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A characterization of power-free morphisms. (English) Zbl 0572.68066

A word is called k th power-free if it does not contain any non-empty factor \(u^ k\). A morphism is k th power-free if it preserves k th power-free words. A morphism is power-free if it is k th power-free for every \(k>1\). We show that it is decidable whether a morphism is power- free; more precisely, we prove that a morphism h is power-free iff: h is a square-free morphism and, for each letter a, the image \(h(a^ 2)\) is cube-free.

MSC:

68Q45 Formal languages and automata
20M35 Semigroups in automata theory, linguistics, etc.
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[1] Bean, D.; Ehrenfeucht, A.; McNulty, G., Avoidable patterns in strings of symbols, Pacific J. math., 85, 2, 261-294, (1979) · Zbl 0428.05001
[2] Berstel, J., Sur LES mots sans carré définis par un morphisme, (), 16-25 · Zbl 0425.20046
[3] Berstel, J., Some recent results on square-free words (STACS’84), Tech. rept. LITP no. 84-6, (1984)
[4] Crochemore, M., Sharp characterizations of square-free morphisms, Theoret. comput. sci., 18, 221-226, (1982) · Zbl 0482.68085
[5] Ehrenfeucht, A.; Rozenberg, G., Repetitions in homomorphisms and languages, (), 192-196 · Zbl 0502.68020
[6] Lothaire, M., Combinatoric on words, () · Zbl 1001.68093
[7] Salomaa, A., Jewels of formal language theory, (1981), Pitman London · Zbl 0487.68063
[8] Thue, A., Über unendliche zeichenreihen, Norske vid. selsk. skr. mat. nat. kl (kristiana), 7, 1-22, (1906) · JFM 39.0283.01
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