منابع مشابه
Periodicity, morphisms, and matrices
In 1965, Fine and Wilf proved the following theorem: if (fn)n¿0 and (gn)n¿0 are periodic sequences of real numbers, of period lengths h and k, respectively, and fn = gn for 06 n¡h+ k − gcd(h; k), then fn = gn for all n¿ 0. Furthermore, the constant h + k − gcd(h; k) is best possible. In this paper, we consider some variations on this theorem. In particular, we study the case where fn 6 gn inste...
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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...
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We consider so-called Toeplitz words which can be viewed as generalizations of one-way innnite periodic words. We compute their subword complexity, and show that they can always be generated by iterating periodically a nite number of morphisms. Moreover, we deene a structural classiication of Toeplitz words which is reeected in the way how they can be generated by iterated morphisms.
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— For a given endomorphism h on a finitely generaled jree monoid there are only flnitely many primitive words w for which h(w) = w for some n^2. Also, one can effectively find ail such w. Using this it is shown that it is decidable whether or not a morphism h defines an ultimately periodic infinité word when iterated on a given word. This latter resuit thus solves the DOL periodicity problem. R...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2003
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(02)00398-5