5-State Rotation-Symmetric Number-Conserving Cellular Automata are not Strongly Universal
Formal Languages and Automata Theory
2016-10-04 v1 Cellular Automata and Lattice Gases
Abstract
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.
Cite
@article{arxiv.1610.00333,
title = {5-State Rotation-Symmetric Number-Conserving Cellular Automata are not Strongly Universal},
author = {Katsunobu Imai and Hisamichi Ishizaka and Victor Poupet},
journal= {arXiv preprint arXiv:1610.00333},
year = {2016}
}