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On the semantics of place/transition Petri nets

Published online by Cambridge University Press:  01 August 1997

JOSÉ MESEGUER ,
UGO MONTANARI  and
VLADIMIRO SASSONE
JOSÉ MESEGUER
Affiliation:
SRI International, Menlo Park, California 94025
UGO MONTANARI
Affiliation:
Dipartimento di Informatica, Università di Pisa, Italy
VLADIMIRO SASSONE
Affiliation:
Dipartimento di Informatica, Università di Pisa, Italy
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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 to relate 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.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 7 , Issue 4 , August 1997 , pp. 359 - 397
Copyright
1997 Cambridge University Press

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Footnotes

Research partially supported by ESPRIT Basic Research Action CEDISYS. The first and the third authors have been supported by the US Office of Naval Research Contracts N00014-88-C-0618 and N00014-92-C-0158. The third author also acknowledges funding from EU Human Capital and Mobility grant ERBCHBGCT920005 and from BRICS Basic Research in Computer Science, Centre of the Danish National Research Foundation.