Advertisement

On the composition of morphisms and inverse morphisms

  • M. Latteux
  • J. Leguy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 154)

Abstract

In order to study composition of morphisms and inverse morphisms, we introduce starry transductions t which are, by definition, those verifying: ε ∃ t(ε) and for all words u, v, t(u) t(v) ⊂t(uv). We show that each starry transduction can be factored with two morphisms and two inverse morphisms. Then, we study some particular starry transductions. So, we prove that each rational substitution can be factored into a single morphism and two inverse morphisms and that each decreasing starry transduction can be factored into a single inverse morphism and two morphisms. That permits us to give an answer to a question posed in [5], by showing that for every rational language R, there exist morphisms h1, h2, h3, g1, g2, g3, such that R=h 3 −1 o h2 o h 1 −1 (a)=g3 o g 2 −1 o g1(a*b).

Keywords

Rational Substitution Finite Deterministic Automaton Deterministic Automaton Rational Language Rational Transduction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    J. BERSTEL, “Transductions and context-free language”, Teubner Verlag, Stuttgart, 1979.Google Scholar
  2. [2]
    L. BOASSON and M. NIVAT, “Sur diverses familles de langages fermées par transduction rationnelle”, Acta Informatica 2 (1973), pp.180–188.Google Scholar
  3. [3]
    R.V. BOOK, “Comparing complexity classes”, J. Comput. System Sc. 9 (1974), pp. 213–229.Google Scholar
  4. [4]
    N. CHOMSKY and M.P. SCHÜTZENBERGER, “The algebraic theory of context-free language”, in Computer programming and formal systems (P. Braffort and D. Hirschberg Eds.), Amsterdam, North-Holland 1963, pp. 118–161.Google Scholar
  5. [5]
    K. CULIK II, F.E. FICH and A. SALOMAA, “A homomorphic characterization of regular languages”, Discrete Appl. Math. 4 (1982), pp.149–152.Google Scholar
  6. [6]
    K. CULIK II, and H. MAURER, “On simple representation of language families”, RAIRO Theor. Informatics 13 (1979), pp. 241–250.Google Scholar
  7. [7]
    S. GINSBURG, J. GOLDSTINE and S. GREIBACH, “Some uniformly erasable families of languages, Theoretical Computer Science 2 (1976), pp. 29–44.Google Scholar
  8. [8]
    S. GREIBACH, “The hardest CF language”, SIAM J. Comput. 2 (1973), pp. 304–310Google Scholar
  9. [9]
    J. KARHUMÄKI and M. LINNA, “A note on morphic characterization of languages”, Discrete Appl. Math. 5 (1983), pp. 243–246.Google Scholar
  10. [10]
    M. LATTEUX, “A propos du lemme de substitution”, Theoretical Computer Science 14 (1981), pp. 119–123.Google Scholar
  11. [11]
    M. LATTEUX and J. LEGUY, “On the usefulness of bifaithful rational cones”, Publication I.T. 40–82, Lille, 1982.Google Scholar
  12. [12]
    J. LEGUY, “Traniductions rationnelles décroissantes”, RAIRO Theor. Informatics 5 (1981), pp. 141–148.Google Scholar
  13. [13]
    M. NIVAT, “Transductions dei langages de Chomsky”, Ann. Inst. Fourier 18 (1968), pp. 339–455.Google Scholar
  14. [14]
    A. SALOMAA, “Formal languages”, Academic Press, New-York, 1973.Google Scholar
  15. [15]
    P. TURAKAINEN, “A homomorphic characterization of principal semi AFLs without using intersection with regular sets”, 1982, Technical report, University of Oulu.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • M. Latteux
    • 1
  • J. Leguy
    • 1
  1. 1.U.E.R. I.E.E.A., InformatiqueUniversite de Lille IVilleneuve D'Ascq Cedex

Personalised recommendations