A morphism g from the free monoid X* into itself is called upper triangular if the matrix of g is upper triangular. We characterize all upper triangular binary morphisms g1 and g2 such that g1g2 = g2g1.

We generalize the Skolem–Mahler–Lech theorem for rational power series in several noncommuting variables having a slender support. This generalization gives a connection between the Skolem–Mahler–Lech theorem and the characterization of slender regular languages proved independently by Păun and Salomaa and by Shallit.

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 | s(n) = t(n)}. It is an open problem whether such equality sets are always eventually periodic. Using methods developed by Ehrenfeucht and Rozenbe rg 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.

We characterize regular languages as the equality sets of sequences generated by compatible uniform HDT0L systems.

We study the DT0L sequence equivalence problem for marked morphisms. We show that to decide this problem it is enough to consider initial terms involving at most 2n morphisms where n is the cardinality of the underlying alphabet.

We show that it is decidable whether or not a given D0L power series and a given DF0L power series over a computable field are equal. This generalizes to power series the result of Ruohonen stating that DF0L-D0L language equivalence is decidable.

We study a power series generalization of DTOL systems with main interest on decidability questions.

We study ETOL power series introduced by Kuich. We show that the ETOL power series coincide with the linear extended Lindenmayerian series introduced by Honkala.