论文标题
完全可及的自动机，原始组和一组同步单词的状态复杂性
Completely Reachable Automata, Primitive Groups and the State Complexity of the Set of Synchronizing Words
论文作者
论文摘要
我们给出了与完全可达到的自动机概念相关的原始排列组的新表征。此外，我们介绍了与某些相关自动机的一组同步单词的状态复杂性相关的同步最大置换组，并表明它们包含在$ 2 $ - 综合群和原始组之间。最后，我们以类似于同步组来定义$ k $ reach的群体，并以我们对原始置换群体的表征进行动机。但是结果表明，$ k $ reach -reach -reach -reach -reach置换$ n $，$ 6 \ le K \ le n -6 $是交替的组或对称组。
We give a new characterization of primitive permutation groups tied to the notion of completely reachable automata. Also, we introduce sync-maximal permutation groups tied to the state complexity of the set of synchronizing words of certain associated automata and show that they are contained between the $2$-homogeneous and the primitive groups. Lastly, we define $k$-reachable groups in analogy with synchronizing groups and motivated by our characterization of primitive permutation groups. But the results show that a $k$-reachable permutation group of degree $n$ with $6 \le k \le n - 6$ is either the alternating or the symmetric group.
