Reachability in Petri

The theory of Well Structured Transition Systems, (WSTS) allows the automatical verification of safety properties of infinite-state systems, such that parts of reachability sets can be finitely represented [7, 11, 10]. Termination, boundedness and coverability are decidable for WSTS [4, 5, 9]. As Petri nets are WSTS, the previous properties are decidable. For complete WSTS [10], the Karp and Miller procedure [13, 10] computes the finite set of maximal elements of the downward closure of the reachability set. This procedure logs a state space exploration of the reachability set with a finite tree allowing to decide some other reachability problems like the reccurent control-state reachability problem.The class of very-WSTS in which this procedure terminates has been determined very recently in [2] and, still, Petri nets are very-WSTS. When the Ideal Karp Miller algorithm terminates, LTL is decidable on very-WSTS under natural but new effective conditions that are also verified on Petri nets [2].