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Post correspondence problem: Words possible as primitive solutions

  • Automata and Formal Languages I
  • Conference paper
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Automata, Languages and Programming (ICALP 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 944))

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Abstract

Three types of “primitive” or “prime” solutions for PCP have earlier been investigated. The sets of words belonging to one of the three types (for some instance of PCP) form an increasing hierarchy. In our main result we show that the hierarchy is proper, except the binary case. We also give a sharpened characterization of the finite type.

Work supported by Project 11281 of the Academy of Finland

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References

  1. K. Culik II, “A Purely Homomorphic Characterization of Recursively Enumerable Sets”, J. Assoc. Comput. Mach. 26 (1979) 345–350.

    Google Scholar 

  2. K. Culik II and J. KarhumÄki, “On the Equality Sets for Homomorphisms on Free Monoids with Two Generators”, R.A.I.R.O. Informatique théorique 14 (1980) 349–369.

    Google Scholar 

  3. M. Harrison, Introduction to Formal Language Theory, Addison-Wesley (1978)

    Google Scholar 

  4. M. Lipponen, “Primitive Words and Languages Associated to PCP”, E.A.T.C.S. Bulletin 53 (1994) 217–226.

    Google Scholar 

  5. R.C. Lyndon and M.P. Schützenberger, “The Equation a M = b N c P in a Free Group”, Michigan Math. J. 9 (1962) 289–298.

    Google Scholar 

  6. A. Mateescu and A. Salomaa, “PCP-Prime Words and Primality Types”, R.A.I.R.O. Informatique théorique 27 (1993) 57–70.

    Google Scholar 

  7. A. Mateescu and A. Salomaa, “On simplest possible solutions for Post Correspondence Problems”, Acta Informatica 30 (1993) 441–457.

    Google Scholar 

  8. E. Post, “A variant of a recursively unsolvable problem”, Bulletin of the American Mathematical Society 53 (1946) 264–268.

    Google Scholar 

  9. G. Rozenberg and A. Salomaa, Cornerstones of Undecidability, Prentice Hall (1994).

    Google Scholar 

  10. A. Salomaa, K. Salomaa and Sheng Yu, “Primality types of instances of the Post Correspondence Problem”, E.A.T.C.S. Bulletin 44 (1991) 226–241.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Turku, 20500, Turku, Finland

    Marjo Lipponen

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  1. Marjo Lipponen
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Zoltán Fülöp Ferenc Gécseg

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© 1995 Springer-Verlag Berlin Heidelberg

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Lipponen, M. (1995). Post correspondence problem: Words possible as primitive solutions. In: Fülöp, Z., Gécseg, F. (eds) Automata, Languages and Programming. ICALP 1995. Lecture Notes in Computer Science, vol 944. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60084-1_63

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  • DOI: https://doi.org/10.1007/3-540-60084-1_63

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60084-8

  • Online ISBN: 978-3-540-49425-6

  • eBook Packages: Springer Book Archive

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