On radius 1 nontrivial reversible and number-conserving cellular automata

Abstract : Reversibility and number-conservation are widely studied physics-like constraints for cellular automata (CA). Although both seem to be 'natural' constraints for a CA, it was conjectured that one-dimensional reversible and number-conserving CA (RNCCA) only has a limited computing ability. Particularly in the case of radius 1/2 (2-neighbor), it was shown that the class of RNCCA is equal to a trivial class of CA, so called shift-identity product cellular automata (SIPCA). But recently it was also shown that a RNCCA of neighborhood size four is computation-universal. In this paper, we list radius 1 (3-neighbor) RNCCAs up to 4-state by exhaustive search. In contrast to the radius 1/2 case, there are three new types of nontrivial RNCCA rules in the case of 4-state. We also show that it is possible to compose new nontrivial RNCCAs by modifying a SIPCA even when the state number is larger than four.
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Communication dans un congrès
Reversible Computation, Jul 2012, Copenhagen, Denmark
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https://hal.archives-ouvertes.fr/hal-00826548
Contributeur : Bruno Martin <>
Soumis le : lundi 27 mai 2013 - 17:15:18
Dernière modification le : lundi 27 mai 2013 - 17:15:18

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  • HAL Id : hal-00826548, version 1

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Bruno Martin, R. Saito, Katsunobu Imai. On radius 1 nontrivial reversible and number-conserving cellular automata. Reversible Computation, Jul 2012, Copenhagen, Denmark. <hal-00826548>

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