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Acta Informatica

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

On characterizations of recursively enumerable languages

  • Michel Latteux
  • Paavo Turakainen
Article

Summary

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.

Keywords

Information System Direct Consequence Operating System Data Structure Communication Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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