A Categorical Semantics for Hierarchical Petri Nets
Category Theory
2021-12-22 v2 Distributed, Parallel, and Cluster Computing
Formal Languages and Automata Theory
Abstract
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.
Cite
@article{arxiv.2102.00096,
title = {A Categorical Semantics for Hierarchical Petri Nets},
author = {Fabrizio Romano Genovese and Jelle Herold and Fosco Loregian and Daniele Palombi},
journal= {arXiv preprint arXiv:2102.00096},
year = {2021}
}
Comments
In Proceedings GCM 2021, arXiv:2112.10217