In: IEICE Trans. on Fundamentals in Electronics, Communications and Computer Science, Vol. 81-A, No. 4, pages 628-634. 1998.
Abstract: A formal necessary and sufficient condition on the general Petri net reachability problem is presented by eliminating all spurious solutions among known nonnegative integer solutions of state equation and unifying all the causes of those spurious solutions into a maximal-strongly-connected and siphon-and-trap subnet. This result is based on the decomposition of a given net and the concepts of ``no immature siphon at the reduced initial marking'' and ``no immature trap at the reduced end marking'' on the subnet, which are both extended from ``no token-free siphon at the initial marking'' and ``no token-free trap at the end marking'' on the net, respectively, which have been both effectively, explicitly or implicitly, used in the well-known fundamental and simple subclasses.
Keywords: Petri nets, immature siphons, immature traps, net decomposition, reachability, spurious solutions, state equation.