Unified Proof System for QBF Preprocessing

ABSTRACT. For quantified Boolean formulas (QBFs), preprocessing is essential to solve many real-world formulas. Application of a preprocessor, however, prevented the extraction of proofs to independently validate correctness of the solver's result. Especially for universal expansion proof checking was not possible so far. In this paper, we introduce a unified proof system based on three simple and elegant quantified asymmetric tautology QRAT rules. In combination with an extended version of universal reduction, they are sufficient to efficiently express all preprocessing techniques used in state-of-the-art preprocessors including universal expansion. Moreover, these rules give rise to new preprocessing techniques. We equip our preprocessor bloqqer with QRAT proof logging and provide a proof checker for QRAT proofs.