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Simplified and improved resolution lower bounds

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2 Author(s)
Beame, P. ; Dept. of Comput. Sci. & Eng., Washington Univ., Seattle, WA, USA ; Pitassi, T.

We give simple new lower bounds on the lengths of resolution proofs for the pigeonhole principle and for randomly generated formulas. For random formulas, our bounds significantly extend the range of formula sizes for which non-trivial lower bounds are known. For example, we show that with probability approaching 1, any resolution refutation of a randomly chosen 3-CNF formula with at most n6/5-ε clauses requires exponential size. Previous bounds applied only when the number of clauses was at most linear in the number of variables. For the pigeonhole principle our bound is a small improvement over previous bounds. Our proofs are more elementary than previous arguments, and establish a connection between resolution proof size and maximum clause size

Published in:

Foundations of Computer Science, 1996. Proceedings., 37th Annual Symposium on

Date of Conference:

14-16 Oct 1996