关于迭代Hairpin完备化

摘要：

有界发夹完备化及其迭代形式是受DNA生物化学中发夹形成的启发而对形式语言进行的操作。本文回答了文献中关于迭代发夹完备化的两个问题。第一个问题是正则语言类在迭代有界发夹完备下是否封闭。在这里，我们表明，这是真的，提供了一个更普遍的结果，适用于所有类的语言是封闭的有限联盟，交集与正规集，并与正规集连接。特别地，所有Chomsky类和所有标准复杂性类在迭代有界发夹完备下都是封闭的。在本文的第二部分，我们解决的问题是否迭代发夹完成的单例总是经常的。与第一个问题相比，这个问题的答案是否定的。我们展示了一个单例语言的例子，它的迭代发夹完成是不规则的，实际上它不是上下文无关的，而是上下文敏感的。

英文摘要：

The (bounded) hairpin completion and its iterated versions are operations on formal lan- guages which have been inspired by the hairpin formation in DNA-biochemistry. The paper answers two questions asked in the literature about the iterated hairpin completion. The first question is whether the class of regular languages is closed under iterated bounded hairpin completion. Here we show that this is true by providing a more general result which applies to all the classes of languages which are closed under finite union, intersection with regular sets, and concatenation with regular sets. In particular, all Chomsky classes and all standard complexity classes are closed under iterated bounded hairpin completion. In the second part of the paper we address the question whether the iterated hairpin completion of a singleton is always regular. In contrast to the first question, this one has a negative answer. We exhibit an example of a singleton language whose iterated hairpin completion is not regular, actually it is not context-free, but context-sensitive.

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