Brzozowski Algorithm Is Generically Super-Polynomial for Deterministic Automata

  • Sven De Felice
  • Cyril Nicaud
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7907)


We study the number of states of the minimal automaton of the mirror of a rational language recognized by a random deterministic automaton with n states. We prove that, for any d > 0, the probability that this number of states is greater than n d tends to 1 as n tends to infinity. As a consequence, the generic and average complexities of Brzozowski minimization algorithm are super-polynomial for the uniform distribution on deterministic automata.


Random Permutation Accessible State Combinatorial Explosion Average Complexity Small Cycle 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Sven De Felice
    • 1
  • Cyril Nicaud
    • 1
  1. 1.LIGMUniversité Paris-Est & CNRSMarne-la-Vallée Cedex 2France

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