Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
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
Bounded Model Construction for Monadic Second-Order Logics
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
QUBE: A System for Deciding Quantified Boolean Formulas Satisfiability
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
ZRES: The Old Davis-Putman Procedure Meets ZBDD
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
A satisfiability procedure for quantified boolean formulae
Discrete Applied Mathematics - The renesse issue on satisfiability
SAT Based BDD Solver for Quantified Boolean Formulas
ICTAI '04 Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence
Toward Good Elimination Orders for Symbolic SAT Solving
ICTAI '04 Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence
Constructing conditional plans by a theorem-prover
Journal of Artificial Intelligence Research
A multi-engine solver for quantified boolean formulas
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Exploiting structure in an AIG based QBF solver
Proceedings of the Conference on Design, Automation and Test in Europe
Extended resolution proofs for conjoining BDDs
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
CirCUs: a hybrid satisfiability solver
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
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In this paper we present a QBF solver that is based on BDD technologies but includes optimizations from search-based algorithms. We enhance the early quantification technique from model checking, favoring aggressive quantification over conjunction of BDDs. BDD Constraint propagation is also described, a strategy inspired by the efficient simplifications applied to CNFs in DPLL-based algorithms. Some dynamic variable elimination heuristics that enforce quantification and bounded space usage are also presented, coping with the difficulties faced by static heuristics included in previous BDD-based solvers. Experimental results show that our solver outperforms both symbolic and search-based competitive solvers in formal verification benchmarks with practical applications in equivalence checking and theorem proving, by completing more problems or finishing in less time. Some preliminary results also show that the solver is able to handle some other hard problems for symbolic solvers in the planning domain with similar efficiency. The benchmarks we used contain QBFs of nearly up to 9000 variables and are available at the QBFLIB website.