Rational omega-Transductions

The rational ω-transductions (defined by F. Gire as bimorphisms) are particular transductions for infinite words. In this paper we give characterizations of these transductions. On the one hand they coincide with the compositions of non erasing and inverse non erasing morphisms, and only three morphisms are necessary. On the other hand they can be defined from bifaithful rational transductions using a limit operation we call adherence.

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