Space complexity of random formulae in resolution

Proceedings 16th Annual IEEE Conference on Computational Complexity Pub Date : 2001-06-18 DOI:10.1109/CCC.2001.933871

Eli Ben-Sasson, Nicola Galesi

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引用次数: 87

Abstract

We study the space complexity of refuting unsatisfiable random k-CNFs in the resolution proof system. We prove that for any large enough /spl Delta/, with high probability a random k-CNF over n variables and /spl Delta/n clauses requires resolution clause space of /spl Omega/(n/spl middot//spl Delta//sup -1+/spl epsiv//k-2-/spl epsiv//), for any 0>/spl radic/n. This bound is nearly tight. Specifically, we show that with high probability, a random 3-CNF with /spl Delta/n clauses requires tree-like refutation size of exp(/spl Omega/(n//spl Delta//sup 1+/spl epsiv//1-/spl epsiv//)), for any 0

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分辨率中随机公式的空间复杂度

研究了分辨率证明系统中驳斥不可满足随机k- cnf的空间复杂度。我们证明了对于任何足够大的/spl δ /，高概率的n变量随机k-CNF和/spl δ /n子句，对于任何0>/spl径向/n，需要分辨率子句空间为/spl ω /(n/spl middot//spl δ //sup -1+/spl epsiv//k-2-/spl epsiv//)。这个界限几乎很紧。具体来说，我们证明了对于任意0

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Proceedings 16th Annual IEEE Conference on Computational Complexity

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