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# Master--slave synchronization of affine cellular automaton pairs

• Necessary and sufficient conditions are given for master--slave synchronization of any pair of unidirectionally coupled one--dimensional affine cellular automata of rank one. In each case the synchronization condition is expressed in terms of the coupling and the arithmetic properties of the automaton local rule. The asymptotic behavior of finite length affine automata of rank one, subjected to Dirichlet boundary conditions, is shown to be equivalent to the synchronization problem.
Mathematics Subject Classification: 15A33, 37B15, 15A90.

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