Abstract: Invariants and state equations play an important role in Petri net analysis. New methods for solving the invariants and state equations of Petri Nets are developed in this paper. Also, the general solutions of the firing vector in the state equation of a Petri net are proposed. And all of these approaches are derived from the full rank decomposition technique for the incidence matrix. Finally, the esistence condition for the integral solution of state equations is discussed, which, as a matter of fact, is a necessary condition for reachability and is significant for the analysis of Petri nets.

Key words: Petri nets, invariant, state equation, full rank decomposition