Lean clause-sets: generalizations of minimally unsatisfiable clause-sets
Discrete Applied Mathematics - The renesse issue on satisfiability
AMUSE: a minimally-unsatisfiable subformula extractor
Proceedings of the 41st annual Design Automation Conference
DATE '03 Proceedings of the conference on Design, Automation and Test in Europe - Volume 1
On Exact Selection of Minimally Unsatisfiable Subformulae
Annals of Mathematics and Artificial Intelligence
MUP: a minimal unsatisfiability prover
Proceedings of the 2005 Asia and South Pacific Design Automation Conference
Local-search Extraction of MUSes
Constraints
Algorithms for Computing Minimal Unsatisfiable Subsets of Constraints
Journal of Automated Reasoning
On Approaches to Explaining Infeasibility of Sets of Boolean Clauses
ICTAI '08 Proceedings of the 2008 20th IEEE International Conference on Tools with Artificial Intelligence - Volume 01
Extracting MUCs from Constraint Networks
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Generalizing Core-Guided Max-SAT
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
QUICKXPLAIN: preferred explanations and relaxations for over-constrained problems
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Diagnosing and solving over-determined constraint satisfaction problems
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Boosting a complete technique to find MSS and MUS thanks to a local search oracle
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Redundancy in logic I: CNF propositional formulae
Artificial Intelligence
Searching for autarkies to trim unsatisfiable clause sets
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
Minimal Unsatisfiability: Models, Algorithms and Applications (Invited Paper)
ISMVL '10 Proceedings of the 2010 40th IEEE International Symposium on Multiple-Valued Logic
Boosting minimal unsatisfiable core extraction
Proceedings of the 2010 Conference on Formal Methods in Computer-Aided Design
A scalable algorithm for minimal unsatisfiable core extraction
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Minimally unsatisfiable boolean circuits
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
On deciding MUS membership with QBF
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Accelerating MUS extraction with recursive model rotation
Proceedings of the International Conference on Formal Methods in Computer-Aided Design
Towards efficient MUS extraction
AI Communications - 18th RCRA International Workshop on “Experimental evaluation of algorithms for solving problems with combinatorial explosion”
On efficient computation of variable MUSes
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
On computing minimal equivalent subformulas
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Understanding, improving and parallelizing MUS finding using model rotation
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Formula preprocessing in MUS extraction
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Asynchronous multi-core incremental SAT solving
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Core minimization in SAT-based abstraction
Proceedings of the Conference on Design, Automation and Test in Europe
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
Exploiting the power of MIP solvers in MAXSAT
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
Minimal sets over monotone predicates in boolean formulae
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
Computing interpolants without proofs
HVC'12 Proceedings of the 8th international conference on Hardware and Software: verification and testing
Preserving partial solutions while relaxing constraint networks
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Minimally Unsatisfiable Subformulas (MUS) find a wide range of practical applications, including product configuration, knowledge-based validation, and hardware and software design and verification. MUSes also find application in recentMaximum Satisfiability algorithms and in CNF formula redundancy removal. Besides direct applications in Propositional Logic, algorithms for MUS extraction have been applied to more expressive logics. This paper proposes two algorithms forMUS extraction. The first algorithm is optimal in its class, meaning that it requires the smallest number of calls to a SAT solver. The second algorithm extends earlier work, but implements a number of new techniques. The resulting algorithms achieve significant performance gains with respect to state of the art MUS extraction algorithms.