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Generative families of positive invariants in coloured nets sub-classes

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Date
1993
Notes
La version de travail de cette communication attachée est intitulée "Computation of Generative Families of Positive Semi-Flows in Two Types of Coloured Nets".
Collection title
Lecture Notes in Computer Science
Collection Id
674
Dewey
Informatique générale
Sujet
Coloured nets; structural analysis; positive flows computation; Farkas' algorithm
DOI
http://dx.doi.org/10.1007/3-540-56689-9_39
Conference name
12th International Conference on applications and theory of Petri nets (APN 1991)
Conference date
06-1991
Conference city
Gjern
Conference country
Danemark
Book title
Advances in Petri Nets 1993, Papers from the 12th International Conference on Applications and Theory of Petri Nets, Gjern, Denmark, June 1991
Author
Rozenberg, Grzegorz
Publisher
Springer
Publisher city
Berlin
Year
1993
Pages number
457
ISBN
978-3-540-56689-2
Book URL
http://dx.doi.org/10.1007/3-540-56689-9
URI
https://basepub.dauphine.fr/handle/123456789/5248
Collections
  • LAMSADE : Publications
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Author
Peyre, Jean-François
Couvreur, Jean-Michel
Haddad, Serge
Type
Communication / Conférence
Item number of pages
51-70
Abstract (EN)
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.X 1 = ... = A.X n 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.

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