General resolution of tseitin formulas is hard

  • Jean-Denis Fouks
Complexity (Session 4)
Part of the Lecture Notes in Computer Science book series (LNCS, volume 510)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Jean-Denis Fouks
    • 1
  1. 1.Laboratoire de Mathématiques et InformatiqueUniversité de Haute-AlsaceMulhouse CedexFrance

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