Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas
Journal of Combinatorial Theory Series A
The complexity of facets resolved
Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
Computer-aided verification of coordinating processes: the automata-theoretic approach
Computer-aided verification of coordinating processes: the automata-theoretic approach
On subclasses of minimal unsatisfiable formulas
Discrete Applied Mathematics - Special issue on Boolean functions and related problems
Logic Synthesis and Verification Algorithms
Logic Synthesis and Verification Algorithms
An efficient algorithm for the minimal unsatisfiability problem for a subclass of CNF
Annals of Mathematics and Artificial Intelligence
Polynomial-time recognition of minimal unsatisfiable formulas with fixed clause-variable difference
Theoretical Computer Science
An Application of Matroid Theory to the SAT Problem
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
Formal methods for the validation of automotive product configuration data
Artificial Intelligence for Engineering Design, Analysis and Manufacturing
A Comparative Study of Two Boolean Formulations of FPGA Detailed Routing Constraints
IEEE Transactions on Computers
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
Verification of Proofs of Unsatisfiability for CNF Formulas
DATE '03 Proceedings of the conference on Design, Automation and Test in Europe - Volume 1
Minimal unsatisfiable formulas with bounded clause-variable difference are fixed-parameter tractable
Journal of Computer and System Sciences
Word level predicate abstraction and refinement for verifying RTL verilog
Proceedings of the 42nd annual Design Automation Conference
Refinement strategies for verification methods based on datapath abstraction
ASP-DAC '06 Proceedings of the 2006 Asia and South Pacific Design Automation Conference
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
Minimal unsatisfiable sets: classification and bounds
ASIAN'04 Proceedings of the 9th Asian Computing Science conference on Advances in Computer Science: dedicated to Jean-Louis Lassez on the Occasion of His 5th Cycle Birthday
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
Deriving small unsatisfiable cores with dominators
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Discovery of minimal unsatisfiable subsets of constraints using hitting set dualization
PADL'05 Proceedings of the 7th international conference on Practical Aspects of Declarative Languages
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
Deriving minimal conflict sets by CS-trees with mark set indiagnosis from first principles
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Synthesizing complementary circuits automatically
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Boosting minimal unsatisfiable core extraction
Proceedings of the 2010 Conference on Formal Methods in Computer-Aided Design
Faster extraction of high-level minimal unsatisfiable cores
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Finding first-order minimal unsatisfiable cores with a heuristic depth-first-search algorithm
IDEAL'11 Proceedings of the 12th international conference on Intelligent data engineering and automated learning
Restoring CSP Satisfiability with MaxSAT
Fundamenta Informaticae - RCRA 2009 Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion
Quantified maximum satisfiability: a core-guided approach
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
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Explaining the causes of infeasibility of Boolean formulas has practical applications in numerous fields, such as artificial intelligence (repairing inconsistent knowledge bases), formal verification (abstraction refinement and unbounded model checking), and electronic design (diagnosing and correcting infeasibility). Minimal unsatisfiable subformulas (MUSes) provide useful insights into the causes of infeasibility. An unsatisfiable formula often has many MUSes. Based on the application domain, however, MUSes with specific properties might be of interest. In this paper, we tackle the problem of finding a smallest-cardinality MUS (SMUS) of a given formula. An SMUS provides a succinct explanation of infeasibility and is valuable for applications that are heavily affected by the size of the explanation. We present (1) a baseline algorithm for finding an SMUS, founded on earlier work for finding all MUSes, and (2) a new branch-and-bound algorithm called Digger that computes a strong lower bound on the size of an SMUS and splits the problem into more tractable subformulas in a recursive search tree. Using two benchmark suites, we experimentally compare Digger to the baseline algorithm and to an existing incomplete genetic algorithm approach. Digger is shown to be faster in nearly all cases. It is also able to solve far more instances within a given runtime limit than either of the other approaches.