Abstract
We study a class of discrete dynamical systems that is motivated by the generic structure of simulations. The systems consist of the following data: (a) a finite graph Y with vertex set {1,…, n} where each vertex has a binary state, (b) functions F i : F 2 n→ F 2 n and (c) an update ordering π. The functions F i update the binary state of vertex i as a function of the state of vertex i and its Y-neighbors and leave the states of all other vertices fixed. The update ordering is a permutation of the Y-vertices. By composing the functions F i in the order given by π one obtains the sequential dynamical system (S DS): [ F Y,π]= ∏ i=1 n F π(i) : F 2 n→ F 2 n. We derive a decomposition result, characterize invertible S DS and study fixed points. In particular we analyse how many different S DS that can be obtained by reordering a given multiset of update functions and give a criterion for when one can derive concentration results on this number. Finally, some specific S DS are investigated.
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