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

Published online by Cambridge University Press:  15 April 2002

Joanna Jędrzejowicz  and
Andrzej Szepietowski
Joanna Jędrzejowicz
Affiliation:
Institute of Mathematics, University of Gdańsk, ul Wita Stwosza 57, 80952 Gdańsk, Poland; (jj@math.univ.gda.pl)
Andrzej Szepietowski
Affiliation:
Institute of Mathematics, University of Gdańsk, ul Wita Stwosza 57, 80952 Gdańsk, Poland; (matszp@math.univ.gda.pl)
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Abstract

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.

Keywords

Formal languagesshufflespace complexity.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 35 , Issue 4 , July 2001 , pp. 379 - 388
Copyright
© EDP Sciences, 2001

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