Multidimensional cellular automata and generalization of Fekete's lemma
General Mathematics
2008-06-17 v3 Dynamical Systems
Abstract
Fekete's lemma is a well known combinatorial result on number sequences: we extend it to functions defined on -tuples of integers. As an application of the new variant, we show that nonsurjective -dimensional cellular automata are characterized by loss of arbitrarily much information on finite supports, at a growth rate greater than that of the support's boundary determined by the automaton's neighbourhood index.
Keywords
Cite
@article{arxiv.0707.3903,
title = {Multidimensional cellular automata and generalization of Fekete's lemma},
author = {Silvio Capobianco},
journal= {arXiv preprint arXiv:0707.3903},
year = {2008}
}
Comments
6 pages, no figures, LaTeX. Improved some explanations; revised structure; added examples; renamed "hypercubes" into "right polytopes"; added references to Arratia's paper on EJC, Calude's book, Cook's proof of Rule 110 universality, and arXiv paper 0709.1173