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International Conference on Theory and Applications of Satisfiability Testing

SAT 2017: Theory and Applications of Satisfiability Testing – SAT 2017 pp 326–343Cite as

From DQBF to QBF by Dependency Elimination

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10491))

Abstract

In this paper, we propose the elimination of dependencies to convert a given dependency quantified Boolean formula (DQBF) to an equisatisfiable QBF. We show how to select a set of dependencies to eliminate such that we arrive at a smallest equisatisfiable QBF in terms of existential variables that is achievable using dependency elimination. This approach is improved by taking so-called don’t-care dependencies into account, which result from the application of dependency schemes to the formula and can be added to or removed from the formula at no cost. We have implemented this new method in the state-of-the-art DQBF solver HQS. Experiments show that dependency elimination is clearly superior to the previous method using variable elimination.

This work was partly supported by the German Research Council (DFG) as part of the project “Solving Dependency Quantified Boolean Formulas” and by the Max Planck Center for Visual Computing and Communication (www.mpc-vcc.org). Ruben Becker is a member of the Saarbrücken Graduate School of Computer Science.

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Notes

  1. 1.

    Note that each cyclic bipartite tournament graph has a cycle of length 4.

  2. 2.

    The approach of dynamically or lazily adding constraints is similar to the cutting plane approach [36] and is used as one of the main ingredients for efficiently solving many NP-hard problems for which only a description with exponentially many constraints is at hand, as for example the traveling salesman problem.

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Authors and Affiliations

  1. Albert-Ludwigs-Universität Freiburg, Freiburg im Breisgau, Germany

    Ralf Wimmer, Christoph Scholl & Bernd Becker

  2. MPI for Informatics, Saarland Informatics Campus, Saarbrücken, Germany

    Andreas Karrenbauer & Ruben Becker

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  1. Ralf Wimmer
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  2. Andreas Karrenbauer
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  3. Ruben Becker
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  4. Christoph Scholl
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  5. Bernd Becker
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Correspondence to Ralf Wimmer .

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Editors and Affiliations

  1. UNSW Sydney, Sydney, New South Wales, Australia

    Serge Gaspers

  2. University of New South Wales , Sydney, New South Wales, Australia

    Toby Walsh

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Wimmer, R., Karrenbauer, A., Becker, R., Scholl, C., Becker, B. (2017). From DQBF to QBF by Dependency Elimination. In: Gaspers, S., Walsh, T. (eds) Theory and Applications of Satisfiability Testing – SAT 2017. SAT 2017. Lecture Notes in Computer Science(), vol 10491. Springer, Cham. https://doi.org/10.1007/978-3-319-66263-3_21

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  • DOI: https://doi.org/10.1007/978-3-319-66263-3_21

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