) in the propositional SAT field (Grégoire, Mazure, and Piette 2008) and to that of axiom pinpointing in Description Logics (Schlobach and Cornet 2003). In the next subsections, we review the most relevant works in these areas.…”

Section: Computing Explanationsmentioning

confidence: 99%

AuRUS: explaining the validation of UML/OCL conceptual schemas

et al. 2013

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Abstract:The validation and the verification of conceptual schemas have attracted a lot of interest during the last years, and several tools have been developed to automate this process as much as possible. This is achieved, in general, by assessing whether the schema satisfies different kinds of desirable properties which ensure that the schema is correct. In this paper we describe AuRUS, a tool we have developed to analyze UML/OCL conceptual schemas and to explain their (in)correctness. When a property is satisfied, AuRUS provides a sample instantiation of the schema showing a particular situation where the property holds. When it is not, AuRUS provides an explanation for such unsatisfiability, i.e., a set of integrity constraints which is in contradiction with the property.

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