具有非最大自动复杂度的正规序列
Normal Sequences with Non-Maximal Automatic Complexity
摘要：
本文探讨了自动复杂性，一个复杂性的概念介绍了沙利特和王在2001年。我们证明了存在一个正规序列$T$使得$I(T) = 0$和$S(T) \leq 1/2$，其中$I(T)$和$S(T)$分别是$T$的自动复杂度的下限和上限.我们还证明了存在一个Champernowne序列$C$，即通过连接所有长度为$1$的字符串，然后连接所有长度为$2$的字符串等形成的序列，使得$S(C) \leq 2/3$。
英文摘要：
This paper examines Automatic Complexity, a complexity notion introduced by Shallit and Wang in 2001. We demonstrate that there exists a normal sequence $T$ such that $I(T) = 0$ and $S(T) \leq 1/2$, where $I(T)$ and $S(T)$ are the lower and upper automatic complexity rates of $T$ respectively. We furthermore show that there exists a Champernowne sequence $C$, i.e. a sequence formed by concatenating all strings of length $1$ followed by concatenating all strings of length $2$ and so on, such that $S(C) \leq 2/3$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
