Cobham定理与自动性
Cobham's Theorem and Automaticity
摘要：
本文在Krebs关于Cobham定理的证明中给出了一定的界，并得到了非周期$a$ -自动序列和非周期$b$ -自动序列公共前缀长度的上界，其中$a$和$b$是乘法独立的.我们还表明，一个自动序列不能有任意大的因素，在共同的Sturmian序列。
英文摘要：
We make certain bounds in Krebs' proof of Cobham's theorem explicit and obtain corresponding upper bounds on the length of a common prefix of an aperiodic $a$-automatic sequence and an aperiodic $b$-automatic sequence, where $a$ and $b$ are multiplicatively independent. We also show that an automatic sequence cannot have arbitrarily large factors in common with a Sturmian sequence.
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。
