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The complexity of resolution refinements

Published online by Cambridge University Press:  12 March 2014

Joshua Buresh-Oppenheim  and
Toniann Pitassi
Joshua Buresh-Oppenheim
Affiliation:
School of Computing Science, Simon Fraser University, Burnaby, BC, Canada. E-mail: jburesho@cs.sfu.ca
Toniann Pitassi
Affiliation:
Computer Science Department, University of Toronto, Toronto, ON, Canada. E-mail: toni@cs.toronto.edu
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 4 , December 2007 , pp. 1336 - 1352
Copyright
Copyright © Association for Symbolic Logic 2007

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