Categories of Nets

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 call Σ-nets, which allow fine-grained control over whether each transition behaves according to the collective or...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science s. 1 - 13
Hlavní autoři: Baez, John C., Genovese, Fabrizio, Master, Jade, Shulman, Michael
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: IEEE 29.06.2021
Témata:
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí: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 call Σ-nets, which allow fine-grained control over whether each transition behaves according to the collective or individual token philosophy. We describe three forms of execution semantics in which pre-nets generate strict monoidal categories, Σ-nets (including whole-grain Petri nets) generate symmetric strict monoidal categories, and Petri nets generate commutative monoidal categories, all by left adjoint functors. We also construct adjunctions relating these categories of nets to each other, in particular showing that all kinds of net can be embedded in the unifying category of Σ-nets, in a way that commutes coherently with their execution semantics.
DOI:10.1109/LICS52264.2021.9470566