From DQBF to QBF by Dependency Elimination

Wimmer, Ralf; Karrenbauer, Andreas; Becker, Ruben; Scholl, Christoph; Becker, Bernd

doi:10.1007/978-3-319-66263-3_21

Cited by 10 publications

(11 citation statements)

References 29 publications

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“…For solving DQBFs, we use the three publicly available solvers iDQ [21], iProver [44], and HQS [78,28] and run them with and without preprocessing using HQSpre. Figures 2, 3, and 4 show cactus plots comparing the computation times including loading, preprocessing, and solving the formulas.…”

Section: Resultsmentioning

confidence: 99%

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

Wimmer

Scholl

Becker

2019

SAT

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Preprocessing turned out to be an essential step for SAT, QBF, and DQBF solvers to reduce/modify the number of variables and clauses of the formula, before the formula is passed to the actual solving algorithm. These preprocessing techniques often reduce the computation time of the solver by orders of magnitude. In this paper, we present the preprocessor HQSpre that was developed for Dependency Quantified Boolean Formulas (DQBFs) and that generalizes different preprocessing techniques for SAT and QBF problems to DQBF. We give a presentation of the underlying theory together with detailed proofs as well as implementation details contributing to the efficiency of the preprocessor. HQSpre has been used with obvious success by the winners of the DQBF track, and, even more interestingly, the QBF tracks of QBFEVAL'18.

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Section: Resultsmentioning

confidence: 99%

“…Driven by the needs of the applications mentioned above, research on DQBF solving has emerged in the past few years, leading to solvers such as iDQ [21], iProver [44], dCAQE [61], and HQS [28,77,78,22]. iDQ [21] reduces the solution of a DQBF to the solution of a series of SAT instantiations.…”

Section: Introductionmentioning

confidence: 99%

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

Wimmer

Scholl

Becker

2019

SAT

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“…For the future, we plan to look into fork extension for enabling quantifier localization in a more general setting, not only restricted to formulas from DQBF de+ . Moreover, we plan to complement the successful approach of the solver HQS which uses partial universal expansion and so-called dependency elimination (Wimmer et al 2017) for transforming a DQBF into a QBF by a technique that alternatively transforms the DQBF into an equisatisfiable DQBF in DQBF de+ , enabling a translation into 3QBF by fork extension.…”

Section: Discussionmentioning

confidence: 99%

“…Encouraged by those results we enhanced the DQBF solver HQS (Wimmer et al 2017) by a special treatment of formulas from DQBF de+ . Whenever we detect that a DQBF belongs to DQBF de+ we translate it into a QBF and process it further by QBF solving.…”

Section: Methodsmentioning

confidence: 99%

“…Driven by the needs of the applications mentioned above, research on DQBF solving has emerged in the past few years, leading to solvers such as IDQ (Fröhlich et al 2014) and HQS Wimmer et al 2015;Wimmer et al 2017). Due to the high worst-case complexity of DQBF solving, identifying special DQBF structures, as we do in this paper, may provide insights for solver improvement.…”

Section: Introductionmentioning

confidence: 98%

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A PSPACE Subclass of Dependency Quantified Boolean Formulas and Its Effective Solving

Scholl

Jiang

Wimmer

et al. 2019

AAAI

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Dependency quantified Boolean formulas (DQBFs) are a powerful formalism, which subsumes quantified Boolean formulas (QBFs) and allows an explicit specification of dependencies of existential variables on universal variables. This enables a succinct encoding of decision problems in the NEXPTIME complexity class. As solving general DQBFs is NEXPTIME complete, in contrast to the PSPACE completeness of QBF solving, characterizing DQBF subclasses of lower computational complexity allows their effective solving and is of practical importance. Recently a DQBF proof calculus based on a notion of fork extension, in addition to resolution and universal reduction, was proposed by Rabe in 2017. We show that this calculus is in fact incomplete for general DQBFs, but complete for a subclass of DQBFs, where any two existential variables have either identical or disjoint dependency sets over the universal variables. We further characterize this DQBF subclass to be Σ P 3 complete in the polynomial time hierarchy. Essentially using fork extension, a DQBF in this subclass can be converted to an equisatisfiable 3QBF with only a linear increase in formula size. We exploit this conversion for effective solving of this DQBF subclass and point out its potential as a general strategy for DQBF quantifier localization. Experimental results show that the method outperforms state-of-the-art DQBF solvers on a number of benchmarks, including the 2018 DQBF evaluation benchmarks.

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