4 research outputs found
Asymptotic enumeration of Minimal Automata
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^{-k+2} of automata is minimal, with C(k,b) a
function, explicitly determined, involving the solution of a transcendental
equation.Comment: 12+5 pages, 2 figures, submitted to STACS 201