论文标题
关于自助语的语言
On the Self Shuffle Language
论文作者
论文摘要
两个单词\（u \）和\（v \）的shuffle product \（u \ shuffle v \）是所有单词的集合，可以通过交织\（u \）和\（v \）获得。由Restivo（2015）的论文\ emph {shuffle产品：新研究指示}的动机，我们研究了混乱产品的特殊情况。在这项工作中，我们考虑了一个单词的混乱，其本身称为\ emph {self shuffle}或\ emph {shuffle square}，首先表明自我散言语言和语言的混乱通常是不同的集合。我们证明，所有单词的语言都以某种单词的自我混乱而产生的语言是上下文敏感的，但不自由上下文。此外，我们证明了自我洗牌\（w \ shuffle w \）唯一确定\（w \）。
The shuffle product \(u\shuffle v\) of two words \(u\) and \(v\) is the set of all words which can be obtained by interleaving \(u\) and \(v\). Motivated by the paper \emph{The Shuffle Product: New Research Directions} by Restivo (2015) we investigate a special case of the shuffle product. In this work we consider the shuffle of a word with itself called the \emph{self shuffle} or \emph{shuffle square}, showing first that the self shuffle language and the shuffle of the language are in general different sets. We prove that the language of all words arising as a self shuffle of some word is context sensitive but not context free. Furthermore, we show that the self shuffle \(w \shuffle w\) uniquely determines \(w\).
