Computer Science – Formal Languages and Automata Theory
Scientific paper
2012-02-08
Computer Science
Formal Languages and Automata Theory
83 pages, 38 figures, 53 tables. arXiv admin note: text overlap with arXiv:0903.2108
Scientific paper
In this paper, we construct a family of weakly universal rotation invariant cellular automaton for all grids $\{p,3\}$ of the hyperbolic plane for $p\geq 13$. The scheme is general for $p\geq 17$ and for $13\leq p<17$, we give such a cellular automaton for $p=13$, which is enough. Also, an important property of this family is that the set of cells of the cellular automaton which are subject to changes is actually a planar set. The problem for $p<13$ for a truly planar construction is still open. The best result, for $p=7$, is four states and was obtained by the same author.
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