Dualities between Nets and Automata Induced by Schizophrenic Objects

Eric Badouel 1 Philippe Darondeau 1
1 MICAS - Modèles et implémentation des calculs syntaxiques
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires
Abstract : The so-called synthesis problem for nets, which consists in deciding whether a given graph is isomorphic to the case graph of some net, and then constructing the net, has been solved in the litterature for various types of nets, ranging from elementary nets to Petri nets. The common principle for the synthesis is the idea of regions in graphs, representing possible extensions of places in nets. When the synthesis problem has a solution, the set of regions viewed as properties of states provides a set-theoretic representation of the transition system. We show that such correspondences between nets and transition systems can be described as dualities induced by schizophrenic objects living in the corresponding categories, leading further the analogy with classical representation theorems. This gives us a means to describe uniformly previously known translations between nets and automata, and to compare on that basis the related categories of nets.
Type de document :
[Research Report] RR-2452, INRIA. 1995
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Contributeur : Rapport de Recherche Inria <>
Soumis le : mercredi 24 mai 2006 - 14:48:29
Dernière modification le : jeudi 11 janvier 2018 - 06:21:19
Document(s) archivé(s) le : dimanche 4 avril 2010 - 22:14:03



  • HAL Id : inria-00074223, version 1



Eric Badouel, Philippe Darondeau. Dualities between Nets and Automata Induced by Schizophrenic Objects. [Research Report] RR-2452, INRIA. 1995. 〈inria-00074223〉



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