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Categories of Nets

Baez, John C. ; Genovese, Fabrizio ; Master, Jade ; Shulman, Michael

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 2021, p.1-13

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Título:
Categories of Nets
Autor: Baez, John C. ; Genovese, Fabrizio ; Master, Jade ; Shulman, Michael
Assuntos: Computer science ; Petri nets ; Semantics
É parte de: 2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 2021, p.1-13
Descrição: 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.
Editor: IEEE
Idioma: Inglês

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