Brute-force model-checking consists in exhaustive exploration of the state-space of a Petri net, and meets the dreaded state-space explosion problem.
In contrast, this paper shows how to solve model-checking problems using a combination of techniques that stay in complexity proportional to the size of the net structure rather than to the state-space size.
We combine an SMT based over-approximation to prove that some behaviors are unfeasible, an under-approximation using memory-less sampling of runs to find witness traces or counter-examples, and a set of structural reduction rules that can simplify both the system and the property.
This approach was able to win by a clear margin the model-checking contest 2020 for reachability queries as well as deadlock detection, thus demonstrating the practical effectiveness and general applicability of the system of rules presented in this paper.

Comment: Extended Journal version of ICATPN 2020 paper published in Fundamenta Informaticae