Journal of the ACM (JACM)
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
New upper bounds for maximum satisfiability
Journal of Algorithms
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
Resolution lower bounds for the weak pigeonhole principle
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
The Approximability of Constraint Satisfaction Problems
SIAM Journal on Computing
The Efficiency of Resolution and Davis--Putnam Procedures
SIAM Journal on Computing
On the Automatizability of Resolution and Related Propositional Proof Systems
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Simplified and improved resolution lower bounds
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
"Planar" Tautologies Hard for Resolution
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Mutilated chessboard problem is exponentially hard for resolution
Theoretical Computer Science
On the automatizability of resolution and related propositional proof systems
Information and Computation
MaxSolver: an efficient exact algorithm for (weighted) maximum satisfiability
Artificial Intelligence
Bucket elimination for multiobjective optimization problems
Journal of Heuristics
New inference rules for efficient Max-SAT solving
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Detecting disjoint inconsistent subformulas for computing lower bounds for Max-SAT
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Resolution in Max-SAT and its relation to local consistency in weighted CSPs
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Improved exact solvers for weighted Max-SAT
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Automated generation of simplification rules for SAT and MAXSAT
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
A complete calculus for Max-SAT
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Algorithms for maximum satisfiability using unsatisfiable cores
Proceedings of the conference on Design, automation and test in Europe
Exploiting Cycle Structures in Max-SAT
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Algorithms for Weighted Boolean Optimization
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Max-ASP: Maximum Satisfiability of Answer Set Programs
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
Within-problem learning for efficient lower bound computation in Max-SAT solving
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
New inference rules for Max-SAT
Journal of Artificial Intelligence Research
Partial max-SAT solvers with clause learning
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Some simplified forms of reasoning with distance-based entailments
Canadian AI'08 Proceedings of the Canadian Society for computational studies of intelligence, 21st conference on Advances in artificial intelligence
Modelling Max-CSP as partial Max-SAT
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
A preprocessor for Max-SAT solvers
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
A Max-SAT inference-based pre-processing for Max-clique
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
Resolution-based lower bounds in MaxSAT
Constraints
Read-once resolution for unsatisfiability-based Max-SAT algorithms
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Parallel search for maximum satisfiability
AI Communications - 18th RCRA International Workshop on “Experimental evaluation of algorithms for solving problems with combinatorial explosion”
Improving SAT-Based weighted MaxSAT solvers
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
A new encoding from MinSAT into MaxSAT
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Natural Max-SAT encoding of Min-SAT
LION'12 Proceedings of the 6th international conference on Learning and Intelligent Optimization
Resolution procedures for multiple-valued optimization
Information Sciences: an International Journal
Artificial Intelligence
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Max-SAT is the problem of finding an assignment minimizing the number of unsatisfied clauses in a CNF formula. We propose a resolution-like calculus for Max-SAT and prove its soundness and completeness. We also prove the completeness of some refinements of this calculus. From the completeness proof we derive an exact algorithm for Max-SAT and a time upper bound. We also define a weighted Max-SAT resolution-like rule, and show how to adapt the soundness and completeness proofs of the Max-SAT rule to the weighted Max-SAT rule. Finally, we give several particular Max-SAT problems that require an exponential number of steps of our Max-SAT rule to obtain the minimal number of unsatisfied clauses of the combinatorial principle. These results are based on the corresponding resolution lower bounds for those particular problems.