Incremental QBF Solving

We consider the problem of incrementally solving a sequence of quantified Boolean formulae (QBF). Incremental solving aims at using information learned from one formula in the process of solving the next formulae in the sequence. Based on a general overview of the problem and related challenges, we present an approach to incremental QBF solving which is application-independent and hence applicable to QBF encodings of arbitrary problems. We implemented this approach in our incremental search-based QBF solver DepQBF and report on implementation details. Experimental results illustrate the potential benefits of incremental solving in QBF-based workflows.Comment: revision (camera-ready, to appear in the proceedings of CP 2014, LNCS, Springer

Building Strategies into QBF Proofs

Strategy extraction is of great importance for quantified Boolean formulas (QBF), both in solving and proof complexity. So far in the QBF literature, strategy extraction has been algorithmically performed from proofs. Here we devise the first QBF system where (partial) strategies are built into the proof and are piecewise constructed by simple operations along with the derivation. This has several advantages: (1) lines of our calculus have a clear semantic meaning as they are accompanied by semantic objects; (2) partial strategies are represented succinctly (in contrast to some previous approaches); (3) our calculus has strategy extraction by design; and (4) the partial strategies allow new sound inference steps which are disallowed in previous central QBF calculi such as Q-Resolution and long-distance Q-Resolution. The last item (4) allows us to show an exponential separation between our new system and the previously studied reductionless long-distance resolution calculus. Our approach also naturally lifts to dependency QBFs (DQBF), where it yields the first sound and complete CDCL-style calculus for DQBF, thus opening future avenues into CDCL-based DQBF solving

Blocked clause elimination for QBF

Abstract. Quantified Boolean formulas (QBF) provide a powerful framework for encoding problems from various application domains, not least because efficient QBF solvers are available. Despite sophisticated evaluation techniques, the performance of such a solver usually depends on the way a problem is represented. However, the translation to processable QBF encodings is in general not unique and may either introduce variables and clauses not relevant for the solving process or blur information which could be beneficial for the solving process. To deal with both of these issues, preprocessors have been introduced which rewrite a given QBF before it is passed to a solver. In this paper, we present novel preprocessing methods for QBF based on blocked clause elimination (BCE), a technique successfully applied in SAT. Quantified blocked clause elimination (QBCE) allows to simulate various structural preprocessing techniques as BCE in SAT. We have implemented QBCE and extensions of QBCE in the preprocessor bloqqer. In our experiments we show that preprocessing with QBCE reduces formulas substantially and allows us to solve considerable more instances than the previous state-of-the-art.