In this paper we prove that a uniformly distributed random circular automaton An of order n synchronizes with high probability (w.h.p.). More precisely, we prove that [Formula presented] The main idea of the proof is to translate the synchronization problem into a problem concerning properties of a random matrix; these properties are then established with high probability by a careful analysis of the stochastic dependence structure among the random entries of the matrix. Additionally, we provide an upper bound for the probability of synchronization of circular automata in terms of chromatic polynomials of circulant graphs.

Circular automata synchronize with high probability

D'Angeli D.;Rodaro E.;
2021

Abstract

In this paper we prove that a uniformly distributed random circular automaton An of order n synchronizes with high probability (w.h.p.). More precisely, we prove that [Formula presented] The main idea of the proof is to translate the synchronization problem into a problem concerning properties of a random matrix; these properties are then established with high probability by a careful analysis of the stochastic dependence structure among the random entries of the matrix. Additionally, we provide an upper bound for the probability of synchronization of circular automata in terms of chromatic polynomials of circulant graphs.
File in questo prodotto:
File Dimensione Formato  
1-s2.0-S0097316520301485-main.pdf

Accesso riservato

: Publisher’s version
Dimensione 515.85 kB
Formato Adobe PDF
515.85 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/1165229
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact