关于单个词的迭代发夹式补全的正则性
On the regularity of iterated hairpin completion of a single word
摘要：
发夹完成是一种抽象操作，其模拟DNA生物操作，其接收DNA链$w = xαy \calpha$作为输入，并输出$w' = x αy \barα \bar{x}$，其中$\bar{x}$表示$x$的沃森-克里克互补。在本文中，我们专注于寻找条件下，一个给定的词的迭代发夹完成是正规的问题。根据启动发夹结构完成的词$α$和$\calpha$的数量以及它们的分布情况，我们对所有词的集合$w$进行分类。对于含有少量$α$和$\calpha$的基本词类$w$，我们证明了$w$的迭代发夹完成是正则的.对于其他类的$α$和$\calpha$的出现次数较高，我们证明了一个必要和充分条件的迭代发夹完成的一个字在这些类是定期的。
英文摘要：
Hairpin completion is an abstract operation modeling a DNA bio-operation which receives as input a DNA strand $w = xαy \calpha$, and outputs $w' = x αy \barα \bar{x}$, where $\bar{x}$ denotes the Watson-Crick complement of $x$. In this paper, we focus on the problem of finding conditions under which the iterated hairpin completion of a given word is regular. According to the numbers of words $α$ and $\calpha$ that initiate hairpin completion and how they are scattered, we classify the set of all words $w$. For some basic classes of words $w$ containing small numbers of occurrences of $α$ and $\calpha$, we prove that the iterated hairpin completion of $w$ is regular. For other classes with higher numbers of occurrences of $α$ and $\calpha$, we prove a necessary and sufficient condition for the iterated hairpin completion of a word in these classes to be regular.
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