Corpus ID: 125953510

Generalized Petri Nets.

@article{Master2019GeneralizedPN,
  title={Generalized Petri Nets.},
  author={Jade Master},
  journal={arXiv: Category Theory},
  year={2019}
}
  • Jade Master
  • 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

Paper Mentions

Open Petri nets
  • J. Baez, Jade Master
  • Computer Science, Mathematics
  • Mathematical Structures in Computer Science
  • 2020
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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

References

SHOWING 1-10 OF 30 REFERENCES
Open Petri nets
  • J. Baez, Jade Master
  • Computer Science, Mathematics
  • Mathematical Structures in Computer Science
  • 2020
TLDR
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
On the Category of Petri Net Computations
  • V. Sassone
  • Mathematics, Computer Science
  • TAPSOFT
  • 1995
TLDR
This work identifies a coreflection right adjoint to \({\cal Q}\)[_] and characterize its replete image, thus yielding an axiomatization of the category of net computations. Expand
Petri Nets Are Monoids
TLDR
A formal basis for expressing the semantics of concurrent languages in terms of Petri nets is provided, and a new understanding of concurrency in Terms of algebraic structures over graphs and categories is provided. Expand
Strong Concatenable Processes: An Approach to the Category of Petri Net Computations
We introduce the notion of strong concatenable process for Petri nets as the least refinement of non-sequential (concatenable) processes which can be expressed abstractly by means of a functor Q[_]Expand
Functorial Models for Petri Nets
TLDR
The notion of pre-nets is introduced, obtaining a fully satisfactory categorical treatment, where the operational semantics of nets yields an adjunction, and since the universal property of adjunctions guarantees that colimit constructions on nets are preserved in the authors' algebraic models, the resulting semantic framework has good compositional properties. Expand
Lending Petri nets
TLDR
It is shown that provability in the logic corresponds to reachability of certain markings in nets, and that proof traces correspond to honored firing sequences in nets. Expand
Axiomatizing net computations and processes
TLDR
The diamond of the four categories gives a full account in algebraic terms of the relations between interleaving and partial ordering observations of place/transition net computations, providing a most concrete and a most abstract extremum, respectively. Expand
Executions in (Semi-)Integer Petri Nets are Compact Closed Categories
TLDR
This work uses compact closeness to infer that allowing negative tokens in a Petri net makes the causal relations between transition firings non-trivial, and this is used to model interesting phenomena in economics and computer science. Expand
An Axiomatization of the Algebra of Petri Net Concatenable Processes
TLDR
This paper gives a completely abstract characterization of the category of concatenable processes of N, thus yielding an axiomatic theory of the noninterleaving behaviour of Petri nets. Expand
Kommunikation mit Automaten
Diese Arbeit befasst sich mit den begrifflichen Grundlagen einer Theorie der Kommunikation. Die Aufgabe dieser Theorie soll es sein, moglichst viele Erscheinungen bei der Informationsubertragung undExpand
...
1
2
3
...