关于发夹不完全性
On the Hairpin Incompletion
摘要：
发夹完备化和它的变体有界发夹完备化是形式语言上的操作，其灵感来自于分子生物学中的发夹形成。另一个变种称为发夹加长最近已被介绍和研究的封闭性和算法问题，涉及几个家庭的语言。在本文中，我们引入了一种新的操作，称为发夹不完全，这不仅是有界发夹完成的扩展，但也限制（有界）发夹延长的变种。此外，发夹不完全操作提供了一种形式语言理论框架，该理论框架对现在称为Whiplash PCR的生物分子技术进行建模。我们研究了语言族在该运算及其迭代运算下的闭包性质。我们证明了一族在与正则集的交、与正则集的连接和有限并下封闭的语言在单侧迭代发夹不完全下是封闭的，一族包含所有线性语言并且在循环置换、左导数和替换下封闭的语言在迭代发夹不完全下也是封闭的。
英文摘要：
Hairpin completion and its variant called bounded hairpin completion are operations on formal languages, inspired by a hairpin formation in molecular biology. Another variant called hairpin lengthening has been recently introduced and studied on the closure properties and algorithmic problems concerning several families of languages. In this paper, we introduce a new operation of this kind, called hairpin incompletion which is not only an extension of bounded hairpin completion, but also a restricted (bounded) variant of hairpin lengthening. Further, the hairpin incompletion operation provides a formal language theoretic framework that models a bio-molecular technique nowadays known as Whiplash PCR. We study the closure properties of language families under both the operation and its iterated version. We show that a family of languages closed under intersection with regular sets, concatenation with regular sets, and finite union is closed under one-sided iterated hairpin incompletion, and that a family of languages containing all linear languages and closed under circular permutation, left derivative and substitution is also closed under iterated hairpin incompletion.
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