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Some new decidability results on positive and negative set constraints

  • Rémi Gilleron
  • Sophie Tison
  • Marc Tommasi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 845)

Abstract

A positive set constraint is of the form exp1\(\subseteq\)exp2, a negative set constraint is of the form exp1\(\subseteq\)exp2 where exp1 and exp2 are set expressions constructed using set variables, function symbols, and the set union, intersection and complement symbols. Decision algorithms for satisfiability of systems of positive and negative set constraints were given by Gilleron et al. [GTT93b], Aiken et al. [AKW93], and Charatonik and Pacholski [CP94]. In this paper, we study properties of the set of solutions of such systems and properties of solutions of interest for applications. The main decidability results are: for positive and negative set constraints, equivalence of systems is decidable, it is decidable whether or not a system has a unique solution; for positive set constraints, it is decidable whether or not a system has a least solution, it is decidable whether or not a system has a finite solution (i.e. the interpretation maps each set variable on a finite set).

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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Rémi Gilleron
    • 1
  • Sophie Tison
    • 1
  • Marc Tommasi
    • 1
  1. 1.LIFL, URA 369 CNRSIEEA Université de Lille IVilleneuve d'Ascq CedexFrance

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