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Variable Dependencies and Q-Resolution

  • Conference paper
Theory and Applications of Satisfiability Testing – SAT 2014 (SAT 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8561))

Abstract

We propose Q(D)-resolution, a proof system for Quantified Boolean Formulas. Q(D)-resolution is a generalization of Q-resolution parameterized by a dependency scheme D. This system is motivated by the generalization of the QDPLL algorithm using dependency schemes implemented in the solver DepQBF. We prove soundness of Q(D)-resolution for a dependency scheme D that is strictly more general than the standard dependency scheme; the latter is currently used by DepQBF. This result is obtained by proving correctness of an algorithm that transforms Q(D)-resolution refutations into Q-resolution refutations and could be of independent practical interest. We also give an alternative characterization of resolution- path dependencies in terms of directed walks in a formula’s implication graph which admits an algorithmically more advantageous treatment.

This research was supported by the ERC (COMPLEX REASON, 239962).

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Authors and Affiliations

  1. Institute of Information Systems, Vienna University of Technology, Vienna, Austria

    Friedrich Slivovsky & Stefan Szeider

Authors
  1. Friedrich Slivovsky
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  2. Stefan Szeider
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Editor information

Editors and Affiliations

  1. Karlsruher Institut für Technologie (KIT), Am Fasanengarten 5, 76131, Karlsruhe, Germany

    Carsten Sinz

  2. TU Wien, Favoritenstraße 9-11, 1040, Wien, Austria

    Uwe Egly

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Slivovsky, F., Szeider, S. (2014). Variable Dependencies and Q-Resolution. In: Sinz, C., Egly, U. (eds) Theory and Applications of Satisfiability Testing – SAT 2014. SAT 2014. Lecture Notes in Computer Science, vol 8561. Springer, Cham. https://doi.org/10.1007/978-3-319-09284-3_21

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  • DOI: https://doi.org/10.1007/978-3-319-09284-3_21

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09283-6

  • Online ISBN: 978-3-319-09284-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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