Le cylindre des langages linéaires | Theory of Computing Systems
Skip to main content
Springer Nature Link
Log in

Le cylindre des langages linéaires

  • Published:
Mathematical systems theory Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. M. Autebert, Le Cylindre des Langages à Compteur,à paraitre.

  2. L. Boasson, Langages algèbriques, paires itérantes et transductions rationnelles,T.C.S. 2 (1976), 209–223.

    Google Scholar 

  3. L. Boasson etM. Nivat, Sur diverses familles de langages fermées par transductions rationnelles,Acta Informatica 2 (1973), 180–188.

    Google Scholar 

  4. S. Ginsburg, TheMathematical Theory of Context-Free Languages, McGraw-Hill, 1966.

  5. S. Ginsburg, J. Goldstine andS. Greibach, Uniformly erasable AFL,J.C.S.S. 10 (1975), 165–182.

    Google Scholar 

  6. S. Greibach, The hardest context-free language,SIAM J. Computing 2 (1973), 304–310.

    Google Scholar 

  7. S. Greibach, Jump Pda's and hierarchies of deterministic context-free languages,SIAM J. Computing 3 (1974), 111–127.

    Google Scholar 

  8. W. Ogden, A helpful result for proving inherent ambiguity,Math. System Theory 2 (1967), 191–194.

    Google Scholar 

  9. I. H. Sudborough, A note on tape-bounded complexity classes and linear context-free languages,Journal of A.C.M. 22 (1975), 499–500.

    Google Scholar 

Download references

Author information

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Nivat
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

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

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Revised:

  • Issue Date:

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

Search

Navigation