Conjunctive Normal Form (CNF) representation as used by most modern Quantified Boolean Formula (QBF) solvers is simple and powerful when reasoning about conflicts, but is not efficient at dealing with solutions. To overcome this inefficiency a number of specialized non-CNF solvers were created. These solvers were shown to have great advantages. Unfortunately, non-CNF solvers cannot benefit from sophisticated CNF-based techniques developed over the years. This paper demonstrates how the power of non-CNF structure can be harvested without the need for specialized solvers; in fact, it is easily incorporated into most existing CNF-based QBF solvers using a pre-existing mechanism of cube learning. We demonstrate this using a state-of-the-art QBF solver DepQBF, and experimentally show the effectiveness of our approach.

Many important problems can be compactly represented as quantified boolean formulas (QBF) and solved by general QBF solvers. To date QBF solvers have mainly focused on determining whether or not the input QBF is true or false. However, additional important information about an application can be gathered from its QBF formulation. In this paper we demonstrate that a circuitbased QBF solver can be exploited to obtain a QResolution proof of the truth or the falsity of a QBF. QBFs have a natural interpretation as a two person game and our main result is to show how, via a simple computation, the moves for the winning player can be computed directly from these proofs. This result shows that the proof is a representation of the winning strategy. In previous approaches the winning strategy has often been represented in a way that makes it hard to verify. In our approach the correctness of the strategy follows directly from the correctness of the proof, which is relatively easy to verify.

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 significantperformance improvements and advances the state of the art in QBF solving.

Many CAD for VLSI problems can be naturally encoded as Quantified Boolean Formulas (QBFs) and solved with QBF solvers. Furthermore, such problems often contain circuit-based information that is lost during the translation to Conjunctive Normal Form (CNF), the format accepted by most modern solvers. In this work, a novel preprocessing framework for circuit-based QBF problems is presented. It leverages structural circuit dominators to reduce the problem size and expedite the solving process. Our circuit-based QBF preprocessor PReDom recursively reduces dominated subcircuits to return a simpler but equisatisfiable QBF instance. A rigorous proof is given for eliminating subcircuits dominated by single outputs, irrespective of input quantifiers. Experimental results are presented for circuit diameter computation problems. With preprocessing times of at most five seconds using PReDom, three state-of-the-art QBF solvers can solve 27% to 45% of our problem instances, compared to none without preprocessing.