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Le cylindre des langages linéaires

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Abstract

Define a cylinder to be a family of languages which is closed under inverse homomorphisms and intersection with regular sets. A number of well-known families of languages are cylinders:

  • —CFL, the family of context-free languages, is a principal cylinder, i.e. the smallest cylinder containing a languageL O described in [6].

  • —the family of deterministic context-free languages is proved to be a nonprincipal cylinder in [7].

  • —the family of unambiguous context-free languages is a cylinder: to prove that it is not principal seems to be a very hard problem.

In this paper we prove that Lin, the family of linear context-free languages, is a nonprincipal cylinder. This is achieved in the standard way by exhibiting a sequence of languages Sn, n∈N, such that Lin is the union of all the principal cylinders generated by these languages and is not the union of any finite number of these cylinders.

This leaves open the problem raised by Sheila Greibach of whether there exists a languageL such that every linear context-free language is the image ofL in some inverse gsm mapping.

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References

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Authors and Affiliations

  1. U.E.R. de Mathématiques, Université de Picardie, Amiens, France

    L. Boasson & M. Nivat

  2. U.E.R. de Mathématiques, Université Paris 7, Paris, France

    L. Boasson & M. Nivat

Authors
  1. L. Boasson
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  2. M. Nivat
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Additional information

Ce travail s'est fait dans le cadre du Laboratoire Associé du C.N.S.R.S. “Informatique Théorique et Programmation".

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Boasson, L., Nivat, M. Le cylindre des langages linéaires. Math. Systems Theory 11, 147–155 (1977). https://doi.org/10.1007/BF01768473

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  • DOI: https://doi.org/10.1007/BF01768473

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