Revisiting the algebra of Petri net processes under the collective token philosophy

  • Authors:

  • Amin Coja-Oghlan;Mark-Oliver Stehr

  • 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

  • Venue:
  • Fundamenta Informaticae - Concurrency specification and programming
  • Year:
  • 2002

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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.