论文标题
为欧米茄常规语言的受体构建简洁的特征样本
Constructing Concise Characteristic Samples for Acceptors of Omega Regular Languages
论文作者
论文摘要
语言$ l $和学习算法$ \ textbf {l} $的特征样本是一个有限的单词样本$ t_l $由其成员标记为$ l $的$ t_l $，因此对于任何样本$ t \ supseteq t_l $ capecipt $ l $一致，在输入$ t $ t $ t $ t $ t $ t $ the $ t $ t $ the $ textbf $ l $ l $ l} $ l};哪个欧米茄自动机具有多项式大小的特征集，这些集合可以在多项式时间内构造吗？我们在这里解决这些问题。简而言之，任何常见类型的非确定性欧米茄自动机，尤其是Büchi，都不具有多项式大小的特征样本。对于确定性的欧米茄自动机，与其正确的一致性自动机是同构的，提供了充分信息的语言，用于构建特征样本的多项式时间算法并从中获得了学习。 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.
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.
