Small Resolution Proofs for QBF using Dependency Treewidth

TL;DR

This paper introduces dependency treewidth, a novel structural parameter that enables efficient solving of QBF instances by accounting for variable interdependencies, surpassing previous treewidth-based methods.

Contribution

The paper develops dependency treewidth, a new parameter for QBF, and algorithms for computing the necessary decompositions, improving tractability over existing methods.

Findings

Dependency treewidth effectively captures variable interdependencies in QBF.

Algorithms for computing dependency treewidth decompositions are proposed.

Dependency treewidth extends the applicability of structural parameter techniques to QBF.

Abstract

In spite of the close connection between the evaluation of quantified Boolean formulas (QBF) and propositional satisfiability (SAT), tools and techniques which exploit structural properties of SAT instances are known to fail for QBF. This is especially true for the structural parameter treewidth, which has allowed the design of successful algorithms for SAT but cannot be straightforwardly applied to QBF since it does not take into account the interdependencies between quantified variables. In this work we introduce and develop dependency treewidth, a new structural parameter based on treewidth which allows the efficient solution of QBF instances. Dependency treewidth pushes the frontiers of tractability for QBF by overcoming the limitations of previously introduced variants of treewidth for QBF. We augment our results by developing algorithms for computing the decompositions that are required to use the parameter.