The complexity of facets resolved
Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
On subclasses of minimal unsatisfiable formulas
Discrete Applied Mathematics - Special issue on Boolean functions and related problems
Polynomial-time recognition of minimal unsatisfiable formulas with fixed clause-variable difference
Theoretical Computer Science
Finding all minimal unsatisfiable subsets
Proceedings of the 5th ACM SIGPLAN international conference on Principles and practice of declaritive programming
AMUSE: a minimally-unsatisfiable subformula extractor
Proceedings of the 41st annual Design Automation Conference
Backjump-Based Techniques versus Conflict-Directed Heuristics
ICTAI '04 Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence
QUICKXPLAIN: preferred explanations and relaxations for over-constrained problems
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Deriving minimal conflict sets by CS-trees with mark set indiagnosis from first principles
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
SARA'07 Proceedings of the 7th International conference on Abstraction, reformulation, and approximation
MUST: provide a finer-grained explanation of unsatisfiability
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Exploiting past and future: pruning by inconsistent partial state dominance
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Efficient combination of decision procedures for MUS computation
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Learning cluster-based structure to solve constraint satisfaction problems
Annals of Mathematics and Artificial Intelligence
On improving MUS extraction algorithms
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Towards efficient MUS extraction
AI Communications - 18th RCRA International Workshop on “Experimental evaluation of algorithms for solving problems with combinatorial explosion”
On computing minimal equivalent subformulas
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Reasoning over biological networks using maximum satisfiability
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Minimal sets over monotone predicates in boolean formulae
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
Preserving partial solutions while relaxing constraint networks
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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We address the problem of extracting Minimal Unsatisfiable Cores (MUCs) from constraint networks. This computationally hard problem has a practical interest in many application domains such as configuration, planning, diagnosis, etc. Indeed, identifying one or several disjoint MUCs can help circumscribe different sources of inconsistency in order to repair a system. In this paper, we propose an original approach that involves performing successive runs of a complete backtracking search, using constraint weighting, in order to surround an inconsistent part of a network, before identifying all transition constraints belonging to a MUC using a dichotomic process. We show the effectiveness of this approach, both theoretically and experimentally.