On the asymptotic enumeration of accessible automata

Elcio Lebensztayn (1)

1 IME-USP - Institute of Mathematics and Statistics [Sao Paulo]

We simplify the known formula for the asymptotic estimate of the number of deterministic and accessible automata with n states over a k-letter alphabet. The proof relies on the theory of Lagrange inversion applied in the context of generalized binomial series.

Mots clés: asymptotic enumeration; finite automata; Lagrange series; generalized binomial series

Domaines: Mathématique discrète [cs.DM]

Elcio Lebensztayn. On the asymptotic enumeration of accessible automata. Discrete Mathematics and Theoretical Computer Science, 2010, Vol. 12 no. 3 (3), pp.75-79. ⟨10.46298/dmtcs.512⟩. ⟨hal-00990449⟩