  We consider the totally asymmetric simple exclusion process (TASEP) in
discrete time with the sublattice parallel dynamics describing particles moving
to the right on the one-dimensional infinite chain with equal hoping
probabilities. Using sequentially two mappings, we show that the model is
equivalent to the TASEP with the backward-ordered sequential update in the case
when particles start and finish their motion not simultaneously. The Green
functions are obtained exactly in a determinant form for different initial and
final conditions.
