自动序列的计数与判定性质
Enumeration and Decidable Properties of Automatic Sequences
摘要：
我们表明，k-自动序列的各个方面-如具有长度为n的无边界因子-都是可判定的，有效的可判定的。因此，许多相关序列要么是k-自动的，要么是k-正则的。这些包括许多以前在文献中研究的序列，如递归函数，外观函数和重复指数。给出了k-正则序列类的一些新的刻画。许多结果扩展到其他序列定义的Pisot计数系统。
英文摘要：
We show that various aspects of k-automatic sequences -- such as having an unbordered factor of length n -- are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or k-regular. These include many sequences previously studied in the literature, such as the recurrence function, the appearance function, and the repetitivity index. We also give some new characterizations of the class of k-regular sequences. Many results extend to other sequences defined in terms of Pisot numeration systems.
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。
