Relating proof complexity measures and practical hardness of SAT
2012 (English)In: Principles and Practice of Constraint Programming: 18th International Conference, CP 2012, Québec City, QC, Canada, October 8-12, 2012. Proceedings / [ed] Michela Milano, Springer, 2012, 316-331 p.Conference paper (Refereed)
Boolean satisfiability (SAT) solvers have improved enormously in performance over the last 10-15 years and are today an indispensable tool for solving a wide range of computational problems. However, our understanding of what makes SAT instances hard or easy in practice is still quite limited. A recent line of research in proof complexity has studied theoretical complexity measures such as length, width, and space in resolution, which is a proof system closely related to state-of-the-art conflict-driven clause learning (CDCL) SAT solvers. Although it seems like a natural question whether these complexity measures could be relevant for understanding the practical hardness of SAT instances, to date there has been very limited research on such possible connections. This paper sets out on a systematic study of the interconnections between theoretical complexity and practical SAT solver performance. Our main focus is on space complexity in resolution, and we report results from extensive experiments aimed at understanding to what extent this measure is correlated with hardness in practice. Our conclusion from the empirical data is that the resolution space complexity of a formula would seem to be a more fine-grained indicator of whether the formula is hard or easy than the length or width needed in a resolution proof. On the theory side, we prove a separation of general and tree-like resolution space, where the latter has been proposed before as a measure of practical hardness, and also show connections between resolution space and backdoor sets.
Place, publisher, year, edition, pages
Springer, 2012. 316-331 p.
, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743 ; 7514 LNCS
Computer programming, Constraint theory, Decision theory, Digital storage, Formal logic
IdentifiersURN: urn:nbn:se:kth:diva-107319DOI: 10.1007/978-3-642-33558-7_25ScopusID: 2-s2.0-84868269243ISBN: 978-364233557-0OAI: oai:DiVA.org:kth-107319DiVA: diva2:576046
18th International Conference on Principles and Practice of Constraint Programming, CP 2012, 8 October 2012 through 12 October 2012, Quebec City, QC