Using stochastic local search to solve quantified Boolean formulae

We present a novel approach to solving Quantified Boolean Formulae (QBFs), exploiting the power of stochastic local search methods for SAT. This makes the search process different in some interesting ways from conventional QBF solvers. First, the resulting solver is incomplete, as it can terminate without a definite result. Second, we can take advantage of the high level of optimisations in a conventional stochastic SAT algorithm. Our new solver, WalkQSAT, is structured as two components, one of which controls the QBF search while the other is a slightly adapted version of the classic SAT local search procedure WalkSAT. The WalkSAT component has no knowledge of QBF, and simply solves a sequence of SAT instances passed to it by the QBF component. We compare WalkQSAT with the state-of-the-art QBF solver QuBE-BJ. We show that WalkQSAT can outperform QuBE-BJ on some instances, and is able to solve two instances that QuBE-BJ could not. WalkQSAT often outperforms our own direct QBF solver, suggesting that with more efficient implementation it would be a very competitive solver. WalkQSAT is an inherently incomplete QBF solver, but still solves many unsatisfiable instances as well as satisfiable ones. We also study run-time distributions of WalkQSAT, and investigate the possibility of tuning WalkSAT's heuristics for use in QBFs.