A Homomorphic Representation of Simple Matrix Languages

In this paper we continue the investigation of simple matrix languages introduced by Ibarra (1970) as a subfamily of matrix languages. Simple matrix languages have many properties similar to those of context-free languages. In the following, we prove that every simple matrix language can be written as a homomorphic image of the intersection of the Dyck context-free language and an equal matrix language (Siromoney, 1969a). We obtain in this way a necessary condition for a language to be a simple matrix language. It is a generalization of the well-known similar result for context-free languages (Salomaa, 1973). This condition is not sufficient; hence we do not obtain a characterization of simple matrix languages as is obtained for context-free languages.