2007/07/26 by Silvio Capobianco, Capobianco, Silvio · 1 citation
Mathematics · #00A05 #37B15 #Dynamical Systems (math.DS) #FOS: Mathematics #General Mathematics (math.GM) #math.DS #math.GM #msc:00A05 #msc:37B15
paper · pdf · doi:10.48550/arxiv.0707.3903
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
Fekete's lemma is a well known combinatorial result on number sequences: we extend it to functions defined on d-tuples of integers. As an application of the new variant, we show that nonsurjective d-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.