Partial Derivatives of Regular Expressions and Finite Automata Constructions (1995)
| Venue: | Theoretical Computer Science |
| Citations: | 49 - 0 self |
BibTeX
@ARTICLE{Antimirov95partialderivatives,
author = {Valentin Antimirov},
title = {Partial Derivatives of Regular Expressions and Finite Automata Constructions},
journal = {Theoretical Computer Science},
year = {1995},
volume = {155},
pages = {291--319}
}
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Abstract
. We introduce a notion of a partial derivative of a regular expression. It is a generalization to the non-deterministic case of the known notion of a derivative invented by Brzozowski. We give a constructive definition of partial derivatives, study their properties, and employ them to develop a new algorithm for turning regular expressions into relatively small NFA and to provide certain improvements to Brzozowski's algorithm constructing DFA. We report on a prototype implementation of our algorithm constructing NFA and present some examples. Introduction In 1964 Janusz Brzozowski introduced word derivatives of regular expressions and suggested an elegant algorithm turning a regular expression r into a deterministic finite automata (DFA); the main point of the algorithm is that the word derivatives of r serve as states of the resulting DFA [5]. In the following years derivatives were recognized as a quite useful and productive tool. Conway [8] uses derivatives to present various comp...
