The Block Neighborhood
Abstract
We define the block neighborhood of a reversible CA, which is related both to its decomposition into a product of block permutations and to quantum computing. We give a purely combinatorial characterization of the block neighborhood, which helps in two ways. First, it makes the computation of the block neighborhood of a given CA relatively easy. Second, it allows us to derive upper bounds on the block neighborhood: for a single CA as function of the classical and inverse neighborhoods, and for the composition of several CAs. One consequence of that is a characterization of a class of "elementary" CAs that cannot be written as the composition of two simpler parts whose neighborhoods and inverse neighborhoods would be reduced by one half.
Cite
@article{arxiv.1012.1334,
title = {The Block Neighborhood},
author = {Pablo Arrighi and Vincent Fabrice Nesme},
journal= {arXiv preprint arXiv:1012.1334},
year = {2010}
}
Comments
Journ\'ees Automates Cellulaires 2010, Turku : Finland (2010)