Santiago Dynamical Systems Seminar: Stabilization of subshifts of finite type by cellular automata

Abstract: A subshift of finite type (SFT) is a set of infinite (d-dimensional) configurations defined by a finite set of local constraints (e.g. the set of 3-coloring of the grid). N. Fatès, I. Marcovici et S. Taati introduced in 2021 the following notion of stabilization: an SFT Σ is stabilizable if there is a cellular automaton F which

1) leave invariant any configuration of Σ, and
2) starting from any finite perturbation of any configuration of Σ, F reaches in finite time a
configuration from Σ.

The goal of this talk is to show that any SFT (in any dimension) is stabilizable, which was an open question of Fatès-Marcovici-Taati-2021. We will also show that, in dimension 1, the stabilization can always be achieved in linear time, which has consequences on the possibility to stabilize configurations under random perturbations.

Speaker: Guillaume Theyssier (CNRS / Aix-Marseille Université)