Building the Minimal Automaton of A*X in Linear Time, When X Is of Bounded Cardinality

Omar Aitmous (1) , Frédérique Bassino (1) , Cyril Nicaud (2)

1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

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.

Domaines: Mathématique discrète [cs.DM]

Omar Aitmous, Frédérique Bassino, Cyril Nicaud. Building the Minimal Automaton of A*X in Linear Time, When X Is of Bounded Cardinality. 21st Annual Symposium on Combinatorial Pattern Matching (CPM 2010), Jun 2010, United States. pp.275-287. ⟨hal-00450674v2⟩