In this paper, we propose a novel algorithm to learn a Büchi automaton from a teacher who knows an ω-regular language. The learned Büchi automaton can be a nondeterministic Büchi automaton or a limit deterministic Büchi automaton. The learning algorithm is based on learning a formalism called family of DFAs (FDFAs) recently proposed by Angluin and Fisman. The main catch is that we use a classification tree structure instead of the standard observation table structure. The worst case storage space required by our algorithm is quadratically better than that required by the table-based algorithm proposed by Angluin and Fisman. We implement the proposed learning algorithms in the learning library ROLL (Regular Omega Language Learning), which also consists of other complete ω-regular learning algorithms available in the literature. Experimental results show that our tree-based learning algorithms have the best performance among others regarding the number of solved learning tasks.

在本文中，我们提出了一种新的算法来从知道ω正则语言的老师那里学习 Büchi 自动机。学习到的 Büchi 自动机可以是非确定性 Büchi 自动机或极限确定性 Büchi 自动机。该学习算法基于学习最近由 Angluin 和 Fisman 提出的称为DFA 族(FDFA) 的形式体系。主要问题是我们使用分类树结构而不是标准的观察表结构。我们的算法所需的最坏情况存储空间比 Angluin 和 Fisman 提出的基于表的算法所需的存储空间要好二次方。我们在学习库ROLL 中实现了建议的学习算法（Regular Omega Language Learning），其中还包含文献中可用的其他完整的ω -regular 学习算法。实验结果表明，我们的基于树的学习算法在解决的学习任务数量方面具有最佳性能。