Green functions for the TASEP with sublattice parallel update

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.