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
Journal of the ACM (JACM)
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Efficient conflict driven learning in a boolean satisfiability solver
Proceedings of the 2001 IEEE/ACM international conference on Computer-aided design
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
A combinatorial characterization of resolution width
Journal of Computer and System Sciences
Clause-Learning Algorithms with Many Restarts and Bounded-Width Resolution
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Clause learning can effectively P-simulate general propositional resolution
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
A new clause learning scheme for efficient unsatisfiability proofs
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 3
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
Resolution Is Not Automatizable Unless W[P] Is Tractable
SIAM Journal on Computing
Narrow Proofs May Be Spacious:Separating Space and Width in Resolution
SIAM Journal on Computing
On the power of clause-learning SAT solvers with restarts
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
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
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
A note on SAT algorithms and proof complexity
Information Processing Letters
Knowledge compilation with empowerment
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
An improved separation of regular resolution from pool resolution and clause learning
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
Local consistency and SAT-solvers
Journal of Artificial Intelligence Research
On computing minimal equivalent subformulas
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Relating proof complexity measures and practical hardness of SAT
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Parameterized Complexity of DPLL Search Procedures
ACM Transactions on Computational Logic (TOCL)
The proof-search problem between bounded-width resolution and bounded-degree semi-algebraic proofs
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
The complexity of proving that a graph is ramsey
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Implicit learning of common sense for reasoning
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
IJCAI'13 Proceedings of the Twenty-Third international joint conference on 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. 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 explicitly designed for it, with high probability it ends up behaving as width-k resolution after no more than O(n2k+2) conflicts and restarts, where n is the number of variables. In other words, width-k resolution can be thought of as O(n2k+2) restarts of the unit-resolution rule with learning.