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Continuity of Functional Transducers: A Profinite Study of Rational Functions
2018
Logical Methods in Computer Science
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
doi:10.23638/lmcs-16(1:24)2020
fatcat:d7juean75ba2dmiumaeigiu7k4