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A periodicity property of iterated morphisms

Published online by Cambridge University Press:  18 July 2007

Juha Honkala
Juha Honkala*
Affiliation:
Department of Mathematics, University of Turku, 20014 Turku, Finland; [email protected]
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Abstract

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*.

Keywords

Iterated morphismperiodicity
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 41 , Issue 2 , April 2007 , pp. 215 - 223
Copyright
© EDP Sciences, 2007

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