Property Checking for 1-Place-Unbounded Petri Nets

The reach ability tree for an unbounded net system is infinite. By using $\omega$ symbol to represent infinitely many markings, cover ability tree can provide a finite form. However, with too much information lost, it can not check properties such as reach ability, deadlock freedom, liveness, etc. In this paper, an improved reachability tree (IRT for short) is constructed to enrich the$\omega$ representation for 1-place-unbounded nets. Based on the tree containing exactly all the reachable markings, an algorithm is proposed to check liveness of the system.