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An Improved Tight Closure Algorithm for Integer Octagonal Constraints

  • Roberto Bagnara
  • Patricia M. Hill
  • Enea Zaffanella
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4905)

Abstract

Integer octagonal constraints (a.k.a. Unit Two Variables Per Inequality or UTVPI integer constraints) constitute an interesting class of constraints for the representation and solution of integer problems in the fields of constraint programming and formal analysis and verification of software and hardware systems, since they couple algorithms having polynomial complexity with a relatively good expressive power. The main algorithms required for the manipulation of such constraints are the satisfiability check and the computation of the inferential closure of a set of constraints. The latter is called tight closure to mark the difference with the (incomplete) closure algorithm that does not exploit the integrality of the variables. In this paper we present and fully justify an O(n 3) algorithm to compute the tight closure of a set of UTVPI integer constraints.

Keywords

Inference Rule Abstract Domain Bottom Element Integer Constraint Closure Procedure 
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 2008

Authors and Affiliations

  • Roberto Bagnara
    • 1
  • Patricia M. Hill
    • 2
  • Enea Zaffanella
    • 1
  1. 1.Department of MathematicsUniversity of ParmaItaly
  2. 2.School of ComputingUniversity of LeedsUK

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