  We propose a method to count the number of reachable markings of a Petri net
without having to enumerate these rst. The method relies on a structural
reduction system that reduces the number of places and transitions of the net
in such a way that we can faithfully compute the number of reachable markings
of the original net from the reduced net and the reduction history. The method
has been implemented and computing experiments show that reductions are eective
on a large benchmark of models.
