Journal of Symbolic Logic

Polynomial Size Proofs of the Propositional Pigeonhole Principle

Samuel R. Buss

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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.

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J. Symbolic Logic, Volume 52, Issue 4 (1987), 916-927.

First available in Project Euclid: 6 July 2007

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Buss, Samuel R. Polynomial Size Proofs of the Propositional Pigeonhole Principle. J. Symbolic Logic 52 (1987), no. 4, 916--927.

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