Affiliations: Humboldt-Universität zu Berlin, Institut für
Informatik, Unter den Linden 6, 10099 Berlin, Germany | Universität Hamburg, Fachbereich Informatik, Arbeitsbereich Theoretische Grundlagen, Vogt-Kölln-Str. 30, 22527 Hamburg, Germany
Abstract: 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.
