A general framework for the derivation of regular expressions
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 3, pp. 281-305.

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.

DOI : https://doi.org/10.1051/ita/2014010
Classification : 68Q45
Mots clés : regular expressions, alternating automata, derivation, partial derivation
@article{ITA_2014__48_3_281_0,
author = {Caron, Pascal and Champarnaud, Jean-Marc and Mignot, Ludovic},
title = {A general framework for the derivation of regular expressions},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {281--305},
publisher = {EDP-Sciences},
volume = {48},
number = {3},
year = {2014},
doi = {10.1051/ita/2014010},
mrnumber = {3302489},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ita/2014010/}
}
Caron, Pascal; Champarnaud, Jean-Marc; Mignot, Ludovic. A general framework for the derivation of regular expressions. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 3, pp. 281-305. doi : 10.1051/ita/2014010. http://www.numdam.org/articles/10.1051/ita/2014010/

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