Reduction and covering of infinite reachability trees

We present a structure for transition systems with which the main decidability results on Petri nets can be generalized to structured transition systems. We define the reduced reachability tree of a structured transition system; it allows one to decide the finite reachability tree problem (also called the finite termination problem) and the finite reachability set problem. A general definition of the coverability set is given and the procedure of Karp and Miller is extended for wellstructured transition systems. We show then that the coverability problem is a decidable problem in the framework of well-structured transition systems. Finally, we introduce structured set of terminal states and we show that the finite reachability tree problem and the finite reachability set problem are decidable. Coverability is an open problem for structured transition systems with a structured set of terminal states.