A general framework for the derivation of regular expressions

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 derivativ...

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Published inRAIRO. Informatique théorique et applications Vol. 48; no. 3; pp. 281 - 305
Main Authors Caron, Pascal, Champarnaud, Jean-Marc, Mignot, Ludovic
Format Journal Article
LanguageEnglish
Published Paris EDP Sciences 01.07.2014
Subjects
68Q45
alternating automata
derivation
partial derivation
Regular expressions
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Summary: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.
Bibliography:istex:948DF1D872D44BBDD591AE2EF4C48F1494974DC8
publisher-ID:ita140013
ark:/67375/80W-8N4GBBQV-J
pascal.caron@univ-rouen.fr, jean-marc.champarnaud@univ-rouen.fr, ludovic.mignot@univ-rouen.fr
PII:S0988375414000101
ISSN:0988-3754
1290-385X
DOI:10.1051/ita/2014010