On the k-freeness of morphisms on free monoids

  • Veikko Keränen
Contributed Papers Formal Languages

DOI: 10.1007/BFb0039605

Part of the Lecture Notes in Computer Science book series (LNCS, volume 247)
Cite this paper as:
Keränen V. (1987) On the k-freeness of morphisms on free monoids. In: Brandenburg F.J., Vidal-Naquet G., Wirsing M. (eds) STACS 87. STACS 1987. Lecture Notes in Computer Science, vol 247. Springer, Berlin, Heidelberg


Let an integer k≧2 be fixed. A word is called k-repetition free, or shortly k-free, if it does not contain any non-empty subword of the form Rk. A morphism h: X* → Y* is called k-free if the word h(w) is k-free for every k-free word w in X*. We investigate the general structure of k-free morphisms and give outlines for the proof of the following result: if a non-trivial morphism h: X* → Y*, where card(X)≧2 and card(Y)≧2, is k-free for some integer k≧2, then, except a certain possibility concerning one infrequent situation in the case k=3, h is a primitive ps-code. Moreover, an effective characterization is provided for all k-free morphisms h: X* → Y* in the case k≧qh+1, and for a wide class of morphisms in the case 2≦k≦qh, where qh=max{|h(a)| | a∈X}.


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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Veikko Keränen
    • 1
  1. 1.Department of MathematicsUniversity of Oulu LinnanmaaOuluFinland

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