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5-State Rotation-Symmetric Number-Conserving Cellular Automata are not Strongly Universal

We study two-dimensional rotation-symmetric number-conserving cellular automata working on the von Neumann neighborhood (RNCA). It is known that such automata with 4 states or less are trivial, so we investigate the possible rules with 5 states. We give a full characterization of these automata and show that they cannot be strongly Turing universal. However, we give example of constructions that allow to embed some boolean circuit elements in a 5-states RNCA.

preprint2016arXivOpen access
Katsunobu ImaiHisamichi IshizakaVictor Poupet
Formal Languages and Automata Theorynlin.CG
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Katsunobu ImaiHisamichi IshizakaVictor Poupet

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