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On the expressive power of the shuffle operator matched with intersection by regular sets
Joanna Jędrzejowicz, Andrzej Szepietowski
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 35 / Issue 4 / July 2001

Published online by Cambridge University Press:

15 April 2002, pp. 379-388

Print publication:

July 2001
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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.