Construction of Reversible Cellular Automata by Amalgamations and Permutations of States
Juan Carlos Seck Tuoh Mora, Manuel González Hernández, Harold V. McIntosh and Sergio V. Chapa Vergara
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.
Keywords: Reversibility, amalgamations, permutations, definiteness, Welch indexes.