A Generalised Model of Hierarchical Nets

A Categorical Semantics for Hierarchical Petri Nets

We show how a particular flavor 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 hiearchic nets can be implemented in a transaction-based smart contract environment.We show how a particular flavor 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 a functorial semantics from a free category-representing the parent net-to the category of sets and spans between them.We conclude the paper by giving an engineering-oriented overview of how our model of hiearchic nets can be implemented in a transaction-based smart contract environment.