Asymptotic enumeration of Minimal Automata

Frédérique Bassino (1) , Julien David (1) , Andrea Sportiello (2)

1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 UNIMI - Università degli Studi di Milano = University of Milan

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.

Mots clés: minimal automata; regular languages; enumeration of random structures

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]

Frédérique Bassino, Julien David, Andrea Sportiello. Asymptotic enumeration of Minimal Automata. STACS'12 (29th Symposium on Theoretical Aspects of Computer Science), Feb 2012, Paris, France. pp.88-99. ⟨hal-00678203⟩