Vesa Halava, Tero Harju, Dirk Nowotka et al.
We study decision problems of the form: given a regular or linear context-free language $L$, is there a word of a given fixed form in $L$, where given fixed forms are based on word operations copy, marked copy, shuffle and their combinations.
Pamela Fleischmann, Tero Harju, Lukas Haschke et al.
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 \(w\).