Understanding cutting planes for QBFs

Abstract

We study the cutting planes systemCP+∀redfor quantified Boolean formulas (QBF), obtained by augmenting propositionalCutting Planeswith a universal reduction rule, and analyse the proof-theoretic strength of this new calculus. While in the propositional case,Cutting Planesis of intermediate strength between resolution and Frege, our findings here show that the situation in QBF is slightly more complex: whileCP+∀redis again weaker than QBF Frege and stronger than the CDCL-based QBF resolution systemsQ-ResandQU-Res, it turns out to be incomparable to even the weakest expansion-based QBF resolution system ∀Exp+Res. A similar picture holds for a semantic versionsemCP+∀red. Technically, our results establish the effectiveness of two lower bound techniques forCP+∀red: via strategy extraction and via monotone feasible interpolation.