Similarity density of the ThueMorse word with overlapfree infinite binary words
Abstract
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 overlapfree infinite binary word, other than the ThueMorse 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2014
 arXiv:
 arXiv:1405.5605
 Bibcode:
 2014arXiv1405.5605D
 Keywords:

 Computer Science  Formal Languages and Automata Theory;
 Computer Science  Discrete Mathematics;
 F.4.3
 EPrint:
 In Proceedings AFL 2014, arXiv:1405.5272