Reversibility of non-saturated linear cellular automata on finite triangular grids

Discrete dynamical systems such as cellular automata are of increasing interest to scientists in a variety of disciplines since they are simple models of computation capable of simulating complex phenomena. For this reason, the problem of reversibility of such systems is very important and, therefore, recurrently taken up by researchers. Unfortunately, the study of reversibility is remarkably hard, especially in the case of two- or higher-dimensional cellular automata. In this paper, we propose a novel and simple method that allows us to completely resolve the reversibility problem of a wide class of linear cellular automata on finite triangular grids with null boundary conditions.