Computation of Generative Families of Positive Semi-flows in Two Types of Coloured Nets

It is well known that a generative family of positive flows provides a more accurate information than a generative family of ordinary ones. For instance with the help of positive flows one can decide the structural boundness of the nets and detect 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. First of all, we show that these two computations are based on the resolution of the parametrized equation A.X1=A.X2=...=A.Xn where A is a matrix and Xi, the unknowns are vectors. Thus an algorithm is presented to solve this equation and at last we show how this algorithm can be used to compute the generative family of semi-flows in the unary regular nets and unary Predicate/Transition nets.