Soundness of Q-resolution with dependency schemes

Q-resolution and Q-term resolution are proof systems for quantified Boolean formulas (QBFs). We introduce generalizations of these proof systems named Q ( D ) -resolution and Q ( D ) -term resolution. Q ( D ) -resolution and Q ( D ) -term resolution are parameterized by a dependency scheme D and use more powerful ?-reduction and ?-reduction rules, respectively. We show soundness of these systems for particular dependency schemes: we prove (1) soundness of Q ( D ) -resolution parameterized by the reflexive resolution-path dependency scheme, and (2) soundness of Q ( D ) -term resolution parameterized by the resolution-path dependency scheme. These results entail soundness of the proof systems used for certificate generation in the state-of-the-art solver DepQBF.

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