Process versus Unfolding Semantics for Place/Transition Petri Nets
Process versus Unfolding Semantics for Place/Transition Petri Nets
In the last few years, the semantics of Petri nets has been investigated in several different ways. Apart from the classical "token game," one can model the behaviour of Petri nets via non-sequential processes, via unfolding constructions, which provide formal relationships between nets and domains, and via algebraic models, which view Petri nets as essentially algebraic theories whose models are monoidal categories. In this paper we show that these three points of view can be reconciled. In our formal development a relevant role is played by DecOcc, a category of occurrence nets appropriately decorated to take into account the history of tokens. The structure of decorated occurrence nets at the same time provides natural unfoldings for Place/Transition (PT) nets and suggests a new notion of processes, the decorated processes, which induce on Petri nets the same semantics as that of unfolding. In addition, we prove that the decorated processes of a net can be axiomatized as the arrows of a symmetric monoidal category which, therefore, provides the aforesaid unification.
petri nets non-sequential processes, petri nets unfoldings, petri nets semantics, models for concurrency, concurrency
171-210
Meseguer, J.
fdb4acf3-5cf5-440b-8618-8aeb9d0159d1
Montanari, U.
45418952-b856-4910-94c1-5ff3c7c19938
Sassone, V.
df7d3c83-2aa0-4571-be94-9473b07b03e7
1996
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.
(1996)
Process versus Unfolding Semantics for Place/Transition Petri Nets.
Theoretical Computer Science, 153 (1-2), .
Abstract
In the last few years, the semantics of Petri nets has been investigated in several different ways. Apart from the classical "token game," one can model the behaviour of Petri nets via non-sequential processes, via unfolding constructions, which provide formal relationships between nets and domains, and via algebraic models, which view Petri nets as essentially algebraic theories whose models are monoidal categories. In this paper we show that these three points of view can be reconciled. In our formal development a relevant role is played by DecOcc, a category of occurrence nets appropriately decorated to take into account the history of tokens. The structure of decorated occurrence nets at the same time provides natural unfoldings for Place/Transition (PT) nets and suggests a new notion of processes, the decorated processes, which induce on Petri nets the same semantics as that of unfolding. In addition, we prove that the decorated processes of a net can be axiomatized as the arrows of a symmetric monoidal category which, therefore, provides the aforesaid unification.
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Published date: 1996
Keywords:
petri nets non-sequential processes, petri nets unfoldings, petri nets semantics, models for concurrency, concurrency
Organisations:
Web & Internet Science
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Local EPrints ID: 261818
URI: http://eprints.soton.ac.uk/id/eprint/261818
ISSN: 0304-3975
PURE UUID: fcf83f82-df99-40e8-9a6a-9357f945eb2c
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Date deposited: 26 Jan 2006
Last modified: 10 Sep 2024 01:40
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Author:
J. Meseguer
Author:
U. Montanari
Author:
V. Sassone
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