  The dynamical rules in auxiliary stochastic process that generates the biased
ensemble of rare events are non-local. For the systems with one type of
particle, it is shown that there are special cases for which the generators of
effective processes can include local interactions. In this paper we
investigate this possibility for a systems of classical particles with more
than one type of particle moving on a one-dimensional lattice with open
boundary conditions. Assuming that the interactions in the original process are
local and site-independent and also it is assumed that the particles have
hard-core interactions. We will show that under certain constraints on the
microscopic reaction rules, the stochastic generator of unconditioned process
can be local but site-dependent. As one examples, A-model with two species of
particles are presented and be investigated the constraints under which the
effective generators are local and site-dependent.
