  First passage under restart has recently emerged as a conceptual framework to
study various stochastic processes under restart mechanism. Emanating from the
canonical diffusion problem by Evans and Majumdar, restart has been shown to
outperform the completion of many first passage processes which otherwise would
take longer time to finish. However, most of the studies so far assumed
continuous time underlying first passage time processes and moreover considered
continuous time resetting restricting out restart processes broken up into
synchronized time steps. To bridge this gap, in this paper, we study discrete
space and time first passage processes under discrete time resetting in a
general set-up. We sketch out the steps to compute the moments and the
probability density function which is often intractable in the continuous time
restarted process. A criterion that dictates when restart remains beneficial is
then derived. We apply our results to a symmetric and a biased random walker
(RW) in one dimensional lattice confined within two absorbing boundaries.
Numerical simulations are found to be in excellent agreement with the
theoretical results. Our method can be useful to understand the effect of
restart on the spatiotemporal dynamics of confined lattice random walks in
arbitrary dimensions.
