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A general framework for the derivation of regular expressions

Published online by Cambridge University Press:  27 May 2014

Pascal Caron ,
Jean-Marc Champarnaud  and
Ludovic Mignot
Pascal Caron
Affiliation:
LITIS, Université de Rouen, 76801 Saint-Étienne du Rouvray Cedex, France.. pascal.caron@univ-rouen.fr, jean-marc.champarnaud@univ-rouen.fr, ludovic.mignot@univ-rouen.fr
Jean-Marc Champarnaud
Affiliation:
LITIS, Université de Rouen, 76801 Saint-Étienne du Rouvray Cedex, France.. pascal.caron@univ-rouen.fr, jean-marc.champarnaud@univ-rouen.fr, ludovic.mignot@univ-rouen.fr
Ludovic Mignot
Affiliation:
LITIS, Université de Rouen, 76801 Saint-Étienne du Rouvray Cedex, France.. pascal.caron@univ-rouen.fr, jean-marc.champarnaud@univ-rouen.fr, ludovic.mignot@univ-rouen.fr
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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.

Keywords

Regular expressionsalternating automataderivationpartial derivation
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 48 , Issue 3: Special issue in the honor of the 14th “Journées montoises d’informatique théorique”. I. , July 2014 , pp. 281 - 305
Copyright
© EDP Sciences 2014

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