  Unfoldings provide an efficient way to avoid the state-space explosion due to
interleavings of concurrent transitions when exploring the runs of a Petri net.
The theory of adequate orders allows one to define finite prefixes of
unfoldings which contain all the reachable markings. In this paper we are
interested in reachability of a single given marking, called the goal. We
propose an algorithm for computing a finite prefix of the unfolding of a 1-safe
Petri net that preserves all minimal configurations reaching this goal. Our
algorithm combines the unfolding technique with on-the-fly model reduction by
static analysis aiming at avoiding the exploration of branches which are not
needed for reaching the goal. We present some experimental results.
