Asymptotic enumeration of Minimal Automata
نویسندگان
چکیده
We determine the asymptotic proportion of minimal automata, within n-state accessible deterministic complete automata over a k-letter alphabet, with the uniform distribution over the possible transition structures, and a binomial distribution over terminal states, with arbitrary parameter b. It turns out that a fraction ∼ 1 − C(k, b)n of automata is minimal, with C(k, b) a function, explicitly determined, involving the solution of a transcendental equation.
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