Localizing Quantifiers for DQBF

Dependency quantified Boolean formulas (DQBFs) are a powerful formalism, which subsumes quantified Boolean formulas (QBFs) and allows an explicit specification of dependencies of existential variables on universal variables. Driven by the needs of various applications that can be encoded by DQBFs in a natural, compact, and elegant way, research on DQBF solving has emerged in the past few years. However, most works focus on closed DQBFs in prenex form (where all quantifiers are placed in front of a propositional formula), and non-prenex DQBFs have almost not been studied in the literature. In this paper we provide a formal definition for syntax and semantics of non-closed non-prenex DQBFs and prove useful properties enabling quantifier localization. Moreover, we make use of our theory by integrating quantifier localization into a state-of-the- art DQBF solver. Experiments with prenex DQBF benchmarks, including those from the QBFEVAL'18 competition, clearly show that quantifier localization pays off in this context.