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iterated morphism

RAIRO - Theoretical Informatics and Applications (1)

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A periodicity property of iterated morphisms
Juha Honkala
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 41 / Issue 2 / April 2007

Published online by Cambridge University Press:

18 July 2007, pp. 215-223

Print publication:

April 2007
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Suppose ƒ : X* → X* is a morphism and u,v ∈ X*. For every nonnegative integer n, let zn be the longest common prefix of ƒn(u) and ƒn(v), and let un,vn ∈ X* be words such that ƒn(u) = znun and ƒn(v) = znvn. We prove that there is a positive integer q such that for any positive integer p, the prefixes of un (resp. vn) of length p form an ultimately periodic sequence having period q. Further, there is a value of q which works for all words u,v ∈ X*.