The (D)QBF Preprocessor HQSpre – Underlying Theory and Its Implementation1

Wimmer, Ralf; Scholl, Christoph; Becker, Bernd

doi:10.3233/sat190115

Cited by 6 publications

(10 citation statements)

References 61 publications

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“…4 Specifically, we choose the solvers dCAQE [47], iDQ [16], HQS [20], and the recently introduced DQBDD [39]. Both HQS and DQBDD internally use HQSPre [51] as a preprocessor. For dCAQE and iDQ, we call HQSPre with a time limit of 300 seconds (the time for preprocessing is included in the total running time).…”

Section: Performance On Standard Benchmark Setsmentioning

confidence: 99%

“…It uses expansion alongside several other techniques to transform a DQBF into an equivalent QBF and leverage advances in QBF solving [50,18]. HQS is paired with a powerful preprocessor named HQSPre that provides an arsenal of additional simplification techniques [51], including an incomplete but efficient method for refuting DQBF by reduction to a QBF encoding [14]. HQSpre is also used in the recently developed solver DQBDD [39], which is similar to HQS but relies on Binary Decision Diagrams (BDDs) instead of AIGs to represent formulas and perform quantifier elimination.…”

Section: Related Workmentioning

confidence: 99%

“…We implemented the CEGIS algorithm in a system named Pedant. In an experimental evaluation, Pedant performs very well compared to a selection of state-of-the-art solvers-notably, it achieves good performance without the aid of the powerful preprocessor HQSPre [51]. One of the benefits of its functioncentric design is that Pedant internally computes a family of Skolem functions, and can output models of true instances at a negligible overhead.…”

Section: Introductionmentioning

confidence: 99%

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Certified DQBF Solving by Definition Extraction

Reichl¹,

Slivovsky²,

Szeider³

2021

Preprint

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We propose a new decision procedure for dependency quantified Boolean formulas (DQBFs) that uses interpolation-based definition extraction to compute Skolem functions in a counter-example guided inductive synthesis (CEGIS) loop. In each iteration, a family of candidate Skolem functions is tested for correctness using a SAT solver, which either determines that a model has been found, or returns an assignment of the universal variables as a counterexample. Fixing a counterexample generally involves changing candidates of multiple existential variables with incomparable dependency sets. Our procedure introduces auxiliary variables-which we call arbiter variables-that each represent the value of an existential variable for a particular assignment of its dependency set. Possible repairs are expressed as clauses on these variables, and a SAT solver is invoked to find an assignment that deals with all previously seen counterexamples. Arbiter variables define the values of Skolem functions for assignments where they were previously undefined, and may lead to the detection of further Skolem functions by definition extraction.A key feature of the proposed procedure is that it is certifying by design: for true DQBF, models can be returned at minimal overhead. Towards certification of false formulas, we prove that clauses can be derived in an expansion-based proof system for DQBF. In an experimental evaluation on standard benchmark sets, a prototype implementation was able to match (and in some cases, surpass) the performance of state-of-the-art-solvers. Moreover, models could be extracted and validated for all true instances that were solved.

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Section: Performance On Standard Benchmark Setsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Certified DQBF Solving by Definition Extraction

Reichl¹,

Slivovsky²,

Szeider³

2021

Preprint

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show abstract

“…The success in SAT, QBF, and DQBF solving is partly due to efficient preprocessing techniques (Eén and Biere 2005;Manthey 2012;Giunchiglia, Marin, and Narizzano 2010;Biere, Lonsing, and Seidl 2011;Wimmer, Scholl, and Becker 2019). Preprocessing is a fast procedure that aims to simplify a given formula in terms of its variable count, clause count, and dependency structure, while keeping the overhead minimized.…”

Section: Introductionmentioning

confidence: 99%

Lifting (D)QBF Preprocessing and Solving Techniques to (D)SSAT

Cheng

Jiang

2023

AAAI

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Dependency stochastic Boolean satisfiability (DSSAT) generalizes stochastic Boolean satisfiability (SSAT) in existential variables being Henkinized allowing their dependencies on randomized variables to be explicitly specified. It allows NEXPTIME problems of reasoning under uncertainty and partial information to be compactly encoded. To date, no decision procedure has been implemented for solving DSSAT formulas. This work provides the first such tool by converting DSSAT into SSAT with dependency elimination, similar to converting dependency quantified Boolean formula (DQBF) to quantified Boolean formula (QBF). Moreover, we extend (D)QBF preprocessing techniques and implement the first standalone (D)SSAT preprocessor. Experimental results show that solving DSSAT via dependency elimination is highly applicable and that existing SSAT solvers may benefit from preprocessing.

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“…Indeed, research on DQBF is picking up steam in all directions-from investigations of restricted cases (Bubeck and Büning 2006) and DQBF proof systems and their proof complexity (Beyersdorff et al 2016;Balabanov, Chiang, and Jiang 2014;Beyersdorff et al 2018), through the development of powerful DQBF solvers and preprocessors (Fröhlich et al 2012;Fröhlich et al 2014;Finkbeiner and Tentrup 2014;Tentrup and Rabe 2019;Wimmer, Scholl, and Becker 2019), to the establishment of an independent DQBF track in the annual QBF Evaluation 1 .…”

Section: Introductionmentioning

confidence: 99%

Fixed-Parameter Tractability of Dependency QBF with Structural Parameters

Ganian

Peitl

Slivovsky

et al. 2020

Proceedings of the Seventeenth International Conference on Principles of Knowledge Representation and Reasoning

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We study dependency quantified Boolean formulas (DQBF), an extension of QBF in which dependencies of existential variables are listed explicitly rather than being implicit in the order of quantifiers. DQBF evaluation is a canonical NEXPTIME-complete problem, a complexity class containing many prominent problems that arise in Knowledge Representation and Reasoning. One approach for solving such hard problems is to identify and exploit structural properties captured by numerical parameters such that bounding these parameters gives rise to an efficient algorithm. This idea is captured by the notion of fixed-parameter tractability (FPT). We initiate the study of DQBF through the lens of fixed-parameter tractability and show that the evaluation problem becomes FPT under two natural parameterizations: the treewidth of the primal graph of the DQBF instance combined with a restriction on the interactions between the dependency sets, and also the treedepth of the primal graph augmented by edges representing dependency sets.

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The (D)QBF Preprocessor HQSpre – Underlying Theory and Its Implementation1

Cited by 6 publications

References 61 publications

Certified DQBF Solving by Definition Extraction

Certified DQBF Solving by Definition Extraction

Lifting (D)QBF Preprocessing and Solving Techniques to (D)SSAT

Fixed-Parameter Tractability of Dependency QBF with Structural Parameters

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