On the expressive power of the shuffle operator matched with intersection by regular sets
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 35 (2001) no. 4, pp. 379-388.

We investigate the complexity of languages described by some expressions containing shuffle operator and intersection. We show that deciding whether the shuffle of two words has a nonempty intersection with a regular set (or fulfills some regular pattern) is NL-complete. Furthermore we show that the class of languages of the form $L\cap R$, with a shuffle language $L$ and a regular language $R$, contains non-semilinear languages and does not form a family of mildly context- sensitive languages.

Classification: 68Q15,  68Q45
Keywords: formal languages, shuffle, space complexity
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title = {On the expressive power of the shuffle operator matched with intersection by regular sets},
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Jȩdrzejowicz, Joanna; Szepietowski, Andrzej. On the expressive power of the shuffle operator matched with intersection by regular sets. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 35 (2001) no. 4, pp. 379-388. http://www.numdam.org/item/ITA_2001__35_4_379_0/

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