Characterization of 1-d Periodic Boundary Reversible CA

Abstract

This paper reports characterization of one dimensional 3-neighborhood periodic boundary cellular automata (CA). It targets characterization of CA rules for efficient synthesis of reversible CA. The concept of reachability tree, as it has been proposed in [Sukanta Das, Anirban Kundu, Biplab K. Sikdar, and P. Pal Chaudhuri. Design of Nonlinear CA Based TPG Without Prohibited Pattern Set In Linear Time. Journal of Electronic Testing : Theory and Applications, 21:95–109, January 2005; Sukanta Das and Biplab K. Sikdar. Classification of CA Rules Targeting Synthesis of Reversible Cellular Automata. In Proceedings of International Conference on Cellular Automata for Research and Industry, ACRI , France, pages 68–77, September 2006; Sukanta Das, Biplab K. Sikdar, and P. Pal Chaudhuri. Characterization of Reachable/Nonreachable Cellular Automata States. In Proceedings of Sixth International Conference on Cellular Automata for Research and Industry, ACRI, The Netherlands , pages 813–822, October 2004], is redefined to classify the CA rules that can form a reversible CA. Such classification also enables synthesis of a reversible periodic boundary CA in linear time.