## On characterizations of recursively enumerable languages.(English)Zbl 0686.68060

V. Geffert [Theor. Comput. Sci. 62, 235-249 (1988; Zbl 0664.68075)] has shown that each recursively enumerable language L over $$\Sigma$$ can be expressed in the form $$L=\{h(x)^{-1}g(x)|$$ x in $$\Delta^+\}\cap \Sigma^*$$ where $$\Delta$$ 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, $$L=\rho (L_ 0)\cap \Sigma^*$$ where $$L_ 0$$ is a minimal linear language and $$\rho$$ is the Dyck reduction $$a\bar a\to \epsilon$$, $$A\bar A\to \epsilon$$.
Reviewer: M.Latteux

### MSC:

 68Q45 Formal languages and automata

### Keywords:

morphism; grammar; recursively enumerable language

Zbl 0664.68075
Full Text:

### References:

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