Multidimensional cellular automata and generalization of Fekete's lemma

Abstract

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. © 2008 Discrete Mathematics and Theoretical Computer Science (DMTCS).