Exploiting Quantifiers Structure in QBF Reasoning

The best currently available solvers for quantified Boolean formulas (QBFs) process their input in prenex form, i.e., all the quantifiers are to appear in the prefix of the formula separated from the purely propositional part representing the matrix. However, in many QBFs deriving from applications, the propositional part is intertwined with the quantifiers structure. In this paper, we show that converting such instances into prenex form, and thus losing the structural information about the quantifiers, interferes with the solving process by thwarting branches that could otherwise have occurred. To tackle this problem we devise suitable extensions to the QBF search algorithm in order to exploit the quantifiers structure, and we implement the extended algorithm in the state-of-the-art solver QuBE. Our experimental analysis shows that substantial speedups can be obtained by working with a structured-prefix form rather than with the traditional prenex form.