Similarity density of the Thue-Morse word with overlap-free infinite   binary words
  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. 
Chen Fei Du (University of Waterloo), Jeffrey Shallit (University of   Waterloo)
cs.FL cs.DM