Counting with rational functions

  • C. Choffrut
  • M. P. Schutzenberger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 226)


Rational functions of a free monoid A* into the free cyclic monoid t* generated by a unique element t, can be viewed as assigning an integer to every word u∈A*. We investigate those functions which count occurrences of some fixed (and special) subsets \(X \subseteq A^ *\) in all words of A* and show that they can be characterized in terms of "bounded variation", a notion which is close to continuity of functions.


Rational Function Bounded Variation Counting Function Sequential Function Free Monoid 
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.


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7. References

  1. [Be]
    BERSTEL J., "Transductions and Context-Free Languages", Teubner, 1979Google Scholar
  2. [Be Per]
    BERSTEL J., & D. PERRIN, "Theory of codes", 1985, Academic Press.Google Scholar
  3. [Ch]
    CHOFFRUT C., A generalization of Ginsburg and Rose's characterization of g-s-m mappings. Proceedings of the 6th ICALP Conférence, 1979, p. 88–103.Google Scholar
  4. [Ei]
    EILENBERG S., "Automata, Languages and Machines", Vol. A. 1974, Academic Press.Google Scholar
  5. [GiRo]
    GINSBURG S. & G.F. ROSE, A characterization of machine mappings, Can. J. of Math., 18, 1986, p. 381–388.Google Scholar
  6. [Jo]
    JOHNSON J.H., Formal models for string similarity, PhD thesis, University of Waterloo, 1983 (also Research Report C8-83-32).Google Scholar
  7. [Kn]
    KNUTH D.E., "The Art of Computer Programming", Vol. 3., 1973, Addison-Wesley.Google Scholar
  8. [La]
    LALLEMENT G., "Semigroups and Combinatorial Applications", 1979, Wiley-Interscience.Google Scholar
  9. [Ni]
    NIVAT M., Transductions des langages de Chomsky, Ann. de l'Inst. Fourier, 18, 1986, p. 339–456.Google Scholar
  10. [Sch 1]
    SCHUTZENBERGER M.P., Sur les relations rationnelles entre monoïdes libres, Theoret. Comput. Sci., 3, 1976, p. 243–259.Google Scholar
  11. [Sch 2]
    SCHUTZENBERGER M.P., Sur une variante des fonctions séquentielles, Theoret. Comput. Sci., 4, 1977, p. 243–259.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • C. Choffrut
    • 1
  • M. P. Schutzenberger
    • 2
  1. 1.Faculté des SciencesUniversité de ROUENMont-Saint-Aignan
  2. 2.U.E.R. de Mathématiques et d'InformatiqueUniversité Paris 7Parix Cedex 05

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