Behaviour of elementary net systems
Advances in Petri nets 1986, part I on Petri nets: central models and their properties
Information and Computation
Selected papers of the Second Workshop on Concurrency and compositionality
The synthesis problem of Petri nets
Acta Informatica
A Uniform Approach to Petri Nets
Foundations of Computer Science: Potential - Theory - Cognition, to Wilfried Brauer on the occasion of his sixtieth birthday
Contextual Occurence Nets and Concurrent Constraint Programming
Proceedings of the International Workshop on Graph Transformations in Computer Science
Lectures on Petri Nets I: Basic Models, Advances in Petri Nets, the volumes are based on the Advanced Course on Petri Nets
Reasoning about Algebraic Generalisation of Petri Nets
Proceedings of the 20th International Conference on Application and Theory of Petri Nets
Petri Nets over Partial Algebra
Unifying Petri Nets, Advances in Petri Nets
On Concurrent Realization of Reactive Systems and Their Morphisms
Unifying Petri Nets, Advances in Petri Nets
Region based synthesis of P/T-nets and its potential applications
ICATPN'00 Proceedings of the 21st international conference on Application and theory of petri nets
Parameterized Net Classes: A Uniform Approach to Petri Net Classes
Unifying Petri Nets, Advances in Petri Nets
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Starting from the algebraic view of Petri nets as monoids (as advocated by Meseguer and Montanari in [MM90]) we present the marking graphs of place transition nets as free monoid graphs and the marking graphs of specific elementary nets as powerset graphs. These are two important special cases of a general categorical version of Petri nets based on a functor M, called M-nets. These nets have a compositional marking graph semantics in terms of F-graphs, a generalization of free monoid and powerset graphs. Moreover we are able to characterize those F-graphs, called reflexive F-graphs, which are realizable by corresponding M-nets. The main result shows that the behavior and realization constructions are adjoint functors leading to an equivalence of the categories MNet of M-nets and RFGraph of reflexive F-graphs. This implies that the behavior construction preserves colimits so that the marking graph construction using F-graphs is compositional.In addition to place transition nets and elementary nets we provide other interesting applications of M-nets and F-graphs. Moreover we discuss the relation to classical elementary net systems. The behavior and realization constructions we have introduced are compatible with corresponding constructions for elementary net systems (with initial state) and elementary transition systems in the sense of [NRT92].