Petri Nets Based on Lawvere Theories
Abstract
We give a definition of $\mathsf{Q}$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 $\mathsf{Q}$nets present free models of $\mathsf{Q}$ in $\mathsf{Cat}$. This gives a functorial description of the operational semantics for an arbitrary category of $\mathsf{Q}$nets. We show how this can be used to construct the semantics for Petri nets, prenets, integer nets, and elementary net systems.
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 arXiv:
 arXiv:1904.09091
 Bibcode:
 2019arXiv190409091M
 Keywords:

 Mathematics  Category Theory
 EPrint:
 32 pages