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Some new decidability results on positive and negative set constraints

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Constraints in Computational Logics (CCL 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 845))

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Abstract

A positive set constraint is of the form exp 1 \(\subseteq\) exp 2, a negative set constraint is of the form exp 1 \(\subseteq\) exp 2 where exp 1 and exp 2 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).

This research was partially supported by “GDR Mathématiques et Informatique” and ESPRIT Basic Research Action 6317 ASMICS2.

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Authors and Affiliations

  1. LIFL, URA 369 CNRS, IEEA Université de Lille I, 59655, Villeneuve d'Ascq Cedex, France

    Rémi Gilleron, Sophie Tison & Marc Tommasi

Authors
  1. Rémi Gilleron
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  2. Sophie Tison
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  3. Marc Tommasi
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Jean-Pierre Jouannaud

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© 1994 Springer-Verlag Berlin Heidelberg

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Gilleron, R., Tison, S., Tommasi, M. (1994). Some new decidability results on positive and negative set constraints. In: Jouannaud, JP. (eds) Constraints in Computational Logics. CCL 1994. Lecture Notes in Computer Science, vol 845. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0016864

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  • DOI: https://doi.org/10.1007/BFb0016864

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58403-2

  • Online ISBN: 978-3-540-48699-2

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