Résumé : We say that a CA F stabilises an SFT X if (1) every element of X is a fixed point of F, and (2) starting from any finite perturbation of a configuration in X, the CA returns to X in finitely many steps. Does every SFT admit a stabilising CA? If so, what is the optimal stabilisation time for a given SFT? Do conjugate SFTs have the same optimal stabilisation times? What about stabilisation from random perturbations? I will present a joint work with Nazim Fatès and Irène Marcovici providing (partial) answers to these questions.

Keywords : tilings; shifts of finite type; cellular automata; self-stabilisation; noise; fault-tolerance; reliable computing; symbolic dynamics