Equality sets of binary D0L sequences

We study D0L sequences over a binary alphabet. If s=(s(n))n≥0 and t=(t(n))n≥0 are D0L sequences, their equality set E(s,t) is defined by E(s,t)={n≥0|s(n)=t(n)}. We show that if s and t are D0L sequences over a binary alphabet then their equality set E(s,t) is eventually periodic.