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A property of three-element codes

  • Juhani Karhumäki
Contibuted Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 166)

Abstract

Let w be a word and A a language of a finitely generated free monoid Σ*. We say that w is ambiguously covered by A if there exist words α and β in A, with α ≠ β, such that w ε pref(αA+) ∑ pref(βA+). We show that if A is a three-element code then any two words which are ambiguously covered by A are comparable, i.e., one of them is a prefix of another. This property is characteristic for three-element codes.

Keywords

Active Research Area Injective Morphism Free Monoid Finite Alphabet Bounded Delay 
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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References

  1. [1]
    Berstel,J. and Perrin,D., The Theory of Codes, (to appear).Google Scholar
  2. [2]
    Harrison, M., Introduction to Formal Language Theory, Addison-Wesley, Reading, Mass. (1978).Google Scholar
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    Lothaire, M., Combinatorics on words, Addison-Wesley, Reading, Mass. (1983).Google Scholar
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    Salomaa, A., Jewels of Formal Language Theory, Computer Science Press, Maryville (1981).Google Scholar
  5. [5]
    Schützenberger,M.P., Une theorie algebraique du codage, Seminaire Dubreil-Pisot, annee 55–56, exp. n. 15 Inst. Henri Poincare, Paris (1956).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Juhani Karhumäki
    • 1
  1. 1.Department of MathematicsUniversity of TurkuTurkuFinland

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