Circular automata synchronize with high probability

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number105356
Number of pages19
JournalJournal of Combinatorial Theory, Series A
Publication statusPublished - Feb 2021


  • math.CO
  • Random matrices
  • Circulant graphs
  • Automata
  • Chromatic polynomials
  • Synchronization

ASJC Scopus subject areas

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


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