Categories of nets

JC Baez, F Genovese, J Master… - 2021 36th Annual ACM …, 2021 - ieeexplore.ieee.org
We present a unified framework for Petri nets and various variants, such as pre-nets and
Kock's whole-grain Petri nets. Our framework is based on a less well-studied notion that we …

Bunched logics: a uniform approach

SR Docherty - 2019 - discovery.ucl.ac.uk
Bunched logics have found themselves to be key tools in modern computer science, in
particular through the industrial-level program verification formalism Separation Logic …

Compositional cyber-physical systems theory

G Bakirtzis - arXiv preprint arXiv:2109.04858, 2021 - arxiv.org
This dissertation builds a compositional cyber-physical systems theory to develop concrete
semantics relating the above diverse views necessary for safety and security assurance. In …

Petri nets based on Lawvere theories

J Master - Mathematical Structures in Computer Science, 2020 - cambridge.org
We give a definition of Q-net, a generalization of Petri nets based on a Lawvere theory Q, for
which many existing variants of Petri nets are a special case. This definition is functorial with …

Yoneda hacking: The algebra of attacker actions

G Bakirtzis, F Genovese, CH Fleming - ACM Transactions on Cyber …, 2022 - dl.acm.org
Our work focuses on modeling the security of systems from their component-level designs.
Towards this goal, we develop a categorical formalism to model attacker actions. Equipping …

A categorical semantics for hierarchical Petri nets

FR Genovese, J Herold, F Loregian… - arXiv preprint arXiv …, 2021 - arxiv.org
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 …

Computational petri nets: Adjunctions considered harmful

F Genovese, A Gryzlov, J Herold, M Perone… - arXiv preprint arXiv …, 2019 - arxiv.org
We review some of the endeavors in trying to connect Petri nets with free symmetric
monoidal categories. We give a list of requirement such connections should respect if they …

The mathematical specification of the statebox language

S Team, F Genovese, J Herold - arXiv preprint arXiv:1906.07629, 2019 - arxiv.org
This document defines the mathematical backbone of the Statebox programming language.
In the simplest way possible, Statebox can be seen as a clever way to tie together different …

A categorical semantics for guarded petri nets

F Genovese, DI Spivak - International Conference on Graph …, 2020 - Springer
We build on the correspondence between Petri nets and free symmetric strict monoidal
categories already investigated in the literature, and present a categorical semantics for …

[PDF][PDF] Generalized petri nets

J Master - Available as arXiv, 1904 - math.ucr.edu
• PreNet is the category of pre-nets: Petri nets equipped with an ordering on the input and
output of each transition. These are are useful for generating processes in a way which …