Complementation of Rational Sets on Scattered Linear Orderings of Finite Rank

  • Olivier Carton
  • Chloé Rispal
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2976)


In a preceding paper (Bruyère and Carton, automata on linear orderings, MFCS’01), automata have been introduced for words indexed by linear orderings. These automata are a generalization of automata for finite, infinite, bi-infinite and even transfinite words studied by Büchi. Kleene’s theorem has been generalized to these words. We show that deterministic automata do not have the same expressive power. Despite this negative result, we prove that rational sets of words of finite ranks are closed under complementation.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Olivier Carton
    • 1
  • Chloé Rispal
    • 2
  1. 1.LIAFAUniversité Paris 7Paris cedex 05France
  2. 2.IGMUniversité de Marne-la-ValléeMarne-la-Vallée Cedex 2France

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