On the expressive power of the shuffle operator matched with intersection by regular sets

@article{Jdrzejowicz2001OnTE,
  title={On the expressive power of the shuffle operator matched with intersection by regular sets},
  author={Joanna Jędrzejowicz and Andrzej Szepietowski},
  journal={RAIRO Theor. Informatics Appl.},
  year={2001},
  volume={35},
  pages={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… 
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