发表机构
Key Laboratory of System Software (Chinese Academy of Sciences); Institute of Software, Chinese Academy of Sciences; School of Computer Science and Informatics, University of Liverpool（系统软件重点实验室（中国科学院）; 中国科学院软件研究所; 利物浦大学计算机科学与信息学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对有序数据域上的确定性寄存器自动机，构建统一主动学习框架，实现多项式时间学习，证明整数域上该类自动机最小化可判定，并改进相关判定问题的复杂度界。
AI 中文摘要
寄存器自动机是配备了内存的有限自动机，可识别无限字母表上的数据语言。在本研究中，我们针对有序数据域（涵盖有理数这类稠密域以及整数这类非稠密域）上的确定性寄存器自动机（DRA），探究主动学习算法。我们表明，稠密和非稠密有序域上DRA的主动学习问题可在单一统一框架内处理。更具体地说，我们利用成员查询、等价查询和可记忆性查询的预言，开发并实现了有序域上DRA的多项式时间主动学习过程。可记忆性查询最初是为学习具有恒等测试域上的DRA而引入的。我们的统一框架还带来一个新结果：整数这类非稠密有序域上DRA的最小化是可判定的，扩展了之前仅针对稠密域的已知结果。最后，我们给出了与主动学习所用查询密切相关的有序域上DRA的若干判定问题的改进复杂度界。
英文摘要
Register automata are finite automata equipped with memory that recognize data languages over infinite alphabets. In this work, we investigate active learning algorithms for deterministic register automata (DRAs) over ordered data domains--covering both dense domains, such as the rationals, and non-dense domains such as the integers. We show that the active learning problem for DRAs over both dense and non-dense ordered domains can be treated within a single unified framework. More specifically, we develop and implement a polynomial-time active learning procedure for DRAs over ordered domains, using oracles for membership, equivalence and memorability queries. The memorability queries were originally introduced for learning DRAs over domains with identity tests. Our unified framework also leads to a new consequence: minimization of DRAs over the non-dense ordered domain of integers is decidable, extending a result previously known only for dense domains. Finally, we give improved complexity bounds of several decision problems for DRAs over ordered domains that are closely related to the queries used in active learning.
