Building the minimal automaton of A*X in linear time, when X is of bounded cardinality

Authors:
Omar AitMous;Frédérique Bassino;Cyril Nicaud
Affiliations:
LIPN, UMR, Université Paris 13, CNRS, Villetaneuse, France;LIPN, UMR, Université Paris 13, CNRS, Villetaneuse, France;LIGM, UMR, CNRS, Université Paris-Est, Marne-la-Vallée, France
Venue:
CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
Year:
2010

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Abstract

We present an algorithm for constructing the minimal automaton recognizing A*X, where the pattern X is a set of m (that is a fixed integer) non-empty words over a finite alphabet A whose sum of lengths is n. This algorithm, inspired by Brzozowski's minimization algorithm, uses sparse lists to achieve a linear time complexity with respect to n.