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Continuity of functional transducers: a profinite study of rational functions

Michaël Cadilhac 1 Olivier Carton 2 Charles Paperman 3
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CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189, Inria Lille - Nord Europe
Abstract : A word-to-word function is continuous for a class of languages V if its inverse maps V-languages to 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 circuit complexity classes. Here, we report on the decidability of continuity for functional transducers and some standard classes of regular languages. To this end, we develop a robust theory rooted in the standard profinite analysis of regular languages. Since previous algebraic studies of transducers have focused on the sole structure of the underlying input automaton, we also compare the two algebraic approaches. We focus on two questions: When are the automaton structure and the continuity properties related, and when does continuity propagate to superclasses?
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Submitted on : Friday, January 15, 2021 - 3:07:49 PM
Last modification on : Thursday, April 7, 2022 - 1:58:23 PM
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Michaël Cadilhac, Olivier Carton, Charles Paperman. Continuity of functional transducers: a profinite study of rational functions. Logical Methods in Computer Science, Logical Methods in Computer Science Association, 2020, ⟨10.23638/LMCS-16(1:24)2020⟩. ⟨hal-03111682⟩



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