Tight Bounds for Tseitin Formulas

Authors Dmitry Itsykson, Artur Riazanov, Petr Smirnov

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Dmitry Itsykson
  • St. Petersburg Department of V.A. Steklov Mathematical Institute of RAS, Russia
Artur Riazanov
  • St. Petersburg Department of V.A. Steklov Mathematical Institute of RAS, Russia
  • The Henry and Marylin Taub Faculty of Computer Science, Technion, Israel
Petr Smirnov
  • HSE University at Saint Petersburg, Russia
  • St. Petersburg Department of V.A. Steklov Mathematical Institute of RAS, Russia

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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)


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).

Subject Classification

ACM Subject Classification
  • Theory of computation → Proof complexity
  • Proof complexity
  • Tseitin formulas
  • treewidth
  • resolution
  • OBDD-based proof systems


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