Vertical representation of $C^{\infty }$-words

Abstract

We present a new framework for dealing with $C^{\infty }$-words, based on their left and right frontiers. This allows us to give a compact representation of them, and to describe the set of $C^{\infty }$-words through an infinite directed acyclic graph $G$. This graph is defined by a map acting on the frontiers of $C^{\infty }$-words. We show that this map can be defined recursively and with no explicit references to $C^{\infty }$-words. We then show that some important conjectures on $C^{\infty }$-words follow from analogous statements on the structure of the graph $G$.

arXiv commentPublished in Theoretical Computer Science

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• Automata and Differentiable Words

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• Automata and Differentiable Words