Resolution lower bounds for the weak pigeonhole principle.

We prove that any Resolution proof for the weak pigeonhole principle, with n holes and any number of pigeons, is of length Ω(2nε), (for some global constant ε > 0). One corollary is that a certain propositional formulation of the statement NP ⊄ P/poly does not have short Resolut...

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Bibliographic Details

Published in:	Journal of the ACM 51, 2 (2004).
Main Author:	Raz, R.
Format:	Article
Language:	English
Subjects:	Theory of computation. Analysis of algorithms and problem complexity. Nonnumerical algorithms and problems. Complexity of proof procedures. Mathematical logic and formal languages. Mathematical logic. Proof theory. Theory.