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Network Models from Petri Nets with Catalysts | | John C. Baez
; John Foley
; Joe Moeller
; | | Date: |
7 Apr 2019 | | Abstract: | Petri networks and network models are two frameworks for the compositional
design of systems of interacting entities. Here we show how to combine them
using the concept of a "catalyst": an entity that is neither destroyed nor
created by any process it engages in. In a Petri net, a place is a catalyst if
its in-degree equals its out-degree for every transition. We show how a Petri
net with a chosen set of catalysts gives a network model. This network model
maps any list of catalysts from the chosen set to the category whose morphisms
are all the processes enabled by this list of catalysts. Applying the
Grothendieck construction, we obtain a category fibered over the category whose
objects are lists of catalysts. This category has as morphisms all processes
enabled by some list of catalysts. While this category has a symmetric monoidal
structure that describes doing processes in parallel, its fibers also have
non-symmetric monoidal structures that describe doing one process and then
another while reusing the catalysts. | | Source: | arXiv, 1904.3550 | | Services: | Forum | Review | PDF | Favorites | |
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