is updated during the first step and the other pairs during the second step.

We stress that the method can also be used to define integrable discrete time Floquet dynamics for quantum spin chains by simply requiring the evolution operator to be unitary (instead of being Markovian) [@ProsenVZ]. We show the efficiency of this general framework by introducing new integrable discrete time generalized exclusion processes, where several particles are allowed to occupy the same site instead of a single particle in usual exclusion processes. As far as we know, these are the first examples of integrable generalized exclusion processes with open boundary conditions.

An advantage of the discrete time picture is that the probabilities ${{\langle\cC'|}}M^n{{|\cC\rangle}}$, *i.e* the matrix elements of the propagator of the model (where ${{|\cC\rangle}}$ is the initial configuration, $M$ is the Markov matrix and ${{\langle\cC'|}}$ is the final configuration), can be easily interpreted as (equilibrium) partition functions of vertex models in $d=1+1$ dimensions for which a lot of techniques have already been developed. It should be possible to compute such probabilities in some specific cases for models defined through our formalism.

The outline of the paper is the following. In section \[sec:integrable\_Floquet\] we introduce the transfer matrix 