On the regularity of {left perpendicular log(b)(alpha n + beta)right perpendicular}(n >= 0)
On the regularity of {left perpendicular log(b)(alpha n + beta)right perpendicular}(n >= 0)
复制标题
关于{左垂线 log(b)(alpha n beta)右垂线}(n >= 0) 的规律性
DOI：
10.1016/j.tcs.2017.10.010
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发表时间：
2018
影响因子：
1.1
通讯作者：
Wen Zhi-Xiong
中科院分区：
文献类型：
--
作者：
Zhang Jie-Meng;Guo Ying-Jun;Wen Zhi-Xiong
设α，β为真实的数，B≥ 2为整数。Allouche和Shallit证明了序列{<$α n+ β <$} n≥ 0是b-正则的当且仅当α是有理数。本文利用基无关正则语言证明了一个类似的结果：序列{} n≥ 0是b-正则的当且仅当α是有理数，其中α> 0，β≥ 0.特别地，当α= 2，β= 0，B= 2时，我们回答了Allouche和Shallit提出的一个问题：序列{} n≥ 1不是2-正则的，这个问题已分别由Bell，Moshe和Rowland证明.
Let α, β be real numbers and b≥ 2 be an integer. Allouche and Shallit showed that the sequence {⌊ α n+ β⌋} n≥ 0 is b-regular if and only if α is rational. In this paper, using a base-independent regular language, we prove a similar result that the sequence {⌊ log b(α n+ β)⌋} n≥ 0 is b-regular if and only if α is rational, where α> 0, β≥ 0. In particular, when α= 2, β= 0 and b= 2, we answer a question of Allouche and Shallit that the sequence {⌊ 1 2+ log 2 n⌋} n≥ 1 is not 2-regular, which has previously been proved by Bell, Moshe and Rowland respectively.