On the Complexity of Hopcroft’s State Minimization Algorithm

  • Jean Berstel
  • Olivier Carton
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3317)


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 = 2 k on which the algorithm runs in time k2 k . 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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jean Berstel
    • 1
  • Olivier Carton
    • 2
  1. 1.Institut Gaspard MongeUniversité de Marne-la-Vallée 
  2. 2.LIAFAUniversité Paris 7 

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