Acta Informatica

, Volume 28, Issue 2, pp 179–186 | Cite as

On characterizations of recursively enumerable languages

  • Michel Latteux
  • Paavo Turakainen


Geffert has shown that earch recursively enumerable languageL overΣ can be expressed in the formL{h(x)−1g(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(L0)∩Σ* whereL0 is a minimal linear language and ρ is the Dyck reductionaā→ε, AĀ→ε.


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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Michel Latteux
    • 1
  • Paavo Turakainen
    • 2
  1. 1.CNRS, UA 369, Department of Computer ScienceUniversity of Lille Flandres ArtoisVilleneuve d'AscqFrance
  2. 2.Department of MathematicsUniversity of OuluOuluFinland

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