Work

Strong (D)QBF Dependency Schemes via Implication-free Resolution Paths

Year: 2024

Type: article

Abstract: We suggest a general framework to study dependency schemes for dependency quantified Boolean formulas (DQBF). As our main contribution, we exhibit a new infinite collection of implication-free DQBF dependency schemes that generalise the reflexive resolution path dependency scheme. We establish soundness of all these schemes, implying that they can be used in any DQBF proof system. We further explore the power of QBF and DQBF resolution systems parameterised by implication-free dependency schemes and show that the hierarchical structure naturally present among the dependency schemes translates isomorphically to a hierarchical structure of parameterised proof systems with respect to p-simulation. As a special case, we demonstrate that our new schemes are exponentially stronger than the reflexive resolution path dependency scheme when used in Q-resolution, thus resulting in the strongest QBF dependency schemes known to date.

Source: ACM Transactions on Computation Theory

DOI: 10.1145/3689345

Authors: Olaf Beyersdorff, Joshua Lewis Blinkhorn, Tomáš Peitl

Institutions: Friedrich Schiller University Jena, TU Wien

Language: English

Topic: Formal Methods in Verification

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Funders: Carl-Zeiss-Stiftung, Deutsche Forschungsgemeinschaft

Award: G4027207014