One-Dimensional Automaton Networks with Monotonic Local Interaction

The behavior of strings that are infinite in both directions and consist of identical finite automata is investigated. The states of a finite number of adjacent automata provide the input for each automaton. The states of a finite number of adjacent automata provide the input for each automaton. Monotonic interaction of automata is considered. An effective means of predicting the following two aspects of the behavior of such systems is given; a) are they “wash-out” systems and b) how do the states of systems of automata with long initial files vary as $t\to\infty$.