On the Semantics of Place/Transition Petri Nets
On the Semantics of Place/Transition Petri Nets
Place/Transition (PT) Petri 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 terms 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; moreover, 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, petri nets unfoldings, petri nets processes, categorical semantics
359-397
Meseguer, J.
fdb4acf3-5cf5-440b-8618-8aeb9d0159d1
Montanari, U.
45418952-b856-4910-94c1-5ff3c7c19938
Sassone, V.
df7d3c83-2aa0-4571-be94-9473b07b03e7
1997
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.
(1997)
On the Semantics of Place/Transition Petri Nets.
Mathematical Structures in Computer Science, 7, .
Abstract
Place/Transition (PT) Petri 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 terms 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; moreover, 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.
Text
petri-MSCS.pdf
- Other
More information
Published date: 1997
Keywords:
petri nets, petri nets unfoldings, petri nets processes, categorical semantics
Organisations:
Web & Internet Science
Identifiers
Local EPrints ID: 261821
URI: http://eprints.soton.ac.uk/id/eprint/261821
PURE UUID: bd2f53f9-1366-43bb-b1d0-2448f09e7968
Catalogue record
Date deposited: 26 Jan 2006
Last modified: 10 Sep 2024 01:40
Export record
Contributors
Author:
J. Meseguer
Author:
U. Montanari
Author:
V. Sassone
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics