一句话：利用范畴框架研究输出在任意幺半群中的确定性转换器，给出其最小形式存在唯一条件，并导出基于成员与等价查询的主动学习算法。
本文研究 monoidal transducers，即边同时产生任意幺半群输出的确定性自动机，输出可以交换或抵消。核心问题是在这种广义输出下，如何定义识别语言的最小转换器，以及何时存在且唯一。方法上，作者采用 Colcombet、Petrişan 和 Stabile 的范畴最小化与学习框架，把最小转换器刻画为框架中的对象，并分析输出幺半群需满足的条件。关键结果包括：给出最小转换器存在且唯一（同构意义下）的充要条件；该范畴框架随即提供基于成员查询和等价查询的抽象主动学习算法；文中还讨论了实现该算法的实践问题。
We study monoidal transducers, transition systems arising as deterministic automata whose transitions also produce outputs in an arbitrary monoid, for instance allowing outputs to commute or to cancel out. We use the categorical framework for minimization and learning of Colcombet, Petrişan and Stabile to recover the notion of minimal transducer recognizing a language, and give necessary and sufficient conditions on the output monoid for this minimal transducer to exist and be unique (up to isomorphism). The categorical framework then provides an abstract algorithm for learning it using membership and equivalence queries, and we discuss practical aspects of this algorithm's implementation.
DOI 原文 · arXiv · PDF（开放获取） · DBLP
@article{abs-2410-01590,
title = {Active Learning of Deterministic Transducers with Outputs in Arbitrary Monoids},
author = {Quentin Aristote},
journal = {Logical Methods in Computer Science},
volume = {Volume 21, Issue 4},
year = {2025},
doi = {10.46298/lmcs-21(4:7)2025}
}