Circular automata synchronize with high probability

Christoph Aistleitner*, Daniele D'Angeli, Abraham Gutierrez, Emanuele Rodaro, Amnon Rosenmann

*Korrespondierende/r Autor/in für diese Arbeit

Publikation: Beitrag in einer FachzeitschriftArtikel

Abstract

In this paper we prove that a uniformly distributed random circular automaton A n 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.

Originalspracheenglisch
Aufsatznummer105356
Seitenumfang19
FachzeitschriftJournal of Combinatorial Theory / A
Jahrgang178
DOIs
PublikationsstatusVeröffentlicht - Feb 2021

ASJC Scopus subject areas

  • !!Theoretical Computer Science
  • !!Discrete Mathematics and Combinatorics
  • !!Computational Theory and Mathematics

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