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Erschienen in:
2010 | OriginalPaper | Buchkapitel
On the Periodicity of Morphic Words
verfasst von : Vesa Halava, Tero Harju, Tomi Kärki, Michel Rigo
Erschienen in: Developments in Language Theory
Verlag: Springer Berlin Heidelberg
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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.