A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Bucket elimination: a unifying framework for reasoning
Artificial Intelligence
A machine program for theorem-proving
Communications of the ACM
Resolution versus Search: Two Strategies for SAT
Journal of Automated Reasoning
Enhancing Davis Putnam with extended binary clause reasoning
Eighteenth national conference on Artificial intelligence
Reduction operations in fuzzy or valued constraint satisfaction
Fuzzy Sets and Systems - Optimisation and decision
Solving weighted CSP by maintaining arc consistency
Artificial Intelligence
Study of lower bound functions for MAX-2-SAT
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
In the quest of the best form of local consistency for weighted CSP
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Existential arc consistency: getting closer to full arc consistency in weighted CSPs
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Adding new clauses for faster local search
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Artificial Intelligence
A logical approach to efficient Max-SAT solving
Artificial Intelligence
Exploiting Cycle Structures in Max-SAT
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
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
Inference rules for high-order consistency in weighted CSP
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
New inference rules for Max-SAT
Journal of Artificial Intelligence Research
MINIMAXSAT: an efficient weighted max-SAT solver
Journal of Artificial Intelligence Research
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Exploiting inference rules to compute lower bounds for MAX-SAT solving
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Relaxed survey propagation for the weighted maximum satisfiability problem
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
MiniMaxSAT: a new weighted Max-SAT solver
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Structural relaxations by variable renaming and their compilation for solving MinCostSAT
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Clone: solving weighted Max-SAT in a reduced search space
AI'07 Proceedings of the 20th Australian joint 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
Using learnt clauses in MAXSAT
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
On SAT modulo theories and optimization problems
SAT'06 Proceedings of the 9th 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
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Max-SAT is an optimization version of the well-known SAT problem. It is of great importance from both a theoretical and a practical point of view. In recent years, there has been considerable interest in finding efficient solving techniques [Alsinet et al., 2003; Xing and Zhang, 2004; Shen and Zhang, 2004; de Givry et al., 2003]. Most of this work focus on the computation of good quality lower bounds to be used within a branch and bound algorithm. Unfortunately, lower bounds are described in a procedural way. Because of that, it is difficult to realize the logic that is behind. In this paper we introduce a logical framework for Max-SAT solving. Using this framework, we introduce an extension of the Davis-Putnam algorithm (that we call Max-DPLL) and the resolution rule. Our framework has the advantage of nicely integrating branch and bound concepts such as the lower and upper bound, as well as hiding away implementation details. We show that Max-DPLL augmented with a restricted form of resolution at each branching point is an effective solving strategy. We also show that the resulting algorithm is closely related with some local consistency properties developed for weighted constraint satisfaction problems.