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Building Strategies into QBF Proofs

Authors Olaf Beyersdorff, Joshua Blinkhorn, Meena Mahajan

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Olaf Beyersdorff
  • Institut für Informatik, Friedrich-Schiller-Universität Jena, Germany
Joshua Blinkhorn
  • Institut für Informatik, Friedrich-Schiller-Universität Jena, Germany
Meena Mahajan
  • The Institute of Mathematical Sciences, HBNI, Chennai, India

Funding

Supported by the EU Marie Curie IRSES grant CORCON, and grant no. 60842 from the John Templeton Foundation.

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Olaf Beyersdorff, Joshua Blinkhorn, and Meena Mahajan. Building Strategies into QBF Proofs. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.STACS.2019.14

Abstract

Strategy extraction is of paramount importance for quantified Boolean formulas (QBF), both in solving and proof complexity. It extracts (counter)models for a QBF from a run of the solver resp. the proof of the QBF, thereby allowing to certify the solver’s answer resp. establish soundness of the system. So far in the QBF literature, strategy extraction has been algorithmically performed from proofs. Here we devise the first QBF system where (partial) strategies are built into the proof and are piecewise constructed by simple operations along with the derivation. 
This has several advantages: (1) lines of our calculus have a clear semantic meaning as they are accompanied by semantic objects; (2) partial strategies are represented succinctly (in contrast to some previous approaches); (3) our calculus has strategy extraction by design; and (4) the partial strategies allow new sound inference steps which are disallowed in previous central QBF calculi such as Q-Resolution and long-distance Q-Resolution.
The last item (4) allows us to show an exponential separation between our new system and the previously studied reductionless long-distance resolution calculus, introduced to model QCDCL solving.
Our approach also naturally lifts to dependency QBFs (DQBF), where it yields the first sound and complete CDCL-type calculus for DQBF, thus opening future avenues into DQBF CDCL solving.

Subject Classification

ACM Subject Classification
  • Theory of computation → Proof complexity
Keywords
  • QBF
  • DQBF
  • resolution
  • proof complexity

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