  The hopping motion of classical particles on a chain coupled to reservoirs at
both ends is studied for parallel dynamics with arbitrary probabilities. The
stationary state is obtained in the form of an alternating matrix product. The
properties of one- and two-dimensional representations are studied in detail
and a general relation of the matrix algebra to that of the sequential limit is
found. In this way the general phase diagram of the model is obtained. The
mechanism of the sequential limit, the formulation as a vertex model and other
aspects are discussed.
