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Procedures for calculating reversible one-dimensional cellular automata

Mora, Juan Carlos Seck Tuoh; Vergara, Sergio V.Chapa; Mart�nez, Genaro Ju�rez; McIntosh, Harold V.

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Authors

Juan Carlos Seck Tuoh Mora

Sergio V.Chapa Vergara

Genaro Ju�rez Mart�nez

Harold V. McIntosh



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
Deposit Date Jun 2, 2010
Publicly Available Date Mar 28, 2024
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

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