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Polishness of some topologies related to word or tree automata

Olivier Finkel ; Olivier Carton ; Dominique Lecomte.

We prove that the B\"uchi topology and the automatic topology are Polish. We also show that this cannot be fully extended to the case of a space of infinite labelled binary trees; in particular the B\"uchi and the Muller topologies are not Polish in this case.

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Continuity of Functional Transducers: A Profinite Study of Rational Functions

Michaël Cadilhac ; Olivier Carton ; Charles Paperman.

A word-to-word function is continuous for a class of languages~$\mathcal{V}$ if its inverse maps $\mathcal{V}$_languages to~$\mathcal{V}$. This notion provides a basis for an algebraic study of transducers, and was integral to the characterization of the sequential transducers computable in some&nbsp;[&hellip;]

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Transfinite Lyndon words

Olivier Carton ; Luc Boasson.

In this paper, we extend the notion of Lyndon word to transfinite words. We prove two main results. We first show that, given a transfinite word, there exists a unique factorization in Lyndon words that are densely non-increasing, a relaxation of the condition used in the case of finite words. In&nbsp;[&hellip;]

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