Generative Families of Positive Invariants in Coloured Nets Sub-Classes

In Petri nets and high-level nets, positive flows provide additional informations to the ones given by the flows. For instance with the help of positive flows one decides the structural boundeness of the nets and one detects the structural implicit places. Up to now, no computation of positive flows has been developed for coloured nets. In this paper, we present a computation of positive flows for two basic families of coloured nets: unary regular nets and unary predicate/transition nets. At first we show that these two computations are reducible to the resolution of the parametrized equation A.X1 = ... = A.Xn where A is a matrix, Xi, the unknowns are vectors and n is the parameter. Then we present an algorithm to solve this equation. At last we show how the solutions of the parametrized equation can be used to solve the complete equations system for unary regular nets and unary predicate/transition nets.