Universality of One-Dimensional Reversible and Number-Conserving Cellular Automata

Kenichi Morita
(Hiroshima University, Japan)

We study one-dimensional reversible and number-conserving cellular automata (RNCCA) that have both properties of reversibility and number-conservation. In the case of 2-neighbor RNCCA, García-Ramos proved that every RNCCA shows trivial behavior in the sense that all the signals in the RNCCA do not interact each other. However, if we increase the neighborhood size, we can find many complex RNCCAs. Here, we show that for any one-dimensional 2-neighbor reversible partitioned CA (RPCA) with s states, we can construct a 4-neighbor RNCCA with 4s states that simulates the former. Since it is known that there is a computationally universal 24-state 2-neighbor RPCA, we obtain a universal 96-state 4-neighbor RNCCA.

In Enrico Formenti: Proceedings 18th international workshop on Cellular Automata and Discrete Complex Systems and 3rd international symposium Journées Automates Cellulaires (AUTOMATA&JAC 2012), La Marana, Corsica, September 19-21, 2012, Electronic Proceedings in Theoretical Computer Science 90, pp. 142–150.
Published: 13th August 2012.

ArXived at: http://dx.doi.org/10.4204/EPTCS.90.12 bibtex PDF
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