## Journal of Symbolic Logic

- J. Symbolic Logic
- Volume 71, Issue 3 (2006), 721-1080

### The complexity of analytic tableaux

Noriko H. Arai,Toniann Pitassi, and Alasdair Urquhart

#### 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.

#### Article information

**Source**

J. Symbolic Logic Volume 71, Issue 3 (2006), 777-790.

**Dates**

First available: 4 August 2006

**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

#### Citation

Arai, Noriko H.; Pitassi, Toniann; Urquhart, Alasdair. The complexity of analytic tableaux. Journal of Symbolic Logic 71 (2006), no. 3, 777--790. doi:10.2178/jsl/1154698576. http://projecteuclid.org/euclid.jsl/1154698576.