Andrew G. D. Rowley

Watched Data Structures for QBF Solvers

In the last few years, we have seen a tremendous boost in the efficiency of SAT solvers, this boost being mostly due to Chaff. Chaff owes some of its efficiency to its “two-literal watching” data structure.

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 WalkSATs heuristics for use in QBFs.

Solving quantified constraint satisfaction problems

We make a number of contributions to the study of the Quantified Constraint Satisfaction Problem (QCSP). The QCSP is an extension of the constraint satisfaction problem that can be used to model combinatorial problems containing contingency or uncertainty. It allows for universally quantified variables that can model uncertain actions and events, such as the unknown weather for a future party, or an opponents next move in a game. In this paper we report significant contributions to two very different methods for solving QCSPs. The first approach is to implement special purpose algorithms for QCSPs; and the second is to encode QCSPs as Quantified Boolean Formulas and then use specialized QBF solvers. The discovery of particularly effective encodings influenced the design of more effective algorithms: by analyzing the properties of these encodings, we identify the features in QBF solvers responsible for their efficiency. This enables us to devise analogues of these features in QCSPs, and implement them in special purpose algorithms, yielding an effective special purpose solver, QCSP-Solve. Experiments show that this solver and a highly optimized QBF encoding are several orders of magnitude more efficient than the initially developed algorithms. A final, but significant, contribution is the identification of flaws in simple methods of generating random QCSP instances, and a means of generating instances which are not known to be flawed.

Watching clauses in Quantified Boolean Formulae

The introduction of watched literals[1], a lazy data structure for satisfiability (SAT) search algorithms, has resulted in great improvements in the run-time of SAT solvers. Watched literals keeps track of two literals remaining in a clause so as to detect when a clause becomes unit or empty. Watched literals is non-trivial to implement in QBF search. Quantified Boolean Formulae (QBFs) are SAT formulae with some variables universally quantified. This changes the semantics of unit and false clauses. The issue of watching literals in QBF is addressed in [2].