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Quantifier Rewriting and Equivalence Models for Quantified Horn Formulas

  • Uwe Bubeck
  • Hans Kleine Büning
  • Xishun Zhao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3569)

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Uwe Bubeck
    • 1
  • Hans Kleine Büning
    • 2
  • Xishun Zhao
    • 3
  1. 1.International Graduate School Dynamic Intelligent SystemsUniversität PaderbornPaderbornGermany
  2. 2.Department of Computer ScienceUniversität PaderbornPaderbornGermany
  3. 3.Institute of Logic and CognitionZhongshan UniversityGuangzhouP.R. China

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