Abstract
A word w is called repetitive if it contains two consecutive equal factors ; otherwise w is nonrepetitive. Thus the word abacacb is repetitive, and abcacbabcbac is nonrepetitive. There is no nonrepetitive word of length 4 over a two letter alphabet ; on the contrary, there exist infinite nonrepetitive words over a three letter alphabet. Most of the explicitly known infinite nonrepetitive words are constructed by iteration of a morphism. In this paper, we show that it is decidable whether an infinite word over a three letter alphabet obtained by iterating a morphism is nonrepetitive. We also investigate nonrepetitive morphisms, i.e. morphisms preserving nonrepetitive words, and we show that it is decidable whether a morphism (over an arbitrary finite alphabet) is nonrepetitive.
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© 1979 Springer-Verlag Berlin Heidelberg
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Berstel, J. (1979). Sur les mots sans carré définis par un morphisme. In: Maurer, H.A. (eds) Automata, Languages and Programming. ICALP 1979. Lecture Notes in Computer Science, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09510-1_2
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DOI: https://doi.org/10.1007/3-540-09510-1_2
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