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Revisiting the Algebra of Petri Net Processes under the Collective Token Philosophy

Coja-Oghlan A., Stehr M-O.

Fundamenta Informaticae

2003

Vol. 54, nr 2,3

151-164

Revisiting the view of ``Petri nets as monoids'' suggested by Meseguer and Montanari, we give a direct proof of the well-known result that the class of Best/Devillers processes, which represents the behavior of Petri nets under the collective token semantics, has a sound and complete axiomatization in terms of symmetric monoidal categories. Using membership equational logic for the axiomatization, we prove the result by an explicit construction of a natural isomorphism between suitable functors. Our interest in the collective token semantics is motivated by earlier work on the use of rewriting logic as a uniform framework for different Petri net classes, especially including high-level Petri nets, where individuality of tokens can be already expressed at the system level.