一句话：提出 Σ-网统一 Petri 网及其变体，并用左伴随函子刻画其执行语义与相互嵌入。
本文旨在为 Petri 网及其多种变体（如 pre-net 和 Kock 的 whole-grain Petri 网）提供统一的范畴框架。作者引入 Σ-网这一较少研究的模型，使每个变迁可以精细地按集合式或个体式 token 哲学执行。通过左伴随函子，pre-net、Σ-网（含 whole-grain Petri 网）和 Petri 网分别生成严格幺半范畴、对称严格幺半范畴和交换幺半范畴。文中还构造了这些网范畴之间的伴随关系，并证明各类网均可嵌入 Σ-网，且该嵌入与执行语义一致。
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 原文 ·
@inproceedings{paperbot6234,
title = {Categories of Nets},
author = {John C. Baez and Fabrizio Genovese and Jade Master and Michael Shulman},
booktitle = {LICS},
year = {2021},
doi = {10.1109/lics52264.2021.9470566}
}