Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas
Journal of Combinatorial Theory Series A
FPGA '99 Proceedings of the 1999 ACM/SIGDA seventh international symposium on Field programmable gate arrays
New methods for 3-SAT decision and worst-case analysis
Theoretical Computer Science
On a generalization of extended resolution
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
On subclasses of minimal unsatisfiable formulas
Discrete Applied Mathematics - Special issue on Boolean functions and related problems
Investigations on autark assignments
Discrete Applied Mathematics - Special issue on Boolean functions and related problems
Boosting complete techniques thanks to local search methods
Annals of Mathematics and Artificial Intelligence
An efficient algorithm for the minimal unsatisfiability problem for a subclass of CNF
Annals of Mathematics and Artificial Intelligence
FMCAD '02 Proceedings of the 4th International Conference on Formal Methods in Computer-Aided Design
An Application of Matroid Theory to the SAT Problem
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
Finding all minimal unsatisfiable subsets
Proceedings of the 5th ACM SIGPLAN international conference on Principles and practice of declaritive programming
Lean clause-sets: generalizations of minimally unsatisfiable clause-sets
Discrete Applied Mathematics - The renesse issue on satisfiability
Formal methods for the validation of automotive product configuration data
Artificial Intelligence for Engineering Design, Analysis and Manufacturing
Annals of Mathematics and Artificial Intelligence
Verification of Proofs of Unsatisfiability for CNF Formulas
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
On finding all minimally unsatisfiable subformulas
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
A branch-and-bound algorithm for extracting smallest minimal unsatisfiable formulas
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Local-search Extraction of MUSes
Constraints
Present and Future of Practical SAT Solving
Complexity of Constraints
Does This Set of Clauses Overlap with at Least One MUS?
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
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
Efficient combination of decision procedures for MUS computation
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Accelerating MUS extraction with recursive model rotation
Proceedings of the International Conference on Formal Methods in Computer-Aided Design
Restoring CSP Satisfiability with MaxSAT
Fundamenta Informaticae - RCRA 2009 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
Constraint Satisfaction Problems in Clausal Form I: Autarkies and Deficiency
Fundamenta Informaticae
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
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Finding out that a SAT problem instance F is unsatisfiable is not enough for applications, where good reasons are needed for explaining the inconsistency (so that for example the inconsistency may be repaired). Previous attempts of finding such good reasons focused on finding some minimally unsatisfiable sub-clause-set F' of F, which in general suffers from the non-uniqueness of F' (and thus it will only find some reason, albeit there might be others). In our work, we develop a fuller approach, enabling a more fine-grained analysis of necessity and redundancy of clauses, supported by meaningful semantical and proof-theoretical characterisations. We combine known techniques for searching and enumerating minimally unsatisfiable sub-clause-sets with (full) autarky search. To illustrate our techniques, we give a detailed analysis of well-known industrial problem instances.