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Resolution lower bounds for the weak pigeonhole principle

2002
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Proceedings of the thiry-fourth annual ACM symposium on Theory of computing - STOC '02
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We prove that any Resolution proof for the weak pigeon hole principle, with n holes and any number of pigeons, is of length Ω(2 n ), (for some constant > 0). One corollary is that a certain propositional formulation of the statement N P 6 P = p o l ydoes not have short Resolution proofs. The Pigeon Hole Principle (PHP) is one of the most widely studied tautologies in propositional proof theory. The tautology P H P n is a DNF encoding of the following statement: There is no one to one mapping

doi:10.1145/509984.509987
fatcat:7pu7sukc5vcsrhoua54tsakile