Solving QBF with Counterexample Guided Refinement

Janota, Mikoláš; Klieber, William; Marques-Silva, João; Clarke, Edmund M.

doi:10.1007/978-3-642-31612-8_10

Cited by 128 publications

(93 citation statements)

References 24 publications

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“…Therefore, this section mainly describes a method for extracting unsatisfiable cores using a CEGAR-based QBF solver [37,38]. Additionally, it also briefly mentions how this can be also done in QDPLL-based solvers.…”

Section: Core Extraction In Qmaxsatmentioning

confidence: 99%

“…Among the many practical uses of the counterexample guided abstraction refinement (CEGAR) [20], it can also be applied for solving QBF [37,38]. The key idea of CEGAR is to consider an approximate representation of a problem (called the abstraction) instead of its explicit representation that could be too large to construct or unknown.…”

Section: Extracting Cores In Cegar-based Qbfmentioning

confidence: 99%

“…Following the ideas of [37], the method for core extraction described above can be extended to the case of formulas with an arbitrary number of quantification levels. Hence, we assume that we are given a false formula ∃X − → Q .…”

Section: Extending Rareqs With Core Extractionmentioning

confidence: 99%

“…Additionally, it also extends the algorithm for the formulas with an arbitrary number of quantification levels. The reader is referred to [37,38] for further details and properties of the algorithm.…”

Section: Extracting Cores In Cegar-based Qbfmentioning

confidence: 99%

“…Thus, this new approach requires QBF solvers to be able to produce unsatisfiable cores. As a result, the second contribution of this paper is to show how recent 2QBF solvers based on abstraction refinement [37,38] can be modified to produce unsatisfiable cores.…”

Section: Introductionmentioning

confidence: 99%

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Quantified maximum satisfiability

2015

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In recent years, there have been significant improvements in algorithms both for Quantified Boolean Formulas (QBF) and for Maximum Satisfiability (MaxSAT). This paper studies an optimization extension of QBF and considers the problem in a quantified MaxSAT setting. More precisely, the general QMaxSAT problem is defined for QBFs with a set of soft clausal constraints and consists in finding the largest subset of the soft constraints such that the remaining QBF is true. Two approaches are investigated. One is based on relaxing the soft clauses and performing an iterative search on the cost function. The other approach, which is the main contribution of the paper, is inspired by recent work on MaxSAT, and exploits the iterative identification of unsatisfiable cores. The paper investigates the application of these approaches to the two concrete problems of computing smallest minimal unsatisfiable subformulas (SMUS) and smallest minimal equivalent subformulas (SMES), decision versions of which are well-known problems in the second level of the polynomial hierarchy. Experimental results, obtained on representative problem instances, indicate that the core-guided approach for the SMUS and SMES problems outperforms the use of iterative search over the values of the cost function. More significantly, Alexey Ignatiev Constraints the core-guided approach to SMUS also outperforms the state-of-the-art SMUS extractor Digger.

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Section: Core Extraction In Qmaxsatmentioning

confidence: 99%

Section: Extracting Cores In Cegar-based Qbfmentioning

confidence: 99%

Section: Extending Rareqs With Core Extractionmentioning

confidence: 99%

Section: Extracting Cores In Cegar-based Qbfmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantified maximum satisfiability

2015

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QRATPre+: Effective QBF Preprocessing via Strong Redundancy Properties

Lonsing

Egly

2019

Lecture Notes in Computer Science

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We present version 2.0 of QRATPre+, a preprocessor for quantified Boolean formulas (QBFs) based on the QRAT proof system and its generalization QRAT + . These systems rely on strong redundancy properties of clauses and universal literals. QRATPre+ is the first implementation of these redundancy properties in QRAT and QRAT + used to simplify QBFs in preprocessing. It is written in C and features an API for easy integration in other QBF tools. We present implementation details and report on experimental results demonstrating that QRATPre+ improves upon the power of state-of-the-art preprocessors and solvers.

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