Remarks on generalized Post Correspondence Problem

  • T. Harju
  • J. Karhumäki
  • D. Krob
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1046)

Abstract

It is shown that Post Correspondence Problem remains undecidable even in the case where one of the morphisms is fixed. Accordingly the generalized PCP is undecidable even in the case where both of the morphisms are fixed, and, moreover, the cardinality of their domain alphabet is 7. In particular, GPCP(7) is undecidable. On the other hand, GPCP(2) is not only decidable, but, as we show here, its all solutions can be effectively found.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    C. Choffrut and J. Karhumäki, Test sets for morphisms with bounded delay, Discrete Appl. Math. 12 (1985), 93–101.Google Scholar
  2. 2.
    V. Claus, Some remarks on PCP(k) and related problems, Bull. EATCS 12 (1980), 54–61.Google Scholar
  3. 3.
    K. Culik II and J. Karhumäki, On the equality sets for homomorphisms on free monoids with two generators, RAIRO Theoret. Informatics 14 (1980), 349–369.Google Scholar
  4. 4.
    A. Ehrenfeucht, J. Karhumäki and G. Rozenberg, The (generalized) Post Correspondence Problem with lists consisting of two words is decidable, Theoret. Comput. Sci. 21 (1982), 119–144.CrossRefGoogle Scholar
  5. 5.
    A. Ehrenfeucht, J. Karhumäki and G. Rozenberg, On binary equality languages and a solution to the test set conjecture in the binary case, J. Algebra 85 (1983), 76–85.CrossRefGoogle Scholar
  6. 6.
    S. Eilenberg, Automata, Languages, and Machines, Vol. A, Academic Press, New York, 1974.Google Scholar
  7. 7.
    M. Jantzen, “Confluent String Rewriting”, Springer-Verlag, 1988.Google Scholar
  8. 8.
    A.A. Markov, On the impossibility of certain algorithms in the theory of associative systems, Dokl. Acad. Nauk. 55 (1947), 353–356 (Russian).Google Scholar
  9. 9.
    J. Matijacevic, Simple examples of usolvable associative calculi, Dokl. Akad. Nauk 173 (1967), 1264–1266 (Russian).Google Scholar
  10. 10.
    J.J. Pansiot, A note on Post's Correspondence Problem, Inform. proc. Lett. 12 (1981), 233.CrossRefGoogle Scholar
  11. 11.
    V.A. Pavlenko, Post combinatorial problem with two pairs of words, Dokl. Akad. Nauk. Ukr. SSR (1981), 9–11.Google Scholar
  12. 12.
    E. Post, A variant of a recursively unsolvable problem, Bulletin of Amer. Math. Soc. 52 (1946), 264–268.Google Scholar
  13. 13.
    E. Post, Recursive unsolvability of a problem of Thue, J. Symb. Logic 12 (1947), 1–11.Google Scholar
  14. 14.
    K. Ruohonen, Reversible machines and Post's correspondence problem for biprefix morphisms, J. Inform. Process. Cybernet. EIK 21 (1985), 579–595.Google Scholar
  15. 15.
    G.C. Tzeitin, Associative calculus with an unsolvable equivalence problem, Tr. Mat. Inst. Akad. Nauk 52 (1958), 172–189 (Russian).Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • T. Harju
    • 1
  • J. Karhumäki
    • 1
  • D. Krob
    • 2
  1. 1.Department of MathematicsUniversity of TurkuTurkuFinland
  2. 2.Institute Blaise Pascal (LITP), CNRSUniversite Paris VIIParisFrance

Personalised recommendations