On the Complexity of Hopcroft's State Minimization Algorithm

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.

• Type: Conference
• Year: 2004
• Where: WIA
• Authors: Jean Berstel, Olivier Carton
• Keywords: Algorithm, Artificial Intelligence, Complexity Bound, Deterministic Automaton, WIA 2004