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

Coja-Oghlan, A.; Stehr, M.-O.

In: Workshop Concurrency, Specification and Programming CS & P'2002, Berlin; Oct. 7-9, Vol. 1; H.D. Burkhard, L. Czaja, G. Lindemann, A. Skowron, P. Starke (Eds.), Informatik-Bericht Nr. 161, Humboldt-Univ. zu Berlin, pages 77-88. 7-9 October. 2002.

Abstract: Revisiting the view of "Petri nets ans 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 nets classes, especially including high-level Petri nets, where individuality of tokens can be already expressed at the system level.

Keywords: place/transition nets; Best/Devillers processes; collective token philosophy; membership equational logic; rewriting logic.

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