Breadth-first serialisation of trees and rational languages

TL;DR

This paper introduces the concept of breadth-first signature for infinite trees, linking it to numeration systems, and demonstrates that signatures of rational languages are substitutive sequences.

Contribution

It establishes a novel connection between tree serialisation, numeration systems, and rational language signatures, showing they are substitutive sequences.

Findings

Signatures of rational languages are substitutive sequences.

The notion of breadth-first signature relates infinite trees to numeration system theory.

A new framework for understanding language classes via tree serialisation.

Abstract

We present here the notion of breadth-first signature and its relationship with numeration system theory. It is the serialisation into an infinite word of an ordered infinite tree of finite degree. We study which class of languages corresponds to which class of words and,more specifically, using a known construction from numeration system theory, we prove that the signature of rational languages are substitutive sequences.