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Normalizable Horn Clauses, Strongly Recognizable Relations, and Spi

  • Flemming Nielson
  • Hanne Riis Nielson
  • Helmut Seidl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2477)

Abstract

We exhibit a rich class of Horn clauses, which we call \( \mathcal{H}_{\text{1}} \), whose least models, though possibly infinite, can be computed effectively. We show that the least model of an \( \mathcal{H}_{\text{1}} \) clause consists of so-called strongly recognizable relations and present an exponential normalization procedure to compute it. In order to obtain a practical tool for program analysis, we identify a restriction of \( \mathcal{H}_{\text{1}} \) clauses, which we call \( \mathcal{H}_{\text{2}} \), where the least models can be computed in polynomial time. This fragment still allows to express, e.g., Cartesian product and transitive closure of relations. Inside \( \mathcal{H}_{\text{2}} \), we exhibit a fragment \( \mathcal{H}_{\text{3}} \) where normalization is even cubic. We demonstrate the usefulness of our approach by deriving a cubic control-flow analysis for the Spi calculus [1] as presented in [14].

Keywords

Program analysis uniform Horn clauses strongly recognizable relations Spi calculus 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Flemming Nielson
    • 1
  • Hanne Riis Nielson
    • 1
  • Helmut Seidl
    • 2
  1. 1.Informatics and Mathematical ModellingTechnical University of DenmarkKongens LyngbyDenmark
  2. 2.Universität Trier, FB IV - InformatikTrierGermany

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