Proof Complexity of Fragments of Long-Distance Q-Resolution

  • Tomáš Peitl
  • Friedrich SlivovskyEmail author
  • Stefan Szeider
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11628)


Q-resolution is perhaps the most well-studied proof system for Quantified Boolean Formulas (QBFs). Its proof complexity is by now well understood, and several general proof size lower bound techniques have been developed. The situation is quite different for long-distance Q-resolution (LDQ-resolution). While lower bounds on LDQ-resolution proof size have been established for specific families of formulas, we lack semantically grounded lower bound techniques for LDQ-resolution.

In this work, we study restrictions of LDQ-resolution. We show that a specific lower bound technique based on bounded-depth strategy extraction does not work even for reductionless Q-resolution by presenting short proofs of the QParity formulas. Reductionless Q-resolution is a variant of LDQ-resolution that admits merging but no universal reduction. We also prove a lower bound on the proof size of the completion principle formulas in reductionless Q-resolution. This shows that two natural fragments of LDQ-resolution are incomparable: Q-resolution, which allows universal reductions but no merging, and reductionless Q-resolution, which allows merging but no universal reductions. Finally, we develop semantically grounded lower bound techniques for fragments of LDQ-resolution, specifically tree-like LDQ-resolution and regular reductionless Q-resolution.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Tomáš Peitl
    • 1
  • Friedrich Slivovsky
    • 1
    Email author
  • Stefan Szeider
    • 1
  1. 1.Algorithms and Complexity Group, TU WienViennaAustria

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