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On the Semantics of Petri Nets

On the Semantics of Petri Nets
On the Semantics of Petri Nets
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}.
petri nets semantics, petri nets unfoldings
3-540-55822-5
286-301
Meseguer, J.
fdb4acf3-5cf5-440b-8618-8aeb9d0159d1
Montanari, U.
45418952-b856-4910-94c1-5ff3c7c19938
Sassone, V.
df7d3c83-2aa0-4571-be94-9473b07b03e7
Meseguer, J.
fdb4acf3-5cf5-440b-8618-8aeb9d0159d1
Montanari, U.
45418952-b856-4910-94c1-5ff3c7c19938
Sassone, V.
df7d3c83-2aa0-4571-be94-9473b07b03e7

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

Record type: Conference or Workshop Item (Paper)

Abstract

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}.

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More information

Published date: 1992
Venue - Dates: 3rd International Conference on Concurrency Theory, CONCUR 92., 1992-01-01
Keywords: petri nets semantics, petri nets unfoldings
Organisations: Web & Internet Science

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Local EPrints ID: 261942
URI: http://eprints.soton.ac.uk/id/eprint/261942
ISBN: 3-540-55822-5
PURE UUID: c3ff1abe-579f-4b77-8f0c-60f132f98ce5

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Date deposited: 12 Feb 2006
Last modified: 18 Jul 2017 08:56

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Contributors

Author: J. Meseguer
Author: U. Montanari
Author: V. Sassone

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