Sur les mots sans carré définis par un morphisme

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.