4 research outputs found
Bounds for the discrete correlation of infinite sequences on k symbols and generalized Rudin-Shapiro sequences
Motivated by the known autocorrelation properties of the Rudin-Shapiro
sequence, we study the discrete correlation among infinite sequences over a
finite alphabet, where we just take into account whether two symbols are
identical. We show by combinatorial means that sequences cannot be "too"
different, and by an explicit construction generalizing the Rudin-Shapiro
sequence, we show that we can achieve the maximum possible difference.Comment: Improved Introduction and new Section 6 (Lovasz local lemma
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.Comment: In Proceedings AFL 2014, arXiv:1405.527