Recognizable infinite tree sets and their complexity

  • A. Saoudi
  • D. E. Muller
  • P. E. Schupp
Automata And Formal Languages
Part of the Lecture Notes in Computer Science book series (LNCS, volume 472)


In this paper we consider the extension of Nerode theorem to infinite trees. Unfortunately, we prove that this extension is not possible. We give some characterisations of Recognizable and Rational ω-tree sets in terms of ω-tree automata. We consider some complexity measures of Recognizable and Rational ω-tree sets and prove that these measures define infinite hierarchies.


Tree automata Büchi automata Muller automata and Rabin automata 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • A. Saoudi
    • 1
  • D. E. Muller
    • 2
  • P. E. Schupp
    • 2
  1. 1.L.I.T.P.Univ. Paris VIIParisFrance
  2. 2.Department of MathematicsUniv. of Illinois at Urbana-ChampaignUrbanaU.S.A.

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