Automata on infinite trees with counting constraints

  • Danièle Beauquier
  • Damian Niwiński
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 668)


We investigate finite automata on infinite trees with the usual Muller criterion for the success of an infinite computation path, but with the acceptance paradigm modified in that not all the computation paths need to be successful. Instead, it is required that the number of successful paths must belong to a specified set of cardinals Γ. We show that Muller automata with the acceptance constraint of the form “there are at least γ accepting paths” can be always simulated by tree automata with a weaker criterion for successful paths, namely Büchi acceptance condition. We also show that this is the most general class of constraints for which a simulation by Büchi automata is always possible. Next, we characterize the maximal class of constraints which can be simulated by classical Muller automata (known to be more powerful than Büchi automata). The condition requiered of the set Γ there, is that the intersection with natural numbers forms a recognizable set. Finally, we exhibit a set of trees which is recognized by a classical Büchi automaton but fails to be recognized by any Muller automaton with a non trivial cardinality constraint (i.e., except for Γ = 0).


Finite Automaton Cardinal Number Computation Path Acceptance Condition Cardinality Constraint 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Danièle Beauquier
    • 1
  • Damian Niwiński
    • 2
  1. 1.LITP-IBPParis Cedex 05France
  2. 2.Institute of InformaticsUniversity of WarsawWarszawaPoland

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