弱鸽洞原理的分辨率下界

Proceedings 17th IEEE Annual Conference on Computational Complexity Pub Date : 2002-05-19 DOI:10.1109/CCC.2002.1004322

Ran Raz

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引用次数: 316

摘要

我们证明了具有n个洞和任意数目鸽子的弱鸽子洞原理的任何分辨证明长度为/spl Omega/(2/sup n/spl isin//)，(对于某常数/spl isin/ > 0)。一个推论是命题NP /spl nsub/ P/poly的某个命题表述没有短分辨证明。

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Resolution lower bounds for the weak pigeon hole principle

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.

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Proceedings 17th IEEE Annual Conference on Computational Complexity

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