Abstract
| Original language | English |
|---|---|
| Number of pages | 19 |
| Journal | arXiv.org e-Print archive |
| Publication status | Published - 6 Jun 2019 |
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Keywords
- math.CO
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Circular automata synchronize with high probability. / Aistleitner, Christoph; D'Angeli, Daniele; Gutierrez, Abraham; Rodaro, Emanuele; Rosenmann, Amnon.
In: arXiv.org e-Print archive, 06.06.2019.Research output: Contribution to journal › Article › Research
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TY - JOUR
T1 - Circular automata synchronize with high probability
AU - Aistleitner, Christoph
AU - D'Angeli, Daniele
AU - Gutierrez, Abraham
AU - Rodaro, Emanuele
AU - Rosenmann, Amnon
PY - 2019/6/6
Y1 - 2019/6/6
N2 - In this paper we prove that a uniformly distributed random circular automaton $\mathcal{A}_n$ of order $n$ synchronizes with high probability (whp). More precisely, we prove that $$ \mathbb{P}\left[\mathcal{A}_n \text{ synchronizes}\right] = 1- O\left(\frac{1}{n}\right). $$ The main idea of the proof is to translate the synchronization problem into properties of a random matrix; these properties are then handled with tools of the probabilistic method. Additionally, we provide an upper bound for the probability of synchronization of circular automata in terms of chromatic polynomials of circulant graphs.
AB - In this paper we prove that a uniformly distributed random circular automaton $\mathcal{A}_n$ of order $n$ synchronizes with high probability (whp). More precisely, we prove that $$ \mathbb{P}\left[\mathcal{A}_n \text{ synchronizes}\right] = 1- O\left(\frac{1}{n}\right). $$ The main idea of the proof is to translate the synchronization problem into properties of a random matrix; these properties are then handled with tools of the probabilistic method. Additionally, we provide an upper bound for the probability of synchronization of circular automata in terms of chromatic polynomials of circulant graphs.
KW - math.CO
M3 - Article
JO - arXiv.org e-Print archive
JF - arXiv.org e-Print archive
ER -