  We consider networks of finite-state machines having local transitions
conditioned by the current state of other automata. In this paper, we depict a
reduction procedure tailored for a given reachability property of the form
``from global state s there exists a sequence of transitions leading to a state
where an automaton g is in a local state T'. By exploiting a causality analysis
of the transitions within the individual automata, the proposed reduction
removes local transitions while preserving all the minimal traces that satisfy
the reachability property. The complexity of the procedure is polynomial in the
total number of local states and transitions, and exponential in the number of
local states within one automaton. Applied to automata networks modelling
dynamics of biological systems, we observe that the reduction shrinks down
significantly the reachable state space, enhancing the tractability of the
model-checking of large networks.
