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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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Locality and Centrality: The Variety ZG

Antoine Amarilli ; Charles Paperman.

We study the variety ZG of monoids where the elements that belong to a group are central, i.e., commute with all other elements. We show that ZG is local, that is, the semidirect product ZG * D of ZG by definite semigroups is equal to LZG, the variety of semigroups where all local monoids are in ZG.&nbsp;[&hellip;]

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