DOL Sequences and their Equality Sets

摘要

We study D0L sequences and their equality sets. If s = (s(n))(n >= 0) and t = (t (n))(n >= 0) are D0L sequences, their equality set is defined by E (s; t) = {n >= 0 vertical bar s (n) = t (n) }. It is an open problem whether such equality sets are always eventually periodic. Using methods developed by Ehrenfeucht and Rozenberg we show that a D0L equality set is eventually periodic if it contains at least one infinite arithmetic progression. As a main tool we use elementary morphisms introduced by Ehrenfeucht and Rozenberg.