Improvements to the Evaluation of Quanti ed Boolean

We present a theorem-prover for quantiied Boolean formulae and evaluate it on random quantiied formulae and formulae that represent problems from automated planning. Even though the notion of quantiied Boolean formula is theoretically important, automated reasoning with QBF has not been thoroughly investigated. Universal quantiiers are needed in representing many computational problems that cannot be easily translated to the propo-sitional logic and solved by satissability algorithms. Therefore eecient reasoning with QBF is important. The Davis-Putnam procedure can be extended to evaluate quantiied Boolean formulae. A straightforward algorithm of this kind is not very eecient. We identify universal quantiiers as the main area where improvements to the basic algorithm can be made. We present a number of techniques for reducing the amount of search that is needed, and evaluate their eeectiveness by running the algorithm on a collection of formulae obtained from planning and generated randomly. For the structured problems we consider, the techniques lead to a dramatic speed-up.