Resolution lower bounds for the weak pigeon hole principle

Abstract

We prove that any resolution proof for the weak pigeonhole principle, with n holes and any number of pigeons, is of length /spl Omega/(2/sup n/spl isin//), (for some constant /spl isin/ > 0). One corollary is that a certain propositional formulation of the statement NP /spl nsub/ P/poly does not have short resolution proofs.