标题： 被动学习事件记录自动机 显示英文标题

标题： Learning Event-recording Automata Passively

摘要： 本文提出了一种状态合并算法，用于通过正负样本（以符号时间词的形式）学习由事件记录自动机（ERA）定义的定时语言。 我们的算法LEAP（被动学习事件记录自动机）基于合并技术，从这些样本中构建一个可能非确定性的 ERA。 我们证明了在保持样本一致性的同时，确定两个 ERA 状态是否可以合并是一个 NP 完全问题，并通过一种实用的 SMT 基于解决方案来解决这个问题。 我们的实现通过示例展示了该算法的有效性。 我们还表明，使用合适的样本，可以使用我们的算法推断出每个 ERA 定义的语言。 显示英文摘要

摘要： This paper presents a state-merging algorithm for learning timed languages definable by Event-Recording Automata (ERA) using positive and negative samples in the form of symbolic timed words. Our algorithm, LEAP (Learning Event-recording Automata Passively), constructs a possibly nondeterministic ERA from such samples based on merging techniques. We prove that determining whether two ERA states can be merged while preserving sample consistency is an NP-complete problem, and address this with a practical SMT-based solution. Our implementation demonstrates the algorithm's effectiveness through examples. We also show that every ERA-definable language can be inferred using our algorithm with a suitable sample.