Skip to main content
SpringerLink
Log in

On some variants of Post's Correspondence Problem

  • Published:
Acta Informatica Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  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. Claus, V.: Die Grenze zwischen Entscheidbarkeit und Nichtentscheidbarkeit. Fernstudienkurs für die Fernuniversität Hagen. Open University of Hagen, Hagen 1979

    Google Scholar 

  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 1980

    Google Scholar 

  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. 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 1983

  6. Greibach, S.: A remark on code sets and context-free languages. IEEE Trans. Comput. C-24, 741–742 (1975)

    Google Scholar 

  7. Harrison, M.: Introduction to Formal Language Theory. Reading, MA: Addison-Wesley 1978

    Google Scholar 

  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, 1976

  9. Karhumäki, J.: Generalized Parikh mappings and homomorphisms. Information Control 47, 155–165 (1980)

    Google Scholar 

  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. 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, 1963

  12. Pansiot, J.J.: A note on Post's Correspondence Problem. Information Processing Lett. 12, 233 (1981)

    Google Scholar 

  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. Salomaa, A.: Jewels of Formal Language Theory. Potomac: Computer Science Press 1981

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Tampere University of Technology, SF-33101, Tampere 10, Finland

    Keijo Ruohonen

Authors
  1. Keijo Ruohonen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ruohonen, K. On some variants of Post's Correspondence Problem. Acta Informatica 19, 357–367 (1983). https://doi.org/10.1007/BF00290732

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00290732

Keywords

Search

Navigation