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.