Hack’s theorem (‘72)
Let N be a Free-Choice PN:
- N has a live and safe initial marking if and only if
- every MG reduction is strongly connected and not empty, and
the set of all reductions covers the net
- every SM reduction is strongly connected and not empty, and
the set of all reductions covers the net
Let m be a marking of N:
- m is safe if and only if
there exists an SM cover in which every component has exactly one token