One-Dimensional Cellular Automata with Reflective Boundary Conditions and Radius Three

Abstract

A family of one-dimensional finite linear cellular automata with reflective boundary condition over the field Zi is defined. The generalizations are the radius and the field that states take values. Here, we establish a connection between reversibility of cellular automata and the rule matrix of the cellular automata with radius three. Also, we prove that the reverse CA of this family again falls into this family.