ALMA：使用模2多重性自动机的自动机学习器
ALMA: Automata Learner using Modulo 2 Multiplicity Automata
AI总结：
本文提出Java工具ALMA，利用模2多重性自动机及成员查询与等价查询，实现对有限词和无限词正则语言自动机的多项式时间学习，并支持强无歧义Büchi自动机学习与自动机最小化。
摘要：
我们提出ALMA（使用模2多重性自动机的自动机学习器），这是一个基于Java的工具，能够学习任何接受有限词或无限词正则语言且具有可实现成员查询函数的自动机。用户既可以传入自己的成员查询函数作为输入，也可以使用为模2多重性自动机和非确定性Büchi自动机预定义的成员查询函数。在学习过程中，ALMA可以在每次等价查询后输出观察表的状态；在终止时，它可以输出所学模2多重性自动机的维度、转移矩阵和最终向量。用户可以通过对所学自动机执行成员查询来测试一个词是否被接受。ALMA遵循Beimel等人（Learning functions represented as multiplicity automata. J. ACM 47(3), 2000）的多项式时间学习算法，该算法使用成员查询和等价查询，并用模2多重性自动机表示假设。ALMA还实现了Angluin等人（Strongly unambiguous Büchi automata are polynomially predictable with membership queries. CSL 2020）针对强无歧义Büchi自动机的多项式时间学习算法，以及Sakarovitch（Elements of Automata Theory. 2009）针对模2多重性自动机的最小化算法。
英文摘要：
We present ALMA (Automata Learner using modulo 2 Multiplicity Automata), a Java-based tool that can learn any automaton accepting regular languages of finite or infinite words with an implementable membership query function. Users can either pass as input their own membership query function, or use the predefined membership query functions for modulo 2 multiplicity automata and non-deterministic Büchi automata. While learning, ALMA can output the state of the observation table after every equivalence query, and upon termination, it can output the dimension, transition matrices, and final vector of the learned modulo 2 multiplicity automaton. Users can test whether a word is accepted by performing a membership query on the learned automaton. ALMA follows the polynomial-time learning algorithm of Beimel et. al. (Learning functions represented as multiplicity automata. J. ACM 47(3), 2000), which uses membership and equivalence queries and represents hypotheses using modulo 2 multiplicity automata. ALMA also implements a polynomial-time learning algorithm for strongly unambiguous Büchi automata by Angluin et. al. (Strongly unambiguous Büchi automata are polynomially predictable with membership queries. CSL 2020), and a minimization algorithm for modulo 2 multiplicity automata by Sakarovitch (Elements of Automata Theory. 2009).
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