Cellular Automata on Racks
Group Theory
2018-08-01 v1
Abstract
In this paper we initiate the study of cellular automata on racks. A rack is a set with a self-distributive binary operation. The rack acts on the set of configurations from to a set . We define the cellular automaton on a rack as a continuous self-mapping of defined from a system of local rules. The cellular automata on racks do not commute with the rack action. However, under certain conditions, the cellular automata on racks do commute with the rack action. We study the equivariant cellular automta (which commute with the rack action) on racks and prove several properties of these cellular automata including the analog of Curtis-Hedlund's theorem for cellular automata on groups.
Cite
@article{arxiv.1807.11630,
title = {Cellular Automata on Racks},
author = {Naqeeb ur Rehman and Muhammad Khuram Shahzad},
journal= {arXiv preprint arXiv:1807.11630},
year = {2018}
}