Infinite labeled trees: From rational to Sturmian trees

Nicolas Gast 1, 2 Bruno Gaujal 1, 2
1 MESCAL - Middleware efficiently scalable
Inria Grenoble - Rhône-Alpes, LIG - Laboratoire d'Informatique de Grenoble
Abstract : This paper studies infinite unordered d-ary trees with nodes labeled by {0, 1}. We introduce the notions of rational and Sturmian trees along with the definitions of (strongly) balanced trees and mechanical trees, and study the relations among them. In particular, we show that (strongly) balanced trees exist and coincide with mechanical trees in the irrational case, providing an effective construction. Such trees also have a minimal factor complexity, hence are Sturmian. We also give several examples illustrating the inclusion relations between these classes of trees.
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Nicolas Gast, Bruno Gaujal. Infinite labeled trees: From rational to Sturmian trees. Theoretical Computer Science, Elsevier, 2010, 411, pp.1146 - 1166. ⟨10.1016/j.tcs.2009.12.009⟩. ⟨hal-01086034⟩

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