一句话：研究函数性转换器相对于正则语言类的连续性判定，建立 profinite 代数理论并比较两种代数方法。
论文研究函数性转换器的连续性问题：若一个词到词的函数的逆映射把语言类 V 中的语言仍映回 V，则称其关于 V 连续。该概念为转换器的代数研究提供基础，并曾用于刻画可在某些电路复杂度类中计算的序列转换器。作者针对函数性转换器以及若干标准正则语言类，报告连续性判定问题的可判定性；为此，基于正则语言的标准 profinite 分析发展了一套稳健理论。与以往仅关注底层输入自动机结构的转换器代数研究不同，论文还比较了两种代数路径，并聚焦两个问题：自动机结构与连续性性质何时相关，以及连续性何时传播到超类。
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?
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@article{CadilhacCP19,
title = {Continuity of Functional Transducers: A Profinite Study of Rational Functions},
author = {Michaël Cadilhac and Olivier Carton and Charles Paperman},
journal = {Logical Methods in Computer Science},
volume = {Volume 16, Issue 1},
year = {2020},
doi = {10.23638/lmcs-16(1:24)2020}
}