Year: 2013
Type: preprint
Abstract: We prove that a random binary automaton with $n$ states is synchronizing with high probability and the asymptotic is exactly $1-Θ(\frac{1}{n})$ as conjectured in [Cameron, 2011]. We also present a deterministic algorithm which decides whether a given random automaton is synchronizing in expected time linear in $n$ and prove that it is optimal. This is an expanded and heavily revised version of the conference paper [Berlinkov, 2016] with an addition of the algorithmic result described above.
Source: arXiv (Cornell University)
Author: Berlinkov, Mikhail V.
Institution: Ural Federal University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Ural Federal University
OpenAlex ID: W2952936801