LIPIcs.STACS.2012.88.pdf
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Asymptotic enumeration of Minimal Automata
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29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Theoretical Aspects of Computer Science (STACS) - License:
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
- Publication Date: 2012-02-24
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Frédérique Bassino, Julien David, and Andrea Sportiello. Asymptotic enumeration of Minimal Automata. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 88-99, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)
https://doi.org/10.4230/LIPIcs.STACS.2012.88
https://doi.org/10.4230/LIPIcs.STACS.2012.88
Abstract
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.
Keywords
- minimal automata
- regular languages
- enumeration of random structures
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