The complexity of analytic tableaux
Noriko H. Arai, Toniann Pitassi, and Alasdair Urquhart
Source: J. Symbolic Logic Volume 71, Issue 3
(2006), 777-790.
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 is close to optimal, since we give a
matching lower bound that is tight to
within a polynomial.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1154698576
Digital Object Identifier: doi:10.2178/jsl/1154698576
Mathematical Reviews number (MathSciNet): MR2250820
Zentralblatt MATH identifier: 1109.03066
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