Classifications of Petri net transitions and their application to firing sequence and reachability problems

Introduces behavioral and structural classifications of transitions that are useful for finding "legal" transition sequences in Petri nets. Our classifications provide some useful information on whether or not firing a transition can lead to any token-free siphon (or deadlock) in a net. As an application, we consider the general reachability problem formulated in terms of nonnegative integer solutions of the state equation and their net representations, and show how proofs of existing reachability theorems can be simplified, and that they can be extended to a more general case.