A weakly universal weighted cellular automaton in the heptagrid with 6 states
Abstract
In this paper we prove that there is a weakly universal weighted cellular automaton in the heptagrid, the tessellation {7,3} of the hyperbolic plane, with 6 states. The present paper improves the same result deposited on arXiv:2301.10691v1 and also arXiv:2301.10691v2. In the deposited papers, the result is proved with 7 states. In the present replacement the number of states is reduced to 6. Such a reducing is not trivial and requires substantial changes in the implementation. The maximal weight is now 34, a very strong reduction with the best result with 7 states. Also, the table has 137 entries, signifcantly less than the 160 entries of the paper with 7 states. The reduction is obtained by a new implementation of the tracks which play a key role as far as without tracks there is no computational universality result.
Keywords
Cite
@article{arxiv.2301.10691,
title = {A weakly universal weighted cellular automaton in the heptagrid with 6 states},
author = {Maurice Margenstern},
journal= {arXiv preprint arXiv:2301.10691},
year = {2023}
}
Comments
37 pages, 21 figures. arXiv admin note: substantial text overlap with arXiv:2108.13094, arXiv:2104.01561, arXiv:2107.04843