Year: 2025
Type: article
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.
Source: Journal of Automated Reasoning
Authors: Olaf Beyersdorff, Benjamin Böhm, Meena Mahajan
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Funders: Arthritis National Research Foundation, Friedrich-Schiller-Universität Jena, Department of Science and Technology, Ministry of Science and Technology, India, Deutscher Akademischer Austauschdienst, Deutsche Forschungsgemeinschaft, Simons Institute for the Theory of Computing, University of California Berkeley, Science and Engineering Research Board
Award: G4027207014
OpenAlex ID: W4416203133