Breadth-First Serialisation of Trees and Rational Languages
We present here the notion of breadth-first signature of trees and of prefix-closed languages; and its relationship with numeration system theory. A signature is the serialisation into an infinite word of an ordered infinite tree of finite degree. Using a known construction from numeration system theory, we prove that the signature of (prefix-closed) rational languages are substitutive words and conversely that a special subclass of substitutive words define (prefix-closed) rational languages.
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