Procedures for calculating reversible one-dimensional cellular automata
Mora, J. C. , Vergara, S. V. , Martinez, G. J. and McIntosh, H. V. (2005) Procedures for calculating reversible one-dimensional cellular automata. Physica D: Nonlinear Phenomena, 202 (1-2). pp. 131-141. ISSN 0167-2789
Publisher's URL: http://dx.doi.org/10.1016/j.physd.2005.01.018
Two algorithms for calculating reversible one-dimensional cellular automata of neighborhood size 2 are presented. It is explained how this kind of automata represents all the rest. Using two basic properties of these systems such as the uniform multiplicity of ancestors and Welch indices, these algorithms only require matrix products and the transitive closure of binary relations to yield the calculation of reversible automata. The features, advantages and differences of these algorithms are described and results for reversible automata of 3, 4, 5 and 6 states are comprised.
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