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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Badouel, E., Chenou, J. (2003). Nets Enriched over Closed Monoidal Structures. In: van der Aalst, W.M.P., Best, E. (eds) Applications and Theory of Petri Nets 2003. ICATPN 2003. Lecture Notes in Computer Science, vol 2679. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44919-1_8
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DOI: https://doi.org/10.1007/3-540-44919-1_8
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