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.

• Type: Journal
• Year: 2002
• Where: JCSS
• Authors: Alexis Maciel, Toniann Pitassi, Alan R. Woods
• Keywords: Exact Complexity, JCSS 2002, Proof Complexity, Weak Pigeonhole Principle