Pair Diagram and Cyclic Properties Characterizing the Inverse of Reversible Automata

Professor Harold V. McIntosh has realized deep and elegant contributions in the analysis and understanding of cellular automata. Inspired in his work about applying graph and algebraic tools in the study of reversible automata, this paper implements some of his ideas and results for characterizing the features of the inverse rule for a reversible one-dimensional cellular automata. In particular, we use the pair diagram for knowing the size of the inverse neighborhood and the position of its evolution and we take advantage of the cyclic behavior in finite configurations for obtaining the inverse local rule.