Acta Informatica

, Volume 19, Issue 4, pp 357–367 | Cite as

On some variants of Post's Correspondence Problem

  • Keijo Ruohonen
Article

Summary

A variant of Post's Correspondence Problem is considered where two different index words are allowed provided that one of them can be obtained from the other by permuting a fixed number of subwords. It is shown that this variant is undecidable. Post's Correspondence Problem is also extended to circular words, doubly infinite words and doubly infinite powers of words, and shown to be undecidable in all these extensions.

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References

  1. 1.
    Brandstadt, A.: Closure properties of certain families of formal languages with respect to a generalization of cyclic closure. R.A.I.R.O. Informatique théorique 15, 233–252 (1981)Google Scholar
  2. 2.
    Claus, V.: Die Grenze zwischen Entscheidbarkeit und Nichtentscheidbarkeit. Fernstudienkurs für die Fernuniversität Hagen. Open University of Hagen, Hagen 1979Google Scholar
  3. 3.
    Čulik II, K.: Homomorphisms: Decidability, equality and test sets. In: Formal Language Theory. Perspectives and Open Problems. Book, R.V. (ed.), pp. 167–194. New York: Academic Press 1980Google Scholar
  4. 4.
    Ehrenfeucht, A., Karhumäki, J., Rozenberg, G.: The (generalized) Post correspondence problem with lists consisting of two words is decidable. Theoret. Comput. Sci. 21, 119–144 (1982)Google Scholar
  5. 5.
    Ehrenfeucht, A., Rozenberg, G., Ruohonen, K.: Structurally restricted maximal solutions of language equations involving morphisms. Report 42. Tampere University of Technology, Department of Electrical Engineering, Mathematics, Tampere 1983Google Scholar
  6. 6.
    Greibach, S.: A remark on code sets and context-free languages. IEEE Trans. Comput. C-24, 741–742 (1975)Google Scholar
  7. 7.
    Harrison, M.: Introduction to Formal Language Theory. Reading, MA: Addison-Wesley 1978Google Scholar
  8. 8.
    Ibarra, O., Kim, C.: A useful device for showing the solvability of some decision problems. Proc. 8th Ann. Symp. on Theory of Computing, pp. 135–140, 1976Google Scholar
  9. 9.
    Karhumäki, J.: Generalized Parikh mappings and homomorphisms. Information Control 47, 155–165 (1980)Google Scholar
  10. 10.
    Lecerf, Y.: Récursive insolubilité de l'équation générale de diagonalisation de deux monomorphismes de monoïdes libres φx = ψx. Comptes Rendus 257, 2940–2943 (1963)Google Scholar
  11. 11.
    Lecerf, Y.: Machines de Turing réversibles. Récursive insolubilité en nεN de l'équation u = θ n u, oú θ est un “isomorphisme de codes”. Ibid., pp. 2597–2600, 1963Google Scholar
  12. 12.
    Pansiot, J.J.: A note on Post's Correspondence Problem. Information Processing Lett. 12, 233 (1981)Google Scholar
  13. 13.
    Pavlenko, V.A.: The combinatorial problem of Post with two word pairs (In Russian). Dokl. Akad. Nauk Ukr. SSR, Ser. A, 7, 9–11 (1981)Google Scholar
  14. 14.
    Salomaa, A.: Jewels of Formal Language Theory. Potomac: Computer Science Press 1981Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Keijo Ruohonen
    • 1
  1. 1.Institute of MathematicsTampere University of TechnologyTampere 10Finland

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