Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
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
A machine program for theorem-proving
Communications of the ACM
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Partial Implicit Unfolding in the Davis-Putnam Procedure for Quantified Boolean Formulae
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
Lemma and Model Caching in Decision Procedures for Quantified Boolean Formulas
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Towards a Symmetric Treatment of Satisfaction and Conflicts in Quantified Boolean Formula Evaluation
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
QUBE: A System for Deciding Quantified Boolean Formulas Satisfiability
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
SAT Based BDD Solver for Quantified Boolean Formulas
ICTAI '04 Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence
IEEE Transactions on Computers
A backbone-search heuristic for efficient solving of hard 3-SAT formulae
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
A new method for solving hard satisfiability problems
AAAI'92 Proceedings of the tenth national conference on Artificial intelligence
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
CSP properties for quantified constraints: definitions and complexity
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
A survey of the satisfiability-problems solving algorithms
International Journal of Advanced Intelligence Paradigms
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Solving Quantified Boolean Formulas (QBF) has become an important and attractive research area, since several problem classes might be formulated efficiently as QBF instances (e.g. planning, non monotonic reasoning, two-player games, model checking, etc). Many QBF solvers has been proposed, most of them perform decision tree search using the DPLL-like techniques. To set free the variable ordering heuristics that are traditionally constrained by the static order of the QBF quantifiers, a new symbolic search based approach (QBdd(Sat)) is proposed. It makes an original use of binary decision diagram to represent the set of models (or prime implicants) of the boolean formula found using search-based satisfiability solver. Our approach is enhanced with two interesting extensions. First, powerful reduction operators are introduced in order to dynamically reduce the BDD size and to answer the validity of the QBF. Second, useful cuts are achieved on the search tree thanks to the nogoods generated from the BDD representation. Using DPLL-likes (resp. local search) techniques, our approach gives rise to a complete QBdd(DPLL) (resp. incomplete QBdd(LS)) solver. Our preliminary experimental results show that on some classes of instances from the QBF evaluation, QBdd(DPLL) and QBdd(LS) are competitive with state-of-the-art QBF solvers.