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

Joanna Jędrzejowicz; Andrzej Szepietowski

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 35, Issue: 4, page 379-388
  • ISSN: 0988-3754

Abstract

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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 ∩ 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.

How to cite

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Jędrzejowicz, Joanna, and Szepietowski, Andrzej. "On the expressive power of the shuffle operator matched with intersection by regular sets." RAIRO - Theoretical Informatics and Applications 35.4 (2010): 379-388. <http://eudml.org/doc/221957>.

@article{Jędrzejowicz2010,
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. },
author = {Jędrzejowicz, Joanna, Szepietowski, Andrzej},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Formal languages; shuffle; space complexity.; complexity of languages},
language = {eng},
month = {3},
number = {4},
pages = {379-388},
publisher = {EDP Sciences},
title = {On the expressive power of the shuffle operator matched with intersection by regular sets},
url = {http://eudml.org/doc/221957},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Jędrzejowicz, Joanna
AU - Szepietowski, Andrzej
TI - On the expressive power of the shuffle operator matched with intersection by regular sets
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 4
SP - 379
EP - 388
AB - 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.
LA - eng
KW - Formal languages; shuffle; space complexity.; complexity of languages
UR - http://eudml.org/doc/221957
ER -

References

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  1. T. Araki and N. Tokura, Flow languages equal recursively enumerable languages. Acta Inform.15 (1981) 209-217.  
  2. D. Haussler and P. Zeiger, Very special languages and representations of recursively enumerable languages via computation stories. Inform. and Control47 (1980) 201-212.  
  3. J. Jedrzejowicz and A. Szepietowski, Shuffle languages are in P. Theoret. Comput. Sci. 250 (2001) 31-53.  
  4. C. Martin-Vide and A. Mateescu, Special families of sewing languages, in Workshop - Descriptional complexity of automata, grammars and related structures. Magdeburg (1999) 137-143.  
  5. C.H. Papadimitriou, Computational Complexity. Addison-Wesley Publ. Co (1994).  
  6. A.C. Shaw, Software descriptions with flow expressions. IEEE Trans. Software Engrg.3 (1978) 242-254.  
  7. K. Wagner and G. Wechsung, Computational Complexity. Reidel, Dordrecht, The Netherlands (1986).  
  8. M.K. Warmuth and D. Haussler, On the complexity of iterated shuffle. J. Comput. Syst. Sci.28 (1984) 345-358.  

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