Parikh Mapping and Iteration

  • Jürgen Dassow
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2235)


The Parikh mapping maps each word over an alphabet with n letters to an n-dimensional vector whose components give the number of occurrences of the letters in the word.We consider the Parikh images of sequences and languages obtained by iterated applications of morphisms (or sets of substitutions). Furthermore we modify the Parikh mapping such that it can be iterated and study the corresponding sequences.


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  1. 1.
    D. König, Theorie der endlichen und unendlichen Graphen. Chelsea, New York, 1959.Google Scholar
  2. 2.
    J. Dassow, On Parikh-languages of L systems without interaction. Rostock. Math. Colloq. 15 (1980) 103–110.MATHMathSciNetGoogle Scholar
  3. 3.
    J. Dassow, S. Marcus and Gh. Păun, Iterative reading of numbers and “black holes”. Periodica Math. Hungarica 27 (1993) 137–152.MATHCrossRefGoogle Scholar
  4. 4.
    J. Dassow, S. Marcus and Gh. Păun, Iterative reading of numbers: the ordered case. In: G. Rozenberg and A. Salomaa, Developments in Language Theory, World Scientific, Singapore, 1994, 157–168.Google Scholar
  5. 5.
    S. Ginsburg, The Mathematical Theory of Context-Free Languages. McGrw Hill Book Co., New York, 1966.Google Scholar
  6. 6.
    S. Ginsburg and E.H. Spanier, Bounded ALGOL-like languages. ???Google Scholar
  7. 7.
    E.M. Gurari and O.H. Ibarra, The complexity of the equivalence problem for counter languages, semilinear sets, and simple programs. In: Conference Record Tenth Annual ACM Symposium Theory of Computing, Atlanta, 1979, 142–152.Google Scholar
  8. 8.
    G.T. Herman and G. Rozenberg, Developmental Systems and Languages, North-Holland, 1974.Google Scholar
  9. 9.
    M. Nielsen, On the decidability of some equivalence problems for D0L systems. Inform. Control 25 (1974) 166–193.CrossRefMATHGoogle Scholar
  10. 10.
    R.J. Parikh, On context-free languages.Journal of the ACM 13 (1966) 570–581.MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    G. Rozenberg and A. Salomaa, The Mathematical Theory of L Systems. Academic Press, 1980.Google Scholar
  12. 12.
    A. Salomaa, Formal Languages. Academic Press, 1973.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Jürgen Dassow
    • 1
  1. 1.Fakultät für InformatikOtto-von-Guericke-Universität MagdeburgMagdeburg

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