Construction of Reversible Cellular Automata by Amalgamations and Permutations of States

This paper explains the properties of amalgamations and permutations of states in the matrix representation of reversible one-dimensional cellular automata where both evolution rules have neighborhood size 2 and a Welch index equal to 1. These properties are later used for constructing reversible automata and defining a compact nomenclature to identify them. Some examples are provided.