Verallgemeinerte kommutative Sprachen

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


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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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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