Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas
Journal of Combinatorial Theory Series A
Journal of the ACM (JACM)
Approximating treewidth, pathwidth, frontsize, and shortest elimination tree
Journal of Algorithms
On subclasses of minimal unsatisfiable formulas
Discrete Applied Mathematics - Special issue on Boolean functions and related problems
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
An efficient algorithm for the minimal unsatisfiability problem for a subclass of CNF
Annals of Mathematics and Artificial Intelligence
Faster SAT and smaller BDDs via common function structure
Proceedings of the 2001 IEEE/ACM international conference on Computer-aided design
Polynomial-time recognition of minimal unsatisfiable formulas with fixed clause-variable difference
Theoretical Computer Science
Early Quantification and Partitioned Transition Relations
ICCD '96 Proceedings of the 1996 International Conference on Computer Design, VLSI in Computers and Processors
An Application of Matroid Theory to the SAT Problem
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
The complexity of facets (and some facets of complexity)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Approximating minimal unsatisfiable subformulae by means of adaptive core search
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
AMUSE: a minimally-unsatisfiable subformula extractor
Proceedings of the 41st annual Design Automation Conference
Toward Good Elimination Orders for Symbolic SAT Solving
ICTAI '04 Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence
Minimal unsatisfiable formulas with bounded clause-variable difference are fixed-parameter tractable
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Bucket elimination: a unifying framework for probabilistic inference
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Local-search Extraction of MUSes
Constraints
Using unsatisfiable cores to debug multiple design errors
Proceedings of the 18th ACM Great Lakes symposium on VLSI
An approach for extracting a small unsatisfiable core
Formal Methods in System Design
Contradictory antecedent debugging in bounded model checking
Proceedings of the 19th ACM Great Lakes symposium on VLSI
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Does This Set of Clauses Overlap with at Least One MUS?
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
SARA'07 Proceedings of the 7th International conference on Abstraction, reformulation, and approximation
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
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
Computing small unsatisfiable cores in satisfiability modulo theories
Journal of Artificial Intelligence Research
On improving MUS extraction algorithms
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
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
A scalable algorithm for minimal unsatisfiable core extraction
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
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
Towards efficient MUS extraction
AI Communications - 18th RCRA International Workshop on “Experimental evaluation of algorithms for solving problems with combinatorial explosion”
Improved single pass algorithms for resolution proof reduction
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
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After establishing the unsatisfiability of a SAT instance encoding a typical design task, there is a practical need to identify its minimal unsatisfiable subsets, which pinpoint the reasons for the infeasibility of the design. Due to the potentially expensive computation, existing tools for the extraction of unsatisfiable subformulas do not guarantee the minimality of the results. This paper describes a practical algorithm that decides the minimal unsatisfiability of any CNF formula through BDD manipulation. This algorithm has a worse-case complexity that is exponential only in the treewidth of the CNF formula. We provide an empirical evaluation of the algorithm, highlighting its efficiency on a set of hard problems as well as its ability to work with existing subformula extraction tools to achieve optimal results.