Partial derivatives of an extended regular expression

  • Authors:

  • Pascal Caron;Jean-Marc Champarnaud;Ludovic Mignot

  • Affiliations:

  • LITIS, Université de Rouen, Saint-Étienne du Rouvray Cedex, France;LITIS, Université de Rouen, Saint-Étienne du Rouvray Cedex, France;LITIS, Université de Rouen, Saint-Étienne du Rouvray Cedex, France

  • Venue:
  • LATA'11 Proceedings of the 5th international conference on Language and automata theory and applications
  • Year:
  • 2011

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Abstract

The notion of expression derivative due to Brzozowski leads to the construction of a deterministic automaton from an extended regular expression, whereas the notion of partial derivative due to Antimirov leads to the construction of a non-deterministic automaton from a simple regular expression. In this paper, we generalize Antimirov partial derivatives to regular expressions extended to complementation and intersection. For a simple regular expression with n symbols, Antimirov automaton has at most n+1 states. As far as an extended regular expression is concerned, we show that the number of states can be exponential.