A study is made of the stability of steady states of probabilistic cellular automata defined on countable graphs. An important class of states are the quasi-deterministic states in which the "error sets" are confined to small isolated sets in the graph. In particular, quasi-deterministic states of majority vote systems defined on trees are discussed and criteria for their existence and stability are obtained.

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Persistent URL dx.doi.org/10.1016/S0019-9958(77)80006-5
Journal Information and Control
Dawson, D.A. (1977). Stable states of probabilistic cellular automata. Information and Control, 34(2), 93–106. doi:10.1016/S0019-9958(77)80006-5