TY - GEN

T1 - Relating proof complexity measures and practical hardness of SAT

AU - Järvisalo, Matti

AU - Matsliah, Arie

AU - Nordström, Jakob

AU - Živný, Stanislav

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84868269243&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-33558-7_25

DO - 10.1007/978-3-642-33558-7_25

M3 - Article in proceedings

AN - SCOPUS:84868269243

SN - 9783642335570

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 316

EP - 331

BT - Principles and Practice of Constraint Programming - 18th International Conference, CP 2012, Proceedings

T2 - 18th International Conference on Principles and Practice of Constraint Programming, CP 2012

Y2 - 8 October 2012 through 12 October 2012

ER -