License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SAT.2022.5
URN: urn:nbn:de:0030-drops-166792
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Schleitzer, Agnes ; Beyersdorff, Olaf

Classes of Hard Formulas for QBF Resolution

LIPIcs-SAT-2022-5.pdf (0.9 MB)


To date, we know only a few handcrafted quantified Boolean formulas (QBFs) that are hard for central QBF resolution systems such as Q-Res and QU-Res, and only one specific QBF family to separate Q-Res and QU-Res.
Here we provide a general method to construct hard formulas for Q-Res and QU-Res. The construction uses simple propositional formulas (e.g. minimally unsatisfiable formulas) in combination with easy QBF gadgets (Σ₂^b formulas without constant winning strategies). This leads to a host of new hard formulas, including new classes of hard random QBFs.
We further present generic constructions for formulas separating Q-Res and QU-Res, and for separating Q-Res and LD-Q-Res.

BibTeX - Entry

  author =	{Schleitzer, Agnes and Beyersdorff, Olaf},
  title =	{{Classes of Hard Formulas for QBF Resolution}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{5:1--5:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-242-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{236},
  editor =	{Meel, Kuldeep S. and Strichman, Ofer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-166792},
  doi =		{10.4230/LIPIcs.SAT.2022.5},
  annote =	{Keywords: QBF, proof complexity, resolution, separations}

Keywords: QBF, proof complexity, resolution, separations
Collection: 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)
Issue Date: 2022
Date of publication: 28.07.2022

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