The emergence of intelligence in large language models (LLMs) has inspired investigations into their integration into automata learning. This paper introduces the probabilistic Minimally Adequate Teacher (pMAT) formulation, which leverages a probabilistic oracle that could give persistent errors randomly during answering the membership queries for deterministic finite automata (DFA) learning. Given the tendency of LLMs to produce hallucinatory content, we have developed techniques to improve answer accuracy and ensure the correctness of the learned automata. We propose the $\mathtt{Discrimination}$ prompt as well as the $\mathtt{Verification}$ prompt and explore their advantages over common prompts. Additionally, we compare DFA learning performance between the TTT algorithm and common active learning algorithms. To address the exponential number of persistent errors, we implement a dynamic query cache refinement algorithm that identifies and corrects conflicting queries by combining the active and passive learning algorithms. The empirical results demonstrate the robustness and efficiency of our approach, providing a theoretical foundation for automata learning with LLMs in the loop.

本研究针对大型语言模型在自动机学习中的应用空白，提出了一种概率最小充分教师(pMAT)的框架，利用概率性oracle逐步改进membership query的回答准确性。研究表明，借助特定的$\mathtt{Discrimination}$和$\mathtt{Verification}$提示及动态查询缓存优化算法，能够有效提高DFA学习的表现，从而为LLMs在自动机学习中的运用奠定理论基础。

将大型语言模型作为确定性有限自动机学习的随机最小充分教师