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DOI: 10.4230/LIPIcs.SAT.2022.6

Tight Bounds for Tseitin Formulas

Authors: Dmitry Itsykson, Artur Riazanov, and Petr Smirnov

Published in: LIPIcs, Volume 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)

Abstract

We show that for any connected graph G the size of any regular resolution or OBDD(∧, reordering) refutation of a Tseitin formula based on G is at least 2^Ω(tw(G)), where tw(G) is the treewidth of G. These lower bounds improve upon the previously known bounds and, moreover, they are tight. For both of the proof systems, there are constructive upper bounds that almost match the obtained lower bounds, hence the class of Tseitin formulas is almost automatable for regular resolution and for OBDD(∧, reordering).

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Dmitry Itsykson, Artur Riazanov, and Petr Smirnov. Tight Bounds for Tseitin Formulas. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 6:1-6:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{itsykson_et_al:LIPIcs.SAT.2022.6,
  author =	{Itsykson, Dmitry and Riazanov, Artur and Smirnov, Petr},
  title =	{{Tight Bounds for Tseitin Formulas}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{6:1--6:21},
  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 =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022.6},
  URN =		{urn:nbn:de:0030-drops-166805},
  doi =		{10.4230/LIPIcs.SAT.2022.6},
  annote =	{Keywords: Proof complexity, Tseitin formulas, treewidth, resolution, OBDD-based proof systems}
}

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Tight Bounds for Tseitin Formulas

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