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A Little Blocked Literal Goes a Long Way

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Book cover Theory and Applications of Satisfiability Testing – SAT 2017 (SAT 2017)

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

Abstract

Q-resolution is a generalization of propositional resolution that provides the theoretical foundation for search-based solvers of quantified Boolean formulas (QBFs). Recently, it has been shown that an extension of Q-resolution, called long-distance resolution, is remarkably powerful both in theory and in practice. However, it was unknown how long-distance resolution is related to \(\mathsf {QRAT}\), a proof system introduced for certifying the correctness of QBF-preprocessing techniques. We show that \(\mathsf {QRAT}\) polynomially simulates long-distance resolution. Two simple rules of \(\mathsf {QRAT}\) are crucial for our simulation—blocked-literal addition and blocked-literal elimination. Based on the simulation, we implemented a tool that transforms long-distance-resolution proofs into \(\mathsf {QRAT}\) proofs. In a case study, we compare long-distance-resolution proofs of the well-known Kleine Büning formulas with corresponding \(\mathsf {QRAT}\) proofs.

This work has been supported by the Austrian Science Fund (FWF) under projects W1255-N23 and S11408-N23, and by the National Science Foundation (NSF) under grant number CCF-1618574.

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Notes

  1. 1.

    Clause deletion was not used in the simulation, but is allowed in the \(\mathsf {QRAT}\) system.

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Authors and Affiliations

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

    Benjamin Kiesl

  2. Department of Computer Science, The University of Texas at Austin, Austin, USA

    Marijn J. H. Heule

  3. Institute for Formal Models and Verification, JKU Linz, Linz, Austria

    Martina Seidl

Authors
  1. Benjamin Kiesl
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  2. Marijn J. H. Heule
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  3. Martina Seidl
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Correspondence to Benjamin Kiesl .

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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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Kiesl, B., Heule, M.J.H., Seidl, M. (2017). A Little Blocked Literal Goes a Long Way. 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_18

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  • DOI: https://doi.org/10.1007/978-3-319-66263-3_18

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