All Fundamental Particular Solutions are Needed to Express an Arbitrary Firing Count Vector in Petri Nets
Akira Muraya · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences · 2005
For fixed initial and destination states (i.e., markings), M 0 and M d , there exist generally infinite firing count vectors in a Petri net. In this letter, it is shown that all fundamental particular solutions as well as all minimal T-invariants w.r.t. firing count vectors are needed to express an arbitrary firing count vector for the fixed M 0 and M d . An algorithm for finding a special firing count vector which is expressed by using the only one specified fundamental particular solution is also given.