How to lie without being (easily) convicted and the lengths of proofs in propositional calculus

  • Pavel Pudlák
  • Samuel R. Buss
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 933)


We shall describe two general methods for proving lower bounds on the lengths of proofs in propositional calculus and give examples of such lower bounds. One of the methods is based on interactive proofs where one player is claiming that he has a falsifying assignment for a tautology and the second player is trying to convict him of a lie. The second method is based on boolean valuations. For the first method, a log n + log log n -O(logloglog n) lower bound is given on the lengths of interactive proofs of certain permutation tautologies.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Pavel Pudlák
    • 1
  • Samuel R. Buss
    • 2
  1. 1.Mathematics InstituteAcademy of Sciences of the Czech RepublicPrague
  2. 2.Department of MathematicsUniversity of CaliforniaSan Diego

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