Circular automata synchronize with high probability

Publikation: Beitrag in einer FachzeitschriftArtikel

Abstract

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.
Originalspracheenglisch
Seitenumfang19
FachzeitschriftJournal of Combinatorial Theory / A
PublikationsstatusAngenommen/In Druck - 15 Okt 2020

Fingerprint Untersuchen Sie die Forschungsthemen von „Circular automata synchronize with high probability“. Zusammen bilden sie einen einzigartigen Fingerprint.

  • Dieses zitieren