A periodicity property of iterated morphisms
نویسنده
چکیده
Suppose f : X∗ −→ X∗ is a morphism and u, v ∈ X∗. For every nonnegative integer n, let zn be the longest common prefix of f(u) and f(v), and let un, vn ∈ X∗ be words such that f(u) = znun and f(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∗. Mathematics Subject Classification. 68Q45, 68R15.
منابع مشابه
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عنوان ژورنال:
- ITA
دوره 41 شماره
صفحات -
تاریخ انتشار 2007