Runtime vs. Extracted Proof Size: An Exponential Gap for CDCL on QBFs
Olaf Beyersdorff, Benjamin Böhm, Meena Mahajan
Abstract
Conflict-driven clause learning (CDCL) is the dominating algorithmic paradigm for SAT solving and hugely successful in practice. In its lifted version QCDCL, it is one of the main approaches for solving quantified Boolean formulas (QBF). In both SAT and QBF, proofs can be efficiently extracted from runs of (Q)CDCL solvers. While for CDCL, it is known that the proof size in the underlying proof system propositional resolution matches the CDCL runtime up to a polynomial factor, we show that in QBF there is an exponential gap between QCDCL runtime and the size of the extracted proofs in QBF resolution systems. We demonstrate that this is not just a gap between QCDCL runtime and the size of any QBF resolution proof, but even the extracted proofs are exponentially smaller for some instances. Hence searching for a small proof via QCDCL (even with non-deterministic decision policies) will provably incur an exponential overhead for some instances.
BibTeX
@article{Beyersdorff_Böhm_Mahajan_2024, title={Runtime vs. Extracted Proof Size: An Exponential Gap for CDCL on QBFs}, volume={38}, url={https://ojs.aaai.org/index.php/AAAI/article/view/28631}, DOI={10.1609/aaai.v38i8.28631}, abstractNote={Conflict-driven clause learning (CDCL) is the dominating algorithmic paradigm for SAT solving and hugely successful in practice. In its lifted version QCDCL, it is one of the main approaches for solving quantified Boolean formulas (QBF). In both SAT and QBF, proofs can be efficiently extracted from runs of (Q)CDCL solvers. While for CDCL, it is known that the proof size in the underlying proof system propositional resolution matches the CDCL runtime up to a polynomial factor, we show that in QBF there is an exponential gap between QCDCL runtime and the size of the extracted proofs in QBF resolution systems. We demonstrate that this is not just a gap between QCDCL runtime and the size of any QBF resolution proof, but even the extracted proofs are exponentially smaller for some instances. Hence searching for a small proof via QCDCL (even with non-deterministic decision policies) will provably incur an exponential overhead for some instances.}, number={8}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Beyersdorff, Olaf and Böhm, Benjamin and Mahajan, Meena}, year={2024}, month={Mar.}, pages={7943-7951} }