Journal of the ACM (JACM)
GRASP: A Search Algorithm for Propositional Satisfiability
IEEE Transactions on Computers
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Information and Computation
Space Complexity in Propositional Calculus
SIAM Journal on Computing
Optimality of size-width tradeoffs for resolution
Computational Complexity
Resolution is Not Automatizable Unless W[P] is Tractable
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Variations of a pebble game on graphs
Variations of a pebble game on graphs
Space complexity of random formulae in resolution
Random Structures & Algorithms
A combinatorial characterization of treelike resolution space
Information Processing Letters
A combinatorial characterization of resolution width
Journal of Computer and System Sciences
Towards an optimal separation of space and length in resolution
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Short Proofs May Be Spacious: An Optimal Separation of Space and Length in Resolution
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Handbook of Satisfiability: Volume 185 Frontiers in Artificial Intelligence and Applications
Handbook of Satisfiability: Volume 185 Frontiers in Artificial Intelligence and Applications
Backdoors in the Context of Learning
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Measuring the hardness of SAT instances
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Towards understanding and harnessing the potential of clause learning
Journal of Artificial Intelligence Research
Backdoors to typical case complexity
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Narrow Proofs May Be Spacious:Separating Space and Width in Resolution
SIAM Journal on Computing
On the power of clause-learning SAT solvers as resolution engines
Artificial Intelligence
Clause-learning algorithms with many restarts and bounded-width resolution
Journal of Artificial Intelligence Research
Time-space tradeoffs in resolution: superpolynomial lower bounds for superlinear space
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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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.