Work

Strong stochastic stability of cellular automata

Year: 2025

Type: article

Abstract: We define the notion of stochastic stability, already present in the literature in the context of smooth dynamical systems, for invariant measures of cellular automata perturbed by a random noise, and the notion of strongly stochastically stable cellular automaton. We study these notions on basic examples (nilpotent cellular automata, spreading symbols) using different methods inspired by those presented in [MST19]. We then show that this notion of stability is not trivial by proving that a Turing machine cannot decide if a given invariant measure of a cellular automaton is stable under a uniform perturbation.

Source: Electronic Journal of Probability

DOI: 10.1214/25-ejp1396

Authors: Hugo Marsan, Mathieu Sablik

Institutions: Université Toulouse III - Paul Sabatier, Institut de Mathématiques de Toulouse

Language: English

Topic: Cellular Automata and Applications

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $675

Funders: Agence Nationale de la Recherche, Centre International de Mathématiques et Informatique de Toulouse