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Polynomial size proofs of the propositional pigeonhole principle

Published online by Cambridge University Press:  12 March 2014

Samuel R. Buss
Samuel R. Buss*
Affiliation:
Mathematical Sciences Research Institute, Berkeley, California 94720
*
Department of Mathematics, University of California, Berkeley, California 94720
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Abstract

Cook and Reckhow defined a propositional formulation of the pigeonhole principle. This paper shows that there are Frege proofs of this propositional pigeonhole principle of polynomial size. This together with a result of Haken gives another proof of Urquhart's theorem that Frege systems have an exponential speedup over resolution. We also discuss connections to provability in theories of bounded arithmetic.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 52 , Issue 4 , December 1987 , pp. 916 - 927
Copyright
Copyright © Association for Symbolic Logic 1987

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References

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