On the cardinality of sets of infinite trees recognizable by finite automata

  • Damian Niwiński
Part of the Lecture Notes in Computer Science book series (LNCS, volume 520)


We show that a Rabin recognizable set of trees is uncountable iff it is of the cardinality continuum iff it contains a non-regular tree. If a Rabin recognizable set L is countable, it can be represented as
$$L = M\left[ {{{t_1 } \mathord{\left/{\vphantom {{t_1 } {x_1 , \ldots ,{{t_n } \mathord{\left/{\vphantom {{t_n } {x_n }}} \right.\kern-\nulldelimiterspace} {x_n }}}}} \right.\kern-\nulldelimiterspace} {x_1 , \ldots ,{{t_n } \mathord{\left/{\vphantom {{t_n } {x_n }}} \right.\kern-\nulldelimiterspace} {x_n }}}}} \right]$$
where M is a regular set of finite terms and t1, ..., t n are regular trees. We also design an algorithm which, given a Rabin automaton A, computes the cardinality of the set of trees recognized by A.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Damian Niwiński
    • 1
  1. 1.Institute of MathematicsUniversity of WarsawWarszawa 59Poland

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