Computing the Transitive Closure of a Union of Affine Integer Tuple Relations

  • Anna Beletska
  • Denis Barthou
  • Wlodzimierz Bielecki
  • Albert Cohen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5573)

Abstract

This paper proposes a method to compute the transitive closure of a union of affine relations on integer tuples. Within Presburger arithmetics, complete algorithms to compute the transitive closure exist for convex polyhedra only. In presence of non-convex relations, there exist little but special cases and incomplete heuristics. We introduce a novel sufficient and necessary condition defining a class of relations for which an exact computation is possible. Our method is immediately applicable to a wide area of symbolic computation problems. It is illustrated on representative examples and compared with state-of-the-art approaches.

Keywords

transitive closure affine tuple relations 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Anna Beletska
    • 1
  • Denis Barthou
    • 2
  • Wlodzimierz Bielecki
    • 3
  • Albert Cohen
    • 1
  1. 1.INRIA SaclayFrance
  2. 2.University of Versailles St. QuentinFrance
  3. 3.Technical University of SzczecinPoland

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