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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.
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Silvio Capobianco. Multidimensional cellular automata and generalization of Fekete's lemma. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2008, 10 (3), pp.95--104. ⟨hal-00972330⟩

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