Chen Fei Du (University of Waterloo) |
Jeffrey Shallit (University of Waterloo) |

We consider a measure of similarity for infinite words that generalizes the notion of asymptotic or natural density of subsets of natural numbers from number theory. We show that every overlap-free infinite binary word, other than the Thue-Morse word t and its complement t bar, has this measure of similarity with t between 1/4 and 3/4. This is a partial generalization of a classical 1927 result of Mahler. |

Published: 21st May 2014.

ArXived at: http://dx.doi.org/10.4204/EPTCS.151.16 | bibtex | |

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