The complexity of analytic tableaux

Authors:
Noriko Arai;Toniann Pitassi;Alasdair Urquhart
Affiliations:
National Institute for Informatics, Tokyo;Department of Computer Science, University of Toronto;Department of Philosophy, University of Toronto
Venue:
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Year:
2001

Citing 3
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Abstract

The method of analytic tableaux is employed in many introductory texts and has also been used quite extensively as a basis for automated theorem proving. In this paper, we discuss the complexity of the system as a method for refuting contradictory sets of clauses, and resolve several open questions. We discuss the three forms of analytic tableaux: clausal tableaux, generalized clausal tableaux, and binary tableaux. We resolve the relative complexity of these three forms of tableaux proofs and also resolve the relative complexity of analytic tableaux versus resolution. We show that there is a quasi-polynomial simulation of tree resolution by analytic tableaux; this simulation cannot be improved, since we give a matching lower bound that is tight to within a polynomial.