Journal of Symbolic Logic

The complexity of resolution refinements

Joshua Buresh-Oppenheim and Toniann Pitassi

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 18 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1203350790

Digital Object Identifier
doi:10.2178/jsl/1203350790

Mathematical Reviews number (MathSciNet)
MR2371209

Zentralblatt MATH identifier
1160.03005

Citation

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


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