Abstract
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.
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