Expansive automata networks

Abstract

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Intrinsic universality in automata networks I: Families and simulations

“…such that λ i (x i , m((x| N (i) ) ρ )) = j m i,j x j . One of the most studied case is when Q is actually endowed with a field structure, in particular in the Boolean case where the choice of coefficient is unique and the automata network is entirely determined by the graph G. Note however, that non-Boolean finite fields are worth studying since the graphs for which a given global property holds might differ from the Boolean case (see for instance Proposition 3.5 and Corollary 4.3 of [44]). A very well studied example of a network in this family is the case of additive elementary cellular automata.…”