Journal of the ACM (JACM)
GRASP—a new search algorithm for satisfiability
Proceedings of the 1996 IEEE/ACM international conference on Computer-aided design
Short proofs are narrow—resolution made simple
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Satisfiability, Branch-Width and Tseitin Tautologies
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Constraint Satisfaction, Bounded Treewidth, and Finite-Variable Logics
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
BerkMin: A Fast and Robust Sat-Solver
Proceedings of the conference on Design, automation and test in Europe
A combinatorial characterization of resolution width
Journal of Computer and System Sciences
Clause learning can effectively P-simulate general propositional resolution
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
Understanding the power of clause learning
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Using CSP look-back techniques to solve real-world SAT instances
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Local consistency and SAT-solvers
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
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
Lower bounds for width-restricted clause learning on small width formulas
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Lower bounds for width-restricted clause learning on formulas of small width
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Three
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Complexity issues related to propagation completeness
Artificial Intelligence
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We offer a new understanding of some aspects of practical SAT-solvers that are based on DPLL with unit-clause propagation, clause-learning, and restarts. On the theoretical side, we do so by analyzing a concrete algorithm which we claim is faithful to what practical solvers do. In particular, before making any new decision or restart, the solver repeatedly applies the unit-resolution rule until saturation, and leaves no component to the mercy of non-determinism except for some internal randomness. We prove the perhaps surprising fact that, although the solver is not explicitely designed for it, it ends up behaving as width-k resolution after no more than n 2k + 1 conflicts and restarts, where n is the number of variables. In other words, width-k resolution can be thought as n 2k + 1 restarts of the unit-resolution rule with learning. On the experimental side, we give evidence for the claim that this theoretical result describes real world solvers. We do so by running some of the most prominent solvers on some CNF formulas that we designed to have resolution refutations of width k . It turns out that the upper bound of the theoretical result holds for these solvers and that the true performance appears to be not very far from it.