Quantifier rewriting and equivalence models for quantified horn formulas

Authors:
Uwe Bubeck;Hans Kleine Büning;Xishun Zhao
Affiliations:
International Graduate School Dynamic Intelligent Systems, Universität Paderborn, Paderborn, Germany;Department of Computer Science, Universität Paderborn, Paderborn, Germany;Institute of Logic and Cognition, Zhongshan University, Guangzhou, P.R. China
Venue:
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Year:
2005

Citing 6
Cited 1

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
Propositional Logic: Deduction and Algorithms

Propositional Logic: Deduction and Algorithms
Partial Implicit Unfolding in the Davis-Putnam Procedure for Quantified Boolean Formulae

LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
Resolve and expand

SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
Equivalence models for quantified boolean formulas

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

Dependency quantified horn formulas: models and complexity

SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, quantified Horn formulas with free variables (QHORN*) are investigated. The main result is that any quantified Horn formula Φ of length |Φ| with free variables, |∀| universal quantifiers and an arbitrary number of existential quantifiers can be transformed into an equivalent formula of length O(|∀| ·|Φ|) which contains only existential quantifiers. Moreover, it is shown that quantified Horn formulas with free variables have equivalence models where every existential quantifier is associated with a monotone Boolean function. The results allow a simple representation of quantified Horn formulas as purely existentially quantified Horn formulas (∃HORN*). An application described in the paper is to solve QHORN*-SAT in O(|∀| ·|Φ|) by using this transformation in combination with a linear-time satisfiability checker for propositional Horn formulas.