In this paper we study the ploblem whether the language D(1) of all d-primitive words can be generated by a contextual grammar. It is proved that D(1) can be generated neither by an external contextual grammar nor by an internal contextual grammar, and that it can be generated by a total contextual grammar with choice.

Let Q be the set of all primitive words over a finite alphabet having at least two letters. In this paper, we study the language D(1) of all non-overlapping (d-primitive) words, which is a proper subset of Q. We show that D(1) is a context-sensitive langauage but not a deterministic context-free language. Further it is shown that [D(1)]n is not regular for n ≥ 1.