一句话：证明非确定性 ω-自动机无多项式规模特征样本，并为完全信息化的确定性 ω-自动机给出多项式时间构造与学习算法。
本文研究 ω-正则语言的接受器是否存在多项式规模的特征样本，以及能否在多项式时间内构造。特征样本 T_L 保证任何包含它的、与 L 一致的样本都会使学习算法输出等价于 L 的假设。作者首先证明常见非确定性 ω-自动机（尤其是 Büchi 自动机）不存在多项式规模的特征样本。随后，对于与其右同余自动机同构的确定性 ω-自动机，即完全信息化语言，给出多项式时间构造特征样本并从中学习的算法。针对 Büchi、coBüchi、parity、Rabin、Streett 和 Muller 等类型，构造特征集还需各自自动机的等价性判定和语言是否属于信息化类的成员测试，作者提供了这些确定性多项式时间算法。
A characteristic sample for a language $L$ and a learning algorithm $\textbf{L}$ is a finite sample of words $T_L$ labeled by their membership in $L$ such that for any sample $T \supseteq T_L$ consistent with $L$, on input $T$ the learning algorithm $\textbf{L}$ returns a hypothesis equivalent to $L$. Which omega automata have characteristic sets of polynomial size, and can these sets be constructed in polynomial time? We address these questions here. In brief, non-deterministic omega automata of any of the common types, in particular B\"uchi, do not have characteristic samples of polynomial size. For deterministic omega automata that are isomorphic to their right congruence automata, the fully informative languages, polynomial time algorithms for constructing characteristic samples and learning from them are given. The algorithms for constructing characteristic sets in polynomial time for the different omega automata (of types B\"uchi, coB\"uchi, parity, Rabin, Street, or Muller), require deterministic polynomial time algorithms for (1) equivalence of the respective omega automata, and (2) testing membership of the language of the automaton in the informative classes, which we provide.
@article{paperbot2712,
title = {Constructing Concise Characteristic Samples for Acceptors of Omega Regular Languages},
author = {Dana Angluin and Dana Fisman},
journal = {Logical Methods in Computer Science},
volume = {Volume 20, Issue 4},
year = {2024},
doi = {10.46298/lmcs-20(4:10)2024}
}