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Quantifier Elimination via Functional Composition

  • Jie-Hong R. Jiang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5643)

Abstract

This paper poses the following basic question: Given a quantified Boolean formula ∃ x. ϕ, what should a function/formula f be such that substituting f for x in ϕ yields a logically equivalent quantifier-free formula? Its answer leads to a solution to quantifier elimination in the Boolean domain, alternative to the conventional approach based on formula expansion. Such a composite function can be effectively derived using symbolic techniques and further simplified for practical applications. In particular, we explore Craig interpolation for scalable computation. This compositional approach to quantifier elimination is analyzably superior to the conventional one under certain practical assumptions. Experiments demonstrate the scalability of the approach. Several large problem instances unsolvable before can now be resolved effectively. A generalization to first-order logic characterizes a composite function’s complete flexibility, which awaits further exploitation to simplify quantifier elimination beyond the propositional case.

Keywords

Model Check Propositional Logic Composite Function Predicate Logic Conjunctive Normal Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jie-Hong R. Jiang
    • 1
  1. 1.Department of Electrical Engineering / Graduate Institute of Electronics EngineeringNational Taiwan UniversityTaipeiTaiwan

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