Functorial Semantics for Petri Nets under the Individual Token Philosophy
Functorial Semantics for Petri Nets under the Individual Token Philosophy
Although the algebraic semantics of place/transition Petri nets under the collective token philosophy has been fully explained in terms of (strictly) symmetric (strict) monoidal categories, the analogous construction under the individual token philosophy is not completely satisfactory because it lacks universality and also functoriality. We introduce the notion of pre-net to recover these aspects, obtaining a fully satisfactory categorical treatment centered on the notion of adjunction. This allows us to present a purely logical description of net behaviours under the individual token philosophy in terms of theories and theory morphisms in partial membership equational logic, yielding a complete match with the theory developed by the authors for the collective token view of nets
petri nets processes, petri nets semantics, collective token philosophy, individual token philosophy
18 pp.
Bruni, R.
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Meseguer, J.
fdb4acf3-5cf5-440b-8618-8aeb9d0159d1
Montanari, U.
45418952-b856-4910-94c1-5ff3c7c19938
Sassone, V.
df7d3c83-2aa0-4571-be94-9473b07b03e7
1999
Bruni, R.
826fb8bb-f463-4440-8536-ef7f2da1a23a
Meseguer, J.
fdb4acf3-5cf5-440b-8618-8aeb9d0159d1
Montanari, U.
45418952-b856-4910-94c1-5ff3c7c19938
Sassone, V.
df7d3c83-2aa0-4571-be94-9473b07b03e7
Bruni, R., Meseguer, J., Montanari, U. and Sassone, V.
(1999)
Functorial Semantics for Petri Nets under the Individual Token Philosophy.
Category Theory and Computer Science, CTCS '99..
.
Record type:
Conference or Workshop Item
(Paper)
Abstract
Although the algebraic semantics of place/transition Petri nets under the collective token philosophy has been fully explained in terms of (strictly) symmetric (strict) monoidal categories, the analogous construction under the individual token philosophy is not completely satisfactory because it lacks universality and also functoriality. We introduce the notion of pre-net to recover these aspects, obtaining a fully satisfactory categorical treatment centered on the notion of adjunction. This allows us to present a purely logical description of net behaviours under the individual token philosophy in terms of theories and theory morphisms in partial membership equational logic, yielding a complete match with the theory developed by the authors for the collective token view of nets
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Published date: 1999
Venue - Dates:
Category Theory and Computer Science, CTCS '99., 1999-01-01
Keywords:
petri nets processes, petri nets semantics, collective token philosophy, individual token philosophy
Organisations:
Web & Internet Science
Identifiers
Local EPrints ID: 261958
URI: http://eprints.soton.ac.uk/id/eprint/261958
PURE UUID: 3f277513-2bb4-49fa-ba7b-319b5145bd35
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Date deposited: 13 Feb 2006
Last modified: 10 Sep 2024 01:40
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Contributors
Author:
R. Bruni
Author:
J. Meseguer
Author:
U. Montanari
Author:
V. Sassone
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