## Cadilhac, Michaël and Carton, Olivier and Paperman, Charles - Continuity of Functional Transducers: A Profinite Study of Rational Functions

lmcs:4336 - Logical Methods in Computer Science, February 21, 2020, Volume 16, Issue 1
Continuity of Functional Transducers: A Profinite Study of Rational Functions

Authors: Cadilhac, Michaël and Carton, Olivier and Paperman, Charles

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 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?

Volume: Volume 16, Issue 1
Published on: February 21, 2020
Submitted on: March 1, 2018
Keywords: Computer Science - Formal Languages and Automata Theory,Computer Science - Logic in Computer Science