Useful necessary and sufficient condition for reachability of extended marked graphs

In this paper, by using the state equation of a Petri net, we derived a necessary and sufficient condition for reachability of extended marked graphs (EMGs). In particular, these conditions can be checked easily because they are presented in terms of the initial token distribution, the final token distribution, and the net structure. Furthermore, by using this necessary and sufficient condition, we can derive also the necessary and sufficient condition for a behavioral trap in EMGs.