Exploiting QBF Duality on a Circuit Representation

Search based solvers for Quantified Boolean Formulas (QBF) have adapted the SAT solver techniques of unit propagation and clause learning to prune falsifying assignments. The technique of cube learning has been developed to help them prune satisfying assignments. Cubes, however, have not been able to achieve the same degree of effectiveness as clauses. In this paper we demonstrate how a circuit representation for QBF can support the propagation of dual truth values. The dual values support the identical techniques of unit propagation and clause learning, except now it is satisfying assignments rather than falsifying assignments that are pruned. Dual value propagation thus exploits the circuit representation and the duality of QBF formulas so that the same effective SAT techniques can now be used to prune both falsifying and satisfyingly assignments. We show empirically that dual propagation yields significant performance improvements and advances the state of the art in QBF solving.