The Ehrenfeucht-Mycielski sequence

Abstract

We study the disjunctive binary sequence introduced by Ehrenfeucht and Mycielski in [1]. The match length associated to the bits of the sequence is shown to be a crucial tool in the analysis of the sequence. We show that the match length between two consecutive bits in the sequence differs at most by 1 and give a lower bound for the limiting density of the sequence. Experimental computation in the automata package has been very helpful in developing these results. © Springer-Verlag Berlin Heidelberg 2003.