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General resolution of tseitin formulas is hard

  • Complexity (Session 4)
  • Conference paper
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Automata, Languages and Programming (ICALP 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 510))

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Abstract

G being a graph, we define its cyclomatic cohesion γ(G).Then,using Tseitin method [Tse 70], we construct a contradictory formula C(G) and prove our main theorem:

Every resolution of C(G) contains,at least, 2γ(G) distinct clauses.

Applying it with Margulis graphs, we obtain an exponentially growing lower bound for the complexity of resolution. A similar result was obtained by A. Urquhart [Urq 87] with a different method valid only for a specific family of graphs. Moreover we give a new algorithm recognizing these formulas in linear time.

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References

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Authors and Affiliations

  1. Laboratoire de Mathématiques et Informatique, Université de Haute-Alsace, 4, rue des frères Lumière, 68093, Mulhouse Cedex, France

    Jean-Denis Fouks

Authors
  1. Jean-Denis Fouks
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Editor information

Javier Leach Albert Burkhard Monien Mario Rodríguez Artalejo

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© 1991 Springer-Verlag Berlin Heidelberg

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Fouks, JD. (1991). General resolution of tseitin formulas is hard. In: Albert, J.L., Monien, B., Artalejo, M.R. (eds) Automata, Languages and Programming. ICALP 1991. Lecture Notes in Computer Science, vol 510. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54233-7_131

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  • DOI: https://doi.org/10.1007/3-540-54233-7_131

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54233-9

  • Online ISBN: 978-3-540-47516-3

  • eBook Packages: Springer Book Archive

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