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Reading functions and an extension of Kleene theorem for some families of languages

  • Robert Knast
  • Jacek Martinek
Section A Algebraic & Constructive Theory of Machines, Computations and Languages
Part of the Lecture Notes in Computer Science book series (LNCS, volume 56)

Abstract

A reading function is defined as f : σ* → σ*, where σ is an alphabet. By means of reading functions and the family of regular languages, new families of languages can be defined. In the paper we study properties of the so called permutation type reeding functions. For finitely generated functions of this type the set of basic functions is constructed. Some of these functions generate families of languages properly containing regular sets and having algebraic properties similar to regular languages. An extension of Kleene theorem for families of languages generated by bijective reading functions is presented.

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References

  1. [1]
    Piccard, S., Sur les bases du groupe symétrique, Paris, 1946. Russian trans. in "Kibernet. Sbornik" no 1, Isd.Mir, Moskva, 1965.Google Scholar
  2. [2]
    Brozozowski, J.A., Derivatives of regular-expressions, J. ACM, 11 (1964), 481–494.Google Scholar
  3. [3]
    Eilenberg, S., Automata, languages, and machines, Academic Press, 1974 (vol. A), 1976 (vol. B).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • Robert Knast
    • 1
  • Jacek Martinek
    • 2
  1. 1.Mathematical Institute of the Polish Academy of SciencesPoznańPoland
  2. 2.Regional Computer CenterTechnical University of PoznańPoznańPoland

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