In: Proceedings of the 24th International Conference on Applications and Theory of Petri Nets (ICATPN 2003), Eindhoven, The Netherlands, June 23-27, 2003, pages 64-81. Volume 2679 of Lecture Notes in Computer Science / Wil M. P. van der Aalst and Eike Best (Eds.) --- Springer-Verlag, June 2003.
Abstract: We show how the firing rule of Petri nets relies on a residuation operation for the commutative monoid of natural numbers. On that basis we introduce closed monoidal structures which are residuated monoids. We identify a class of closed monoidal structures (associated with a family of idempotent group dioids) for which one can mimic the token game of Petri nets to define the behaviour of these generalized Petri nets whose flow relations and place contents are valued in the closed monoidal structure.
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