  The explicit biorthogonalization method, developed in [arXiv:1701.00018] for
continuous time TASEP, is generalized to a broad class of determinantal
measures which describe the evolution of several interacting particle systems
in the KPZ universality class. The method is applied to sequential and parallel
update versions of each of the four variants of discrete time TASEP (with
Bernoulli and geometric jumps, and with block and push dynamics) which have
determinantal transition probabilities; to continuous time PushASEP; and to a
version of TASEP with generalized update. In all cases, multipoint distribution
functions are expressed in terms of a Fredholm determinant with an explicit
kernel involving hitting times of certain random walks to a curve defined by
the initial data of the system. The method is further applied to systems of
interacting caterpillars, an extension of the discrete time TASEP models which
generalizes sequential and parallel updates.
