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Generalized implicit definitions on finite structures

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Computer Science Logic (CSL 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1092))

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Abstract

We propose a natural generalization of the concept of implicit definitions over finite structures, allowing non-determinism at an intermediate level of a (deterministic) definition. These generalized implicit definitions offer more expressive power than classical implicit definitions. Moreover, their expressive power can be characterized over unordered finite structures in terms of the complexity class NP ∩ co-NP. Finally, we investigate a subclass of these where the non-determinism is restricted to the choice of a unique relation with respect to an implicit linear order, and prove that it captures UP ∩ co-UP also over the class of all finite structures. These results shed some light on the expressive power of non-deterministic primitives.

Work supported in part by an EC-NSF grant DEUS EX MACHINA, and an NSERC fellowship in Canada.

Work done in the Verso Project at INRIA.

Work partially supported by NSF grant CCR-9403447 and the John C. Whitehead faculty research fund at Haverford College.

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Author information

Authors and Affiliations

  1. University of Toronto, Canada

    Stéphane Grumbach

  2. I.N.R.I.A. Rocquencourt, Domaine de Voluceau BP 105, 78153, Le Chesnay, France

    Stéphane Grumbach

  3. Université de Paris-Sud, France

    Zoé Lacroix

  4. L.R.I., Université de Paris Sud, 91405, Orsay, France

    Zoé Lacroix

  5. Department of Computer Science, Haverford College, 19041-1392, Haverford, PA

    Steven Lindell

Authors
  1. Stéphane Grumbach
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  2. Zoé Lacroix
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  3. Steven Lindell
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Editor information

Hans Kleine Büning

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© 1996 Springer-Verlag Berlin Heidelberg

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Grumbach, S., Lacroix, Z., Lindell, S. (1996). Generalized implicit definitions on finite structures. In: Kleine Büning, H. (eds) Computer Science Logic. CSL 1995. Lecture Notes in Computer Science, vol 1092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61377-3_42

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  • DOI: https://doi.org/10.1007/3-540-61377-3_42

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61377-0

  • Online ISBN: 978-3-540-68507-4

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