Abstract
AbstractWe 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 respect to change in Lawvere theory, and we exploit this to explore the relationships between different kinds of Q-nets. To justify our definition of Q-net, we construct a family of adjunctions for each Lawvere theory explicating the way in which Q-nets present free models of Q in Cat. This gives a functorial description of the operational semantics for an arbitrary category of Q-nets. We show how this can be used to construct the semantics for Petri nets, pre-nets, integer nets, and elementary net systems.
Publisher
Cambridge University Press (CUP)
Subject
Computer Science Applications,Mathematics (miscellaneous)
Reference27 articles.
1. Master, J. (2019). Generalized petri nets. The n-Category Café. Available at https://golem.ph.utexas.edu/category/2019/04/generalized_petri_nets.html.
2. Open Petri nets
3. Petri nets are monoids
4. Formal theory of internal categories;Betti;Le Matematiche,1996
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Regular planar monoidal languages;Journal of Logical and Algebraic Methods in Programming;2024-06
2. Whole-grain Petri Nets and Processes;Journal of the ACM;2022-12-19
3. A Categorical Semantics for Bounded Petri Nets;Electronic Proceedings in Theoretical Computer Science;2022-11-03
4. A Categorical Semantics for Hierarchical Petri Nets;Electronic Proceedings in Theoretical Computer Science;2021-12-21
5. Categories of Nets;2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS);2021-06-29