Petri Net Models
R.J. van Glabbeek
and F.W. Vaandrager.
Petri net models for algebraic theories of concurrency.
In J.W. de Bakker, A.J. Nijman, and P.C. Treleaven, editors,
Proceedings PARLE conference, Eindhoven, Vol. II
259, pages 224-242. Springer-Verlag, 1987.
In this paper we discuss the issue of interleaving
semantics versus True concurrency in an algebraic setting.
We present various equivalence notions on Petri nets which
can be used in the construction of algebraic models:
A central role in the paper will be played by the notion of
real-time consistency. We show that, besides occurrence net
equivalence, none of the equivalences mentioned above
(including the partial order equivalences!) is real-time
consistent. Therefore we introduce the notion of
ST-bisimulation equivalence, which is real-time consistent.
Moreover a complete proof system will be presented for
those finite ST-bisimulation processes in which no action
can occur concurrently with itself.
the occurrence net equivalence of Nielsen, Plotkin and Winskel;
bisimulation equivalence, which leads to a model which
is isomorphic to the graph model of Baeten, Bergstra & Klop;
the concurrent bisimulation equivalence, which is also
described by Nielsen & Thiagarajan, and Goltz;
partial order equivalences which are inspired by work
of Pratt, and Boudol & Castellani.
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