Ergodicity of some classes of cellular automata subject to noise - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2019

Ergodicity of some classes of cellular automata subject to noise

Irène Marcovici
Mathieu Sablik
Siamak Taati
  • Fonction : Auteur
  • PersonId : 978944

Résumé

Cellular automata (CA) are dynamical systems on symbolic configurations on the lattice. They are also used as models of massively parallel computers. As dynamical systems, one would like to understand the effect of small random perturbations on the dynamics of CA. As models of computation, they can be used to study the reliability of computation against noise. We consider various families of CA (nilpotent, permutive, gliders, CA with a spreading symbol, surjective, algebraic) and prove that they are highly unstable against noise, meaning that they forget their initial conditions under slightest positive noise. This is manifested as the ergodicity of the resulting probabilistic CA. The proofs involve a collection of different techniques (couplings, entropy, Fourier analysis), depending on the dynamical properties of the underlying deterministic CA and the type of noise.

Dates et versions

hal-01971315 , version 1 (06-01-2019)

Identifiants

Citer

Irène Marcovici, Mathieu Sablik, Siamak Taati. Ergodicity of some classes of cellular automata subject to noise. 2019. ⟨hal-01971315⟩
242 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More