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

top
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

top

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

top
  1. T. Araki and N. Tokura, Flow languages equal recursively enumerable languages. Acta Inform.15 (1981) 209-217.  Zbl0456.68093
  2. D. Haussler and P. Zeiger, Very special languages and representations of recursively enumerable languages via computation stories. Inform. and Control47 (1980) 201-212.  Zbl0457.68086
  3. J. Jedrzejowicz and A. Szepietowski, Shuffle languages are in P. Theoret. Comput. Sci. 250 (2001) 31-53.  Zbl0952.68079
  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.  Zbl0965.68042
  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.  Zbl0381.68035
  7. K. Wagner and G. Wechsung, Computational Complexity. Reidel, Dordrecht, The Netherlands (1986).  Zbl0584.68061
  8. M.K. Warmuth and D. Haussler, On the complexity of iterated shuffle. J. Comput. Syst. Sci.28 (1984) 345-358.  Zbl0549.68039

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.