为Omega正则语言的接受机构建简洁的特征样本
Constructing Concise Characteristic Samples for Acceptors of Omega Regular Languages
AI总结：
本文研究omega正则语言接受机的特征样本构造问题，指出非确定性omega自动机（如Büchi）不存在多项式大小的特征样本，而为完全信息类的确定性omega自动机提供了多项式时间构造与学习算法。
摘要：
对于语言$L$和学习算法$L$，特征样本是一个由根据其在$L$中的成员关系标记的有限单词样本$T_L$，使得对于任何与$L$一致且包含$T_L$的样本$T$，学习算法$L$在输入$T$时返回一个与$L$等价的假设。哪些omega自动机具有多项式大小的特征集，并且这些集合能否在多项式时间内构造？我们在此解决这些问题。简而言之，任何常见类型的非确定性omega自动机，特别是Büchi自动机，都不具有多项式大小的特征样本。对于与其右同余自动机同构的确定性omega自动机，即完全信息语言，我们给出了在多项式时间内构造特征样本并从中学习的算法。针对不同类型（Büchi、coBüchi、parity、Rabin、Street或Muller）的omega自动机在多项式时间内构造特征集的算法，要求具备以下两点的确定性多项式时间算法：(1) 相应omega自动机的等价性，以及 (2) 测试自动机语言是否属于信息类，这些我们都已提供。
英文摘要：
A characteristic sample for a language $L$ and a learning algorithm $\textbf{L}$ is a finite sample of words $T_L$ labeled by their membership in $L$ such that for any sample $T \supseteq T_L$ consistent with $L$, on input $T$ the learning algorithm $\textbf{L}$ returns a hypothesis equivalent to $L$. Which omega automata have characteristic sets of polynomial size, and can these sets be constructed in polynomial time? We address these questions here. In brief, non-deterministic omega automata of any of the common types, in particular Büchi, do not have characteristic samples of polynomial size. For deterministic omega automata that are isomorphic to their right congruence automata, the fully informative languages, polynomial time algorithms for constructing characteristic samples and learning from them are given. The algorithms for constructing characteristic sets in polynomial time for the different omega automata (of types Büchi, coBüchi, parity, Rabin, Street, or Muller), require deterministic polynomial time algorithms for (1) equivalence of the respective omega automata, and (2) testing membership of the language of the automaton in the informative classes, which we provide.
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