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. © 2011 Springer-Verlag.
CITATION STYLE
Caron, P., Champarnaud, J. M., & Mignot, L. (2011). Partial derivatives of an extended regular expression. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6638 LNCS, pp. 179–191). Springer Verlag. https://doi.org/10.1007/978-3-642-21254-3_13
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