Resolution for quantified Boolean formulas
Information and Computation
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
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
QUBOS: Deciding Quantified Boolean Logic Using Propositional Satisfiability Solvers
FMCAD '02 Proceedings of the 4th International Conference on Formal Methods in Computer-Aided Design
Conflict driven learning in a quantified Boolean Satisfiability solver
Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design
Backjumping for quantified Boolean logic satisfiability
Artificial Intelligence
Word problems requiring exponential time(Preliminary Report)
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Compressing BMC Encodings with QBF
Electronic Notes in Theoretical Computer Science (ENTCS)
Backdoor Sets of Quantified Boolean Formulas
Journal of Automated Reasoning
Bounded universal expansion for preprocessing QBF
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Bounded model checking with QBF
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
sKizzo: a suite to evaluate and certify QBFs
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Quantifier Structure in Search-Based Procedures for QBFs
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
The seventh QBF solvers evaluation (QBFEVAL’10)
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
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Given a quantified boolean formula (QBF) in prenex conjunctive normal form (PCNF), we consider the problem of identifying variable dependencies. In related work, a formal definition of dependencies has been suggested based on quantifier prefix reordering: two variables are independent if swapping them in the prefix does not change satisfiability of the formula. Instead of the general case, we focus on the sets of depending existential variables for all universal variables. This is relevant particularly for expansion-based QBF solvers. We present an approach for efficiently computing existential dependency sets by means of a directed connection relation over variables and demonstrate how this relation can be compactly represented as a tree using a union-find data structure. Experimental results show the effectiveness of our approach.