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

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Computer Science Logic (CSL 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 933))

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Abstract

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.

Partially supported by US-Czechoslovak Science and Technology Program grant No. 93025

Partially supported by US-Czechoslovak Science and Technology Program grant No. 93025 and by NSF grant DMS92-05181

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Authors and Affiliations

  1. Mathematics Institute, Academy of Sciences of the Czech Republic, Prague

    Pavel Pudlák

  2. Department of Mathematics, University of California, San Diego

    Samuel R. Buss

Authors
  1. Pavel Pudlák
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  2. Samuel R. Buss
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Leszek Pacholski Jerzy Tiuryn

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© 1995 Springer-Verlag Berlin Heidelberg

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Pudlák, P., Buss, S.R. (1995). How to lie without being (easily) convicted and the lengths of proofs in propositional calculus. In: Pacholski, L., Tiuryn, J. (eds) Computer Science Logic. CSL 1994. Lecture Notes in Computer Science, vol 933. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022253

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  • DOI: https://doi.org/10.1007/BFb0022253

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60017-6

  • Online ISBN: 978-3-540-49404-1

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