Comparing Different Prenexing Strategies for Quantified Boolean Formulas

Egly, Uwe; Seidl, Martina; Tompits, Hans; Woltran, Stefan; Zolda, Michael

doi:10.1007/978-3-540-24605-3_17

Cited by 33 publications

(42 citation statements)

References 27 publications

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“…In the following, we generalize unit literals and learning (Def. 4,6,8) to arbitrary dependency schemes. Soundness is explained by reordering the quantifiers in the prefix of a PCNF F based on D by Def.…”

Section: Qdpll With Learningmentioning

confidence: 99%

“…A special case in this respect is the analysis of quantifier structure in QBFs, either before [8,16] or after [2] conversion to PCNF. Such approaches allow a QBF solver to overcome the restrictions of linear quantifier prefixes in PCNFs to some extent.…”

Section: Introductionmentioning

confidence: 99%

“…This can be achieved either by reconstructing quantifier trees from PCNFs [2], which is closely related to minimizing quantifier scopes by miniscoping [1], or by analyzing tree structure present in non-PCNF formulae as e.g. in [8,16]. The latter corresponds to directly considering the parse tree of a formula and can be integrated in non-PCNF solvers such as [9,18,28].…”

Section: Introductionmentioning

confidence: 99%

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Integrating Dependency Schemes in Search-Based QBF Solvers

Lonsing

Biere

2010

Theory and Applications of Satisfiability Testing – SAT 2010

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Abstract. Many search-based QBF solvers implementing the DPLL algorithm for QBF (QDPLL) process formulae in prenex conjunctive normal form (PCNF). The quantifier prefix of PCNFs often results in strong variable dependencies which can influence solver performance negatively. A common approach to overcome this problem is to reconstruct quantifier structure e.g. by quantifier trees. Dependency schemes are a generalization of quantifier trees in the sense that more general dependency graphs can be obtained. So far, dependency graphs have not been applied in QBF solving. In this work we consider the problem of efficiently integrating dependency graphs in QDPLL. Thereby we generalize related work on integrating quantifier trees. By analyzing the core parts of QDPLL, we report on modifications necessary to profit from general dependency graphs. In comprehensive experiments we show that QDPLL using a particular dependency graph, despite of increased overhead, outperforms classical QDPLL relying on quantifier prefixes of PCNFs.

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Section: Qdpll With Learningmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Integrating Dependency Schemes in Search-Based QBF Solvers

Lonsing

Biere

2010

Theory and Applications of Satisfiability Testing – SAT 2010

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“…Similar as in first-order logic, however, there are different ways how to obtain an equivalent prenex QBF (cf. [8] for more details on this issue).…”

Section: Quantified Propositional Logicmentioning

confidence: 99%

“…[8]), which, roughly speaking, results from S Π (V 1 ) by deleting all quantifiers. For later purposes, we use in the following the second variant, and define S p…”

Section: Applicability and Adequacy Of The Encodingsmentioning

confidence: 99%

Towards Implementations for Advanced Equivalence Checking in Answer-Set Programming

Tompits

Woltran

2005

Logic Programming

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Abstract. In recent work, a general framework for specifying program correspondences under the answer-set semantics has been defined. The framework allows to define different notions of equivalence, including the well-known notions of strong and uniform equivalence, as well as refined equivalence notions based on the projection of answer sets, where not all parts of an answer set are of relevance (like, e.g., removal of auxiliary letters). In the general case, deciding the correspondence of two programs lies on the fourth level of the polynomial hierarchy and therefore this task can (presumably) not be efficiently reduced to answerset programming. In this paper, we describe an approach to compute program correspondences in this general framework by means of linear-time constructible reductions to quantified propositional logic. We can thus use extant solvers for the latter language as back-end inference engines for computing program correspondence problems. We also describe how our translations provide a method to construct counterexamples in case a program correspondence does not hold.

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Dependency Quantified Horn Formulas: Models and Complexity

Bubeck

Büning

2006

Lecture Notes in Computer Science

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Comparing Different Prenexing Strategies for Quantified Boolean Formulas

Cited by 33 publications

References 27 publications

Integrating Dependency Schemes in Search-Based QBF Solvers

Integrating Dependency Schemes in Search-Based QBF Solvers

Towards Implementations for Advanced Equivalence Checking in Answer-Set Programming

Dependency Quantified Horn Formulas: Models and Complexity

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