  The exact stationary state of an asymmetric exclusion process with fully
parallel dynamics is obtained using the matrix product Ansatz. We give a simple
derivation for the deterministic case by a physical interpretation of the
dimension of the matrices. We prove the stationarity via a cancellation
mechanism and by making use of an explicit representation of the matrix algebra
we easily find closed expressions for the correlation functions in the general
probabalistic case. Asymptotic expressions, obtained by making use of earlier
results, allow us to derive the exact phase diagram.
