Jean-Marc Champarnaud ; Hadrien Jeanne ; Ludovic Mignot - Derivatives of approximate regular expressions

dmtcs:598 - Discrete Mathematics & Theoretical Computer Science, July 12, 2013, Vol. 15 no. 2 -
Derivatives of approximate regular expressionsArticle

Authors: Jean-Marc Champarnaud 1; Hadrien Jeanne 1; Ludovic Mignot 1

  • 1 Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes

Our aim is to construct a finite automaton recognizing the set of words that are at a bounded distance from some word of a given regular language. We define new regular operators, the similarity operators, based on a generalization of the notion of distance and we introduce the family of regular expressions extended to similarity operators, that we call AREs (Approximate Regular Expressions). We set formulae to compute the Brzozowski derivatives and the Antimirov derivatives of an ARE, which allows us to give a solution to the ARE membership problem and to provide the construction of two recognizers for the language denoted by an ARE. As far as we know, the family of approximative regular expressions is introduced for the first time in this paper. Classical approximate regular expression matching algorithms are approximate matching algorithms on regular expressions. Our approach is rather to process an exact matching on approximate regular expressions.

Volume: Vol. 15 no. 2
Section: Automata, Logic and Semantics
Published on: July 12, 2013
Accepted on: June 9, 2015
Submitted on: June 26, 2012
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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