Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas
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The complexity of facets resolved
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GRASP: A Search Algorithm for Propositional Satisfiability
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On subclasses of minimal unsatisfiable formulas
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SATIRE: a new incremental satisfiability engine
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An efficient algorithm for the minimal unsatisfiability problem for a subclass of CNF
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Efficient conflict driven learning in a boolean satisfiability solver
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Polynomial-time recognition of minimal unsatisfiable formulas with fixed clause-variable difference
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Formal methods for the validation of automotive product configuration data
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Reconsidering CEGAR: Learning Good Abstractions without Refinement
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Efficient computation of small abstraction refinements
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
MUP: a minimal unsatisfiability prover
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Local-search Extraction of MUSes
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NMUS: Structural Analysis for Improving the Derivation of All MUSes in Overconstrained Numeric CSPs
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Contradictory antecedent debugging in bounded model checking
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Reconfigurable Computing: The Theory and Practice of FPGA-Based Computation
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Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
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EMSOFT '09 Proceedings of the seventh ACM international conference on Embedded software
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MUST: provide a finer-grained explanation of unsatisfiability
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Finding unsatisfiable subformulas with stochastic method
IDEAL'07 Proceedings of the 8th international conference on Intelligent data engineering and automated learning
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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
A heuristic local search algorithm for unsatisfiable cores extraction
ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part III
Efficient combination of decision procedures for MUS computation
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
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IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Boosting minimal unsatisfiable core extraction
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Computing small unsatisfiable cores in satisfiability modulo theories
Journal of Artificial Intelligence Research
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SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Faster extraction of high-level minimal unsatisfiable cores
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
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IDEAL'11 Proceedings of the 12th international conference on Intelligent data engineering and automated learning
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TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
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ESWC'05 Proceedings of the Second European conference on The Semantic Web: research and Applications
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CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
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Extracting minimum unsatisfiable cores with a greedy genetic algorithm
AI'06 Proceedings of the 19th Australian joint conference on Artificial Intelligence: advances in Artificial Intelligence
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Concurrent architecture and schedule optimization of time-triggered automotive systems
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CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
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ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
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Improving glucose for incremental SAT solving with assumptions: application to MUS extraction
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
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SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
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IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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This paper describes a new algorithm for extracting unsatisfiable subformulas from a given unsatisfiable CNF formula. Such unsatisfiable "cores" can be very helpful in diagnosing the causes of infeasibility in large systems. Our algorithm is unique in that it adapts the "learning process" of a modern SAT solver to identify unsatisfiable subformulas rather than search for satisfying assignments. Compared to existing approaches, this method can be viewed as a bottom-up core extraction procedure which can be very competitive when the core sizes are much smaller than the original formula size. Repeated runs of the algorithm with different branching orders yield different cores. We present experimental results on a suite of large automotive benchmarks showing the performance of the algorithm and highlighting its ability to locate not just one but several cores.