On the Semantics of Petri Nets

Meseguer, J., Montanari, U. and Sassone, V. (1992) On the Semantics of Petri Nets. In, 3rd International Conference on Concurrency Theory, CONCUR 92. Springer, 286-301.


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Petri Place/Transition (PT) nets are one of the most widely used models of concurrency. However, they still lack, in our view, a satisfactory semantics: on the one hand the ``token game'' is too intensional, even in its more abstract interpretations in term of nonsequential processes and monoidal categories; on the other hand, Winskel's basic unfolding construction, which provides a coreflection between nets and finitary prime algebraic domains, works only for safe nets. In this paper we extend Winskel's result to PT nets. We start with a rather general category {PTNets} of PT nets, we introduce a category {DecOcc} of decorated (nondeterministic) occurrence nets and we define adjunctions between {PTNets} and {DecOcc} and between {DecOcc} and {Occ}, the category of occurrence nets. The role of {DecOcc} is to provide natural unfoldings for PT nets, i.e. acyclic safe nets where a notion of family is used for relating multiple instances of the same place. The unfolding functor from {PTNets} to {Occ} reduces to Winskel's when restricted to safe nets, while the standard coreflection between {Occ} and {Dom}, the category of finitary prime algebraic domains, when composed with the unfolding functor above, determines a chain of adjunctions between {PTNets} and {Dom}.

Item Type: Conference or Workshop Item (Paper)
ISBNs: 3540558225
Keywords: petri nets semantics, petri nets unfoldings
Divisions: Faculty of Physical Sciences and Engineering > Electronics and Computer Science > Web & Internet Science
ePrint ID: 261942
Date :
Date Event
Date Deposited: 12 Feb 2006
Last Modified: 31 Mar 2016 14:04
Further Information:Google Scholar
URI: http://eprints.soton.ac.uk/id/eprint/261942

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