Super-state automata and rational trees

  • Frédérique Bassino
  • Marie -Pierre Béal
  • Dominique Perrin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1380)


We introduce the notion of super-state automata constructed from other automata. This construction is used to solve an open question about enumerative sequences in rational trees. We prove that any IN-rational sequence s=(s n)n≥0 of nonnegative integers satisfying the Kraft inequality σn≥0 s n k n ≤1 is the enumerative sequence of leaves by height of a k-ary rational tree. This result had been conjectured and was known only in the case of strict inequality. We also give a new proof of a result about enumerative sequences of nodes in k-ary rational trees.


Rational Tree Adjacency Matrix Finite Automaton Outgoing Edge Rational Sequence 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Frédérique Bassino
    • 1
  • Marie -Pierre Béal
    • 2
  • Dominique Perrin
    • 1
  1. 1.Institut Gaspard MongeUniversité de Marne-la-ValléeNoisy le Grand CedexFrance
  2. 2.Institut Gaspard MongeUniversité Paris 7France

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