Propositional Logic: Deduction and Algorithms
Propositional Logic: Deduction and Algorithms
QUBOS: Deciding Quantified Boolean Logic Using Propositional Satisfiability Solvers
FMCAD '02 Proceedings of the 4th International Conference on Formal Methods in Computer-Aided Design
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
Quantifier structure in search based procedures for QBFs
Proceedings of the conference on Design, automation and test in Europe: Proceedings
Constructing conditional plans by a theorem-prover
Journal of Artificial Intelligence Research
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
The second QBF solvers comparative evaluation
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
Quantifier rewriting and equivalence models for quantified horn formulas
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
A branching heuristics for quantified renamable horn formulas
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Rewriting (dependency-)quantified 2-CNF with arbitrary free literals into existential 2-HORN
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Henkin quantifiers and boolean formulae
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
Henkin quantifiers and Boolean formulae: A certification perspective of DQBF
Theoretical Computer Science
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Dependency quantified Boolean formulas (DQBF) extend quantified Boolean formulas with Henkin-style partially ordered quantifiers. It has been shown that this is likely to yield more succinct representations at the price of a computational blow-up from PSPACE to NEXPTIME. In this paper, we consider dependency quantified Horn formulas (DQHORN), a subclass of DQBF, and show that the computational simplicity of quantified Horn formulas is preserved when adding partially ordered quantifiers. We investigate the structure of satisfiability models for DQHORN formulas and prove that for both DQHORN and ordinary QHORN formulas, the behavior of the existential quantifiers depends only on the cases where at most one of the universally quantified variables is zero. This allows us to transform DQHORN formulas with free variables into equivalent QHORN formulas with only a quadratic increase in length. An application of these findings is to determine the satisfiability of a dependency quantified Horn formula Φ with |∀| universal quantifiers in time O(|∀|·|Φ|), which is just as hard as QHORN-SAT.