Mathematical methods for calculating invariants in Petri nets

Abstract

A computationally feasible procedure for the generation of all invariants satisfying a given homogenous linear Diophantine system Cx = 0 is presented, where C is the flow matrix of an associated P/T net. The computation will be considered on five levels. In order to generate all invariants the introduction of some new concepts (Q+-generators, IN-generators) is required. Using geometrical aspects a short description of the new concepts with a new algorithm is shown. The efficiency of our methods is demonstrated by an application.