Lifting QBF Resolution Calculi to DQBF

  • Olaf Beyersdorff
  • Leroy Chew
  • Renate A. Schmidt
  • Martin Suda
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9710)

Abstract

We examine existing resolution systems for quantified Boolean formulas (QBF) and answer the question which of these calculi can be lifted to the more powerful Dependency QBFs (DQBF). An interesting picture emerges: While for QBF we have the strict chain of proof systems \(\textsf {Q-Res}< \textsf {IR-calc} < \textsf {IRM-calc} \), the situation is quite different in DQBF. The obvious adaptations of Q-Res and likewise universal resolution are too weak: they are not complete. The obvious adaptation of IR-calc has the right strength: it is sound and complete. IRM-calc is too strong: it is not sound any more, and the same applies to long-distance resolution. Conceptually, we use the relation of DQBF to effectively propositional logic (EPR) and explain our new DQBF calculus based on IR-calc as a subsystem of first-order resolution.

Notes

Acknowledgments

This research was supported by grant no. 48138 from the John Templeton Foundation, EPSRC grant EP/L024233/1, and a Doctoral Training Grant from the EPSRC (2nd author).

Martin Suda was supported by the EPSRC grant EP/K032674/1 and the ERC Starting Grant 2014 SYMCAR 639270.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Olaf Beyersdorff
    • 1
  • Leroy Chew
    • 1
  • Renate A. Schmidt
    • 2
  • Martin Suda
    • 2
  1. 1.School of ComputingUniversity of LeedsLeedsUK
  2. 2.School of Computer ScienceUniversity of ManchesterManchesterUK

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