Using SAT in QBF

Abstract

QBF is the problem of deciding the satisfiability of quantified boolean formulae in which variables can be either universally or existentially quantified. QBF generalizes SAT (SAT is QBF under the restriction all variables are existential) and is in practice much harder to solve than SAT. One of the sources of added complexity in QBF arises from the restrictions quantifier nesting places on the variable orderings that can be utilized during backtracking search. In this paper we present a technique for alleviating some of this complexity by utilizing an order unconstrained SAT solver during QBF solving. The innovation of our paper lies in the integration of SAT and QBF. We have developed methods that allow information obtained from each solver to be used to improve the performance of the other. Unlike previous attempts to avoid the ordering constraints imposed by quantifier nesting, our algorithm retains the polynomial space requirements of standard backtracking search. Our empirical results demonstrate that our techniques allow improvements over the current state-of-the-art in QBF solvers. © Springer-Verlag Berlin Heidelberg 2005.