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2002

A New Proof of the Weak Pigeonhole Principle

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A New Proof of the Weak Pigeonhole Principle
The exact complexity of the weak pigeonhole principle is an old and fundamental problem in proof complexity. Using a diagonalization argument, Paris, Wilkieand Woods 16] showed how to prove the weak pigeonholeprinciple with bounded-depth, quasipolynomial-size proofs. Their argument was further re ned by Kraj cek 9]. In this paper, we present a new proof: we show that the the weak pigeonhole principle has quasipolynomial-size LK proofs where every formula consists of a single AND/OR of polylog fan-in. Our proof is conceptually simpler than previous arguments, and is optimal with respect to depth.
Alexis Maciel, Toniann Pitassi, Alan R. Woods
Added 22 Dec 2010
Updated 22 Dec 2010
Type Journal
Year 2002
Where JCSS
Authors Alexis Maciel, Toniann Pitassi, Alan R. Woods
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