On characterizations of recursively enumerable languages (original) (raw)

Geffert has shown that each recursively enumerable language L over Z can be expressed in the form L={h(x)-ig(x)lx in A+}nZ * where A is an alphabet and g, h is a pair of morphisms. Our purpose is to give a simple proof for Geffert's result and then sharpen it into the form where both of the morphisms are nonerasing. In our method we modify constructions used in a representation of recursively enumerable languages in terms of equality sets and in a characterization of simple transducers in terms of morphisms. As direct consequences, we get the undecidability of the Post correspondence problem and various representations of L. For instance, L = p(Lo)n Z* where Lo is a minimal linear language and p is the Dyck reduction a~ ~ e, A,4 ~ e.