6.6 Invariant analysis

The place or transition invariants of a net are the integer solutions of the homogenous system of linear equations $x\cdot C=0$ or $C\cdot y=0$, respectively, where C is the incidence matrix of the net; they are also called P- or T-invariants [Sta90, chapter 11 (110-122)]. The components of P-invariants are interpreted as weights of the respective place. The weighted amount of tokens is invariant with respect to firing. The components of T-invariants can be interpreted as firing numbers of the respective transition (negative values correspond to the reverse firing). Firing all transitions as many times as their firing number indicates leads to the same marking as before. Each bounded and live net has a T-invariant that is positive in all components - such a net is coverable with T-invariants.