On invertible and stably reversible non-uniform cellular automata

Abstract

For non-uniform cellular automata (NUCA) over an arbitrary universe with multiple local transition rules, we introduce and investigate fundamental dynamical properties such as stable injectivity, stable reversibility, and stable post-surjectivity. Over infinite amenable group universes (e.g. infinite abelian groups), we show that it is impossible to obtain injective NUCA by disturbing the local transition rules of a finite number of cells of non-injective cellular automata. Moreover, we establish the equivalence between reversibility, stable reversibility, and stable injectivity for NUCA. The surjectivity and invertibility of several classes of injective and stably injective NUCA are also obtained.