Brzozowski Algorithm Is Generically Super-Polynomial Deterministic Automata
Résumé
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 nd 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.
Domaines
Mathématique discrète [cs.DM]
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