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Reachability is one of the significant properties of Petri nets (PNs). For unbounded PNs, how to determine their reachability is an open issue. In this paper, we propose an algorithm that determines whether the reachability set of an unbounded PN is semilinear. Moreover, in the case that the unbounded PN has semilinear reachability set, the proposed algorithm can construct a new reachability tree (NRT) that exactly characterizes its reachability set. In addition, it can be decided based on NRT whether an unbounded PN suffers from deadlocks. The results are illustrated via examples.

An Algorithm of Recognizing Unbounded Petri Nets With Semilinear Reachability Sets and Constructing Their Reachability Trees