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

Joanna Jȩdrzejowicz; Andrzej Szepietowski — 2001

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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.

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

Joanna Jędrzejowicz; Andrzej Szepietowski — 2010

RAIRO - Theoretical Informatics and Applications

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 and a regular language , contains non-semilinear languages and does not form a family of mildly context- sensitive languages.

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