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arXiv · 2202.07988

On the Self Shuffle Language

Pamela Fleischmann·Tero Harju·Lukas Haschke·Jonas Höfer·Dirk Nowotka
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Abstract

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 \(w\).

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Pamela Fleischmann, Tero Harju, Lukas Haschke, Jonas Höfer, Dirk Nowotka. 2022-02-16. On the Self Shuffle Language. https://arxiv.org/abs/2202.07988

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