A Categorical Semantics for Hierarchical Petri Nets

Fabrizio Romano Genovese
(University of Pisa, Statebox)
Jelle Herold
Fosco Loregian
(Tallinn University of Technology)
Daniele Palombi
(Sapienza University of Rome)

We show how a particular variety of hierarchical nets, where the firing of a transition in the parent net must correspond to an execution in some child net, can be modelled utilizing a functorial semantics from a free category – representing the parent net – to the category of sets and spans between them. This semantics can be internalized via Grothendieck construction, resulting in the category of executions of a Petri net representing the semantics of the overall hierarchical net. We conclude the paper by giving an engineering-oriented overview of how our model of hierarchical nets can be implemented in a transaction-based smart contract environment.

In Berthold Hoffmann and Mark Minas: Proceedings Twelfth International Workshop on Graph Computational Models (GCM 2021), Online, 22nd June 2021, Electronic Proceedings in Theoretical Computer Science 350, pp. 51–68.
Published: 21st December 2021.

ArXived at: https://dx.doi.org/10.4204/EPTCS.350.4 bibtex PDF
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