Corpus ID: 125953510

# Generalized Petri Nets.

@article{Master2019GeneralizedPN,
title={Generalized Petri Nets.},
journal={arXiv: Category Theory},
year={2019}
}
• Published 19 April 2019
• Mathematics
• arXiv: Category Theory
We give a definition of $\mathsf{Q}$-$\mathsf{Net}$, a generalization of Petri nets based on a Lawvere theory $\mathsf{Q}$ for which many existing variants of Petri nets are a special case. This definition is functorial with respect to change in Lawvere theory, and we exploit this to explore the relationships between different kinds of $\mathsf{Q}$-nets. To justify our definition of $\mathsf{Q}$-net, we construct a family of adjunctions for each Lawvere theory explicating the way in which… Expand
6 Citations

#### Paper Mentions

Open Petri nets
• Computer Science, Mathematics
• Mathematical Structures in Computer Science
• 2020
Two forms of semantics for open Petri nets are described using symmetric monoidal double functors out of pen(Petri), including an operational semantics and a reachability semantics that simply says which markings of the outputs can be reached from a given marking of the inputs. Expand
Elements of Petri nets and processes
A formalism for Petri nets based on polynomial-style finite-set configurations and etale maps and an algebraic semantics in terms of free coloured props is presented: the Segal space of P-processes is shown to be the free coloured prop-in-groupoids on P. Expand
Network Models from Petri Nets with Catalysts
• Computer Science, Mathematics
• ArXiv
• 2019
This work shows how to combine Petri networks and network models using the concept of a "catalyst": an entity that is neither destroyed nor created by any process it engages in, which gives a network model. Expand
String Diagrams for Assembly Planning
• Computer Science, Engineering
• Diagrams
• 2020
This paper proposes CompositionalPlanning, a string diagram based framework for assembly planning where string diagrams and their compositional properties serve as the foundation for an engineering tool where CAD designs interact with planning and scheduling algorithms to automatically create high-quality assembly plans. Expand
A Categorical Semantics for Guarded Petri Nets
• Mathematics, Computer Science
• ICGT
• 2020
This work builds on the correspondence between Petri nets and free symmetric strict monoidal categories and shows how the guard semantics can be internalized in the net itself, using the Grothendieck construction. Expand

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