A theory of diagnosis from first principles
Artificial Intelligence
Counterexample-guided abstraction refinement for symbolic model checking
Journal of the ACM (JACM)
Formal methods for the validation of automotive product configuration data
Artificial Intelligence for Engineering Design, Analysis and Manufacturing
Validating the result of a Quantified Boolean Formula (QBF) solver: theory and practice
Proceedings of the 2005 Asia and South Pacific Design Automation Conference
Learning abstractions for model checking
Learning abstractions for model checking
Boolean Functions as Models for Quantified Boolean Formulas
Journal of Automated Reasoning
Algorithms for Computing Minimal Unsatisfiable Subsets of Constraints
Journal of Automated Reasoning
Quantified Constraint Optimization
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Solving (Weighted) Partial MaxSAT through Satisfiability Testing
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Algorithms for Weighted Boolean Optimization
SAT '09 Proceedings of the 12th 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
Abstraction-based algorithm for 2QBF
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Resolution proofs and Skolem functions in QBF evaluation and applications
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
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
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
On solving the partial MAX-SAT problem
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
Deriving minimal conflict sets by CS-trees with mark set indiagnosis from first principles
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Unified QBF certification and its applications
Formal Methods in System Design
Towards efficient MUS extraction
AI Communications - 18th RCRA International Workshop on “Experimental evaluation of algorithms for solving problems with combinatorial explosion”
Solving QBF with counterexample guided refinement
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
Resolution-based certificate extraction for QBF
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
QBF-based boolean function Bi-decomposition
DATE '12 Proceedings of the Conference on Design, Automation and Test in Europe
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In recent years, there have been significant improvements in algorithms both for Quantified Boolean Formulas (QBF) and for Maximum Satisfiability (MaxSAT). This paper studies the problem of solving quantified formulas subject to a cost function, and considers the problem in a quantified MaxSAT setting. Two approaches are investigated. One is based on relaxing the soft clauses and performing a linear search on the cost function. The other approach, which is the main contribution of the paper, is inspired by recent work on MaxSAT, and exploits the iterative identification of unsatisfiable cores. The paper investigates the application of these approaches to the concrete problem of computing smallest minimal unsatisfiable subformulas (SMUS), a decision version of which is a well-known problem in the second level of the polynomial hierarchy. Experimental results, obtained on representative problem instances, indicate that the core-guided approach for the SMUS problem outperforms the use of linear search over the values of the cost function. More significantly, the core-guided approach also outperforms the state-of-the-art SMUS extractor Digger.