A Categorical Semantics for Hierarchical Petri Nets
Fabrizio Romano Genovese (University of Pisa, Statebox), Jelle Herold, (Statebox), Fosco Loregian (Tallinn University of Technology), Daniele, Palombi (Sapienza University of Rome)
TL;DR
This paper introduces a categorical semantics framework for hierarchical Petri nets, enabling formal modeling of nested net executions and practical implementation in smart contract systems.
Contribution
It develops a functorial semantics approach for hierarchical Petri nets and demonstrates how to internalize this model using Grothendieck construction for execution analysis.
Findings
Formal semantics for hierarchical Petri nets established
Implementation approach for smart contract environments proposed
Framework facilitates analysis of nested net executions
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.
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