About the effect of the number of successful paths in an infinite tree on the recognizability by a finite automaton with Buchi conditions

  • D. Beauquier
  • M. Nivat
  • D. Niwiński
Part of the Lecture Notes in Computer Science book series (LNCS, volume 529)


We modify an acceptance condition of Büchi automaton on infinite trees: rather than to require that each computation path is successful, we impose various restrictions on the number of successful paths in a run of the automaton on a tree. All these modifications alter the recognizing power of Büchi automata. We examine the classes induced by the acceptance conditions that require ≤α, ≥α, =α successful paths, where α is a cardinal number. It turns out that, except some trivial cases, the “≤” classes are uncomparable with the class of Büchi acceptable tree languages, while the classes “≥” are strictly included in .


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • D. Beauquier
    • 1
  • M. Nivat
    • 1
  • D. Niwiński
    • 2
  1. 1.LITP-IBP 4 PLace JussieuParis Cedex 05France
  2. 2.Institute of MathematicsUniversity of WarsawWarszawa 59Poland

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