A Non-prenex, Non-clausal QBF Solver with Game-State Learning

Abstract

Abstract. We describe a DPLL-based solver for the problem of quantified boolean formulas (QBF) in non-prenex, non-CNF form. We make two contributions. First, we reformulate clause/cube learning, extending it to non-prenex instances. We call the resulting technique game-state learning. Second, we introduce a propagation technique using ghost literals that exploits the structure of a non-CNF instance in a manner that is symmetric between the universal and existential variables. Experimental results on the QBFLIB benchmarks indicate our approach outperforms other state-of-the-art solvers on certain benchmark families, including the tipfixpoint and tipdiam families of model checking problems.

Contributions to the Theory of Practical Quantified Boolean Formula Solving

“…This definition emphasizes the connection of QBF to two-person games, in which player E (Existential) tries to set existential variables to make the QBF evaluate to true, and player A (Universal) tries to set universal variables to make the QBF evaluate to false. Players set their variable when it is outermost, or for non-prenex, when it is the root of a subformula (see [16] for more details). Only one player has a winning strategy.…”

On Conflicts and Strategies in QBF

“…Propagation can be realized in a number of different ways [30,31,19,21,12,22]. For this presentation we mainly rely on the approach of Goultiaeva et al [12], with some ingredients introduced by Klieber [19,18].…”

“…For this presentation we mainly rely on the approach of Goultiaeva et al [12], with some ingredients introduced by Klieber [19,18]. We note, however that the presented algorithm is not limited to this particular implementation of propagation.…”

“…Other solvers included in the evaluation are the non-CNF-based solver GhostQ [19], CDCLstyle solver with variable dependency computation DepQBF [21], the CEGAR-based solvers RAReQS and AReQS [15,14]. Figure 4 shows cactus plots for two benchmark families.…”

“…In one approach, a solver traverses the search space, while pruning it by propagation, similarly to SAT solvers [30,31,19,21,12,22]. In the second approach, a solver eliminates (expands) quantifiers obtaining thus a SAT problem [26,6,20,3].…”