Procedures for calculating reversible one-dimensional cellular automata

Abstract

We describe two algorithms for calculating reversible one-dimensional cellular automata of neighborhood size 2. We explain how this kind of automaton represents all the other cases. Using two basic properties of reversible automata such as uniform multiplicity of ancestors and Welch indices, these algorithms only require matrix products and transitive closures of binary relations to classify all the possible reversible automata of neighborhood size 2. We expose the features, advantages and differences with other well-known methods. Finally, we present results for reversible automata from three to six states and neighborhood size 2. © 2005 Elsevier B.V. All rights reserved.

Citation

Martínez, G. J., Vergara, S. V., Mora, J. C. S. T., & McIntosh, H. V. (2005). Procedures for calculating reversible one-dimensional cellular automata. Physica D: Nonlinear Phenomena, 202(1-2), 134-141. https://doi.org/10.1016/j.physd.2005.01.018

• Journal Article Type: Article
• Publication Date: Mar 1, 2005
• Journal: Physica D: Nonlinear Phenomena
• Print ISSN: 0167-2789
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 202
• Issue: 1-2
• Pages: 134-141
• DOI: https://doi.org/10.1016/j.physd.2005.01.018
• Keywords: cellular automata, welch theory, algorithms
• Public URL: https://uwe-repository.worktribe.com/output/1051239
• Publisher URL: http://dx.doi.org/10.1016/j.physd.2005.01.018