Journal of Symbolic Logic

The complexity of resolution refinements

Joshua Buresh-Oppenheim and Toniann Pitassi

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Resolution is the most widely studied approach to propositional theorem proving. In developing efficient resolution-based algorithms, dozens of variants and refinements of resolution have been studied from both the empirical and analytic sides. The most prominent of these refinements are: DP (ordered), DLL (tree), semantic, negative, linear and regular resolution. In this paper, we characterize and study these six refinements of resolution. We give a nearly complete characterization of the relative complexities of all six refinements. While many of the important separations and simulations were already known, many new ones are presented in this paper; in particular, we give the first separation of semantic resolution from general resolution. As a special case, we obtain the first exponential separation of negative resolution from general resolution. We also attempt to present a unifying framework for studying all of these refinements.

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J. Symbolic Logic, Volume 72, Issue 4 (2007), 1336-1352.

First available in Project Euclid: 18 February 2008

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Buresh-Oppenheim, Joshua; Pitassi, Toniann. The complexity of resolution refinements. J. Symbolic Logic 72 (2007), no. 4, 1336--1352. doi:10.2178/jsl/1203350790.

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