Strongly autonomous behaviors over finite rings

We give a new characterization of strong autonomy of linear shift-invariant multidimensional behaviors over finite rings. Unlike earlier descriptions of the concept, the new notion coincides directly with known results on past-determinedness when applied to the special case of one-dimensional systems of this type. This is a first step towards formulating a well-posed initial value problem for systems of partial difference equations over finite rings, a question of interest from the point of view of convolutional coding theory.