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Solving Dependency Quantified Boolean Formulas Using Quantifier Localization
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 which can be encoded by DQBFs in a
natural, compact, and elegant way, research on DQBF solving has emerged in the
past few years. However, research focused on closed DQBFs in prenex form (where
all quantifiers are placed in front of a propositional formula), while
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 all instances from the QBFEVAL'18-'20 competitions, clearly show that
quantifier localization pays off in this context