A general framework for the derivation of regular expressions

Pascal Caron; Jean-Marc Champarnaud; Ludovic Mignot

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2014)

  • Volume: 48, Issue: 3, page 281-305
  • ISSN: 0988-3754

Abstract

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The aim of this paper is to design a theoretical framework that allows us to perform the computation of regular expression derivatives through a space of generic structures. Thanks to this formalism, the main properties of regular expression derivation, such as the finiteness of the set of derivatives, need only be stated and proved one time, at the top level. Moreover, it is shown how to construct an alternating automaton associated with the derivation of a regular expression in this general framework. Finally, Brzozowski’s derivation and Antimirov’s derivation turn out to be a particular case of this general scheme and it is shown how to construct a DFA, a NFA and an AFA for both of these derivations.

How to cite

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Caron, Pascal, Champarnaud, Jean-Marc, and Mignot, Ludovic. "A general framework for the derivation of regular expressions." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 48.3 (2014): 281-305. <http://eudml.org/doc/273046>.

@article{Caron2014,
abstract = {The aim of this paper is to design a theoretical framework that allows us to perform the computation of regular expression derivatives through a space of generic structures. Thanks to this formalism, the main properties of regular expression derivation, such as the finiteness of the set of derivatives, need only be stated and proved one time, at the top level. Moreover, it is shown how to construct an alternating automaton associated with the derivation of a regular expression in this general framework. Finally, Brzozowski’s derivation and Antimirov’s derivation turn out to be a particular case of this general scheme and it is shown how to construct a DFA, a NFA and an AFA for both of these derivations.},
author = {Caron, Pascal, Champarnaud, Jean-Marc, Mignot, Ludovic},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {regular expressions; alternating automata; derivation; partial derivation},
language = {eng},
number = {3},
pages = {281-305},
publisher = {EDP-Sciences},
title = {A general framework for the derivation of regular expressions},
url = {http://eudml.org/doc/273046},
volume = {48},
year = {2014},
}

TY - JOUR
AU - Caron, Pascal
AU - Champarnaud, Jean-Marc
AU - Mignot, Ludovic
TI - A general framework for the derivation of regular expressions
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 3
SP - 281
EP - 305
AB - The aim of this paper is to design a theoretical framework that allows us to perform the computation of regular expression derivatives through a space of generic structures. Thanks to this formalism, the main properties of regular expression derivation, such as the finiteness of the set of derivatives, need only be stated and proved one time, at the top level. Moreover, it is shown how to construct an alternating automaton associated with the derivation of a regular expression in this general framework. Finally, Brzozowski’s derivation and Antimirov’s derivation turn out to be a particular case of this general scheme and it is shown how to construct a DFA, a NFA and an AFA for both of these derivations.
LA - eng
KW - regular expressions; alternating automata; derivation; partial derivation
UR - http://eudml.org/doc/273046
ER -

References

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