The Minimum Satisfiability Problem
SIAM Journal on Discrete Mathematics
An algorithm to evaluate quantified Boolean formulae
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Improved approximation algorithms for MAX SAT
Journal of Algorithms
Solving Advanced Reasoning Tasks Using Quantified Boolean Formulas
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Efficient on-the-fly algorithms for the analysis of timed games
CONCUR 2005 - Concurrency Theory
Compressing BMC Encodings with QBF
Electronic Notes in Theoretical Computer Science (ENTCS)
Verification of Boolean programs with unbounded thread creation
Theoretical Computer Science
Clause/term resolution and learning in the evaluation of quantified Boolean formulas
Journal of Artificial Intelligence Research
Extracting certificates from quantified boolean formulas
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Evaluating and certifying QBFs: A comparison of state-of-the-art tools
AI Communications
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Antichains: a new algorithm for checking universality of finite automata
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
sKizzo: a suite to evaluate and certify QBFs
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Integrating dependency schemes in search-based QBF solvers
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
The seventh QBF solvers evaluation (QBFEVAL’10)
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Antichain algorithms for finite automata
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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We consider the problem of QBF solving viewed as a reachability problem in an exponential And-Or graph. Antichain-based algorithms for reachability analysis in large graphs exploit certain subsumption relations to leverage the inherent structure of the explored graph in order to reduce the effect of state explosion, with high performance in practice. In this paper, we propose simple notions of subsumption induced by the structural properties of the And-Or graphs for QBF solving. Subsumption is used to reduce the size of the search tree, and to define compact representations of certificates (in the form of antichains) both for positive and negative instances of QBF. We show that efficient exploration of the reduced search tree essentially relies on solving variants of Max-SAT and Min-SAT. Preliminary stand-alone experiments of this algorithm show that the antichain-based approach is promising.