Towards Uniform Certification in QBF

TL;DR

This paper introduces a new technique for proving simulations between QBF proof systems, showing that extended QBF Frege can simulate several other systems, thereby supporting the case for uniform certification in QBF solving.

Contribution

It develops a novel strategy extraction method that enables simulations mainly within propositional logic, unifying various QBF proof systems under extended QBF Frege.

Findings

Extended QBF Frege p-simulates IR-Calculus, IRM-Calculus, Long-Distance Q-Resolution, and Merge Resolution.

The new technique combines strategy extraction with propositional logic, minimizing use of QBF rules.

Results strengthen the case for uniform certification in QBF solving.

Abstract

We pioneer a new technique that allows us to prove a multitude of previously open simulations in QBF proof complexity. In particular, we show that extended QBF Frege p-simulates clausal proof systems such as IR-Calculus, IRM-Calculus, Long-Distance Q-Resolution, and Merge Resolution. These results are obtained by taking a technique of Beyersdorff et al. (JACM 2020) that turns strategy extraction into simulation and combining it with new local strategy extraction arguments. This approach leads to simulations that are carried out mainly in propositional logic, with minimal use of the QBF rules. Our proofs therefore provide a new, largely propositional interpretation of the simulated systems. We argue that these results strengthen the case for uniform certification in QBF solving, since many QBF proof systems now fall into place underneath extended QBF Frege.