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arXiv · 2301.10691

A weakly universal weighted cellular automaton in the heptagrid with 6 states

Maurice Margenstern
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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.

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Maurice Margenstern. 2023-01-25. A weakly universal weighted cellular automaton in the heptagrid with 6 states. https://arxiv.org/abs/2301.10691

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