An Upper Bound for Minimal Resolution Refutations

  • Hans Kleine Büning
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1584)


We consider upper bounds for minimal resolution refutations of propositional formulas in CNF. We show that minimal refutations of minimal unsatisfiable formulas over n variables and n+k clauses consist of at most 2 k − 1 n 2 applications of the resolution rule.


propositional formulas length of proofs minimal unsatisfiability resolution 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Hans Kleine Büning
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of PaderbornPaderbornGermany

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