1 research outputs found
Multidimensional cellular automata and generalization of Fekete's lemma
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.Comment: 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 0709.117