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On the Periodicity of Morphic Words

Vesa Halava, Tero Harju, Tomi Kärki, Michel Rigo (Eds.), On the Periodicity of Morphic Words , Lecture Notes in Computer Science 6224, Springer-Verlag, 2010.


Given a morphism h prolongable on a and an integer p, we present
an algorithm that calculates which letters occur infinitely often in congruent positions modulo p in the infinite word h^ω(a).
As a corollary, we show that it is decidable whether
a morphic word is ultimately p-periodic.
Moreover, using our algorithm we can find the smallest similarity
relation such that the morphic word is ultimately
relationally p-periodic. The problem of deciding whether
an automatic sequence is ultimately weakly R-periodic
is also shown to be decidable.

BibTeX entry:

  title = {On the Periodicity of Morphic Words },
  volume = {6224},
  series = {Lecture Notes in Computer Science},
  editor = {Halava, Vesa and Harju, Tero and Kärki, Tomi and Rigo, Michel},
  publisher = {Springer-Verlag},
  year = {2010},

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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