Bridging the Gap between Dual Propagation and CNF-based QBF Solving

Abstract

Abstract-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.

On Conflicts and Strategies in QBF

“…These operations can be seen as an extension of traditional CDCL SAT solving [25,24] to QBF [30,12,10] and are discussed in more detail in turn.…”

“…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.…”

“…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].…”

“…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].…”

“…It uses DPLL-style clause learning [30,12], abstraction & refinement learning of RAReQS [15,14], and the flat architecture of qesto [16].…”