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arXiv · 2410.15848

Symmetries of Dependency Quantified Boolean Formulas

Clemens Hofstadler·Manuel Kauers·Martina Seidl
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Abstract

Symmetries have been exploited successfully within the realms of SAT and QBF to improve solver performance in practical applications and to devise more powerful proof systems. As a first step towards extending these advancements to the class of dependency quantified Boolean formulas (DQBFs), which generalize QBF by allowing more nuanced variable dependencies, this work develops a comprehensive theory to characterize symmetries for DQBFs. We also introduce the notion of symmetry breakers of DQBFs, along with a concrete construction, and discuss how to detect DQBF symmetries algorithmically using a graph-based approach. Moreover, we empirically study the presence of symmetries in benchmark formulas and their impact on solving times.

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Clemens Hofstadler, Manuel Kauers, Martina Seidl. 2024-10-21. Symmetries of Dependency Quantified Boolean Formulas. https://arxiv.org/abs/2410.15848

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