Summary
Geffert has shown that earch recursively enumerable languageL overΣ can be expressed in the formL{h(x) −1 g(x)∣x inΔ +}∩Σ * whereΔ is an alphabet andg, 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 ofL. For instance,L =ρ(L 0)∩Σ * whereL 0 is a minimal linear language and ρ is the Dyck reductionaā→ε, AĀ→ε.
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Latteux, M., Turakainen, P. On characterizations of recursively enumerable languages. Acta Informatica 28, 179–186 (1990). https://doi.org/10.1007/BF01237236
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DOI: https://doi.org/10.1007/BF01237236