On the complexity of hopcroft’s state minimization algorithm

Authors:
Jean Berstel;Olivier Carton
Affiliations:
Institut Gaspard Monge, Université de Marne-la-Vallée;LIAFA, Université Paris 7
Venue:
CIAA'04 Proceedings of the 9th international conference on Implementation and Application of Automata
Year:
2004

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Abstract

Hopcroft’s algorithm for minimizing a deterministic automaton has complexity O(n log n). We show that this complexity bound is tight. More precisely, we provide a family of automata of size n = 2k on which the algorithm runs in time k2k. These automata have a very simple structure and are built over a one-letter alphabet. Their sets of final states are defined by de Bruijn words.