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## Generative families of positive invariants in Coloured nets sub-classes.

Couvreur, J.M.;
Haddad, S.;
Peyre, J.F.
In:
Rozenberg, G.: *Lecture Notes in Computer Science, Vol. 674; Advances in Petri Nets 1993*, pages 51-70.
Springer-Verlag,
1993.
Third author's new name: Pradat-Peyre.

Abstract:
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 boundedness 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 colored
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 X_{1} = ... = A X_{n} where A is a
matrix, X_{i}, the unknown are vectors and n is the parameter.
Then we present an algorithm to solve this equation. At last we show how
this solution of the parametrized equation can be used to solve the
complete equations system for unary regular nets and unary
predicate/transition nets.

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