Abstract
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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© 1985 Springer-Verlag Berlin Heidelberg
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Braquelaire, J.P., Courcelle, B. (1985). The solution of two star-height problems for regular trees. In: Nivat, M., Perrin, D. (eds) Automata on Infinite Words. LITP 1984. Lecture Notes in Computer Science, vol 192. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-15641-0_28
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DOI: https://doi.org/10.1007/3-540-15641-0_28
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