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Verallgemeinerte kommutative Sprachen

  • Ioannis Keklikoglou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 104)

Abstract

Using the binomial coefficients for words, introduced by S. Eilenberg [1], we define the generalized Parikh operator \(P_k :A* \to IN_O^{n + n^2 + ... + n^k }\) (k ε IN), where n≔# A (A is finite alphabet). A set L ⊑ A* is k-commutative iff p k −1 (pk (L))=L. Closure properties of the family Lk of k-commutative languages are investigated and the existence of a proper hierarchy in the class LFC of all finite commutative languages is proved. For this last result we study Thue-Morse sequences.

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Literatur

  1. [1]
    Eilenberg S., Automata,languages. Vol B, Akademic Press, New York, San Francisco, London 1976.Google Scholar
  2. [2]
    Greibach S., The hardest contextfree language. SIAM J.Computing 2 (1973)Google Scholar
  3. [3]
    Huynh T., On the complexity of semilinear sets. Research Report A79/16, University of Saarbrücken.Google Scholar
  4. [4]
    Kelikoglou I., Verallgemeinerte kommutative Sprachen, Dissertation, Darmstadt 1980.Google Scholar
  5. [5]
    Morse M., Hedlung G., Unending Chess,symbolic dynamics and a problem in semigroups. Duke Math. Journal 11 (1944)Google Scholar
  6. [6]
    Ochsenschläger P.,Verallgemeinerte Parikh-Abbildungen und DOL-Systeme. Technischer Bericht AFS-33,TH Darmstadt,FB Informatik, 1977.Google Scholar
  7. [7]
    Prodinger H., Erweiterung des freien Monoids Σ*, Dissertation, Wien 1978.Google Scholar
  8. [8]
    Thue A., Über die gegenseitige Lage gewisser Zeichenreihen. Videskap. Skrifter I Math.-Naturv.-Klasse 1912 No.1.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Ioannis Keklikoglou
    • 1
  1. 1.Fachbereich Informatik Technische Hochschule DarmstadtDarmstadtW. Germany

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