The solution of two star-height problems for regular trees

  • J. P. Braquelaire
  • B. Courcelle
Part III Automata On Infinite Trees
Part of the Lecture Notes in Computer Science book series (LNCS, volume 192)


Regular trees can be defined by two types of rational expressions, For these two types we solve the star-height problem i.e. we show how to construct a rational expression of minimal star-height from the minimal graph of the given tree (i.e. the analogous of the minimal deterministic automaton for regular langages). In one case, the minimal star-height is the rank (in the sense of Eggan) of the minimal graph. There corresponds a caracterization of the star-height of a prefix-free regular langage w.r.t rational expressions of a special kind (called determinstic) as the rank of its minimal deterministic automaton considered as a graph.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • J. P. Braquelaire
    • 1
  • B. Courcelle
    • 1
  1. 1.U.E.R. of Mathematics and InformaticUniversity of Bordeaux ITalence

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