Petri nets based on Lawvere theories
| Autor: | Jade Master |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Computer science
Semantics (computer science) Generalization Mathematics - Category Theory Petri net Net (mathematics) Operational semantics Computer Science Applications Algebra Mathematics (miscellaneous) FOS: Mathematics Hardware_INTEGRATEDCIRCUITS Lawvere theory Category Theory (math.CT) Special case Category theory |
| Zdroj: | Mathematical Structures in Computer Science. 30:833-864 |
| ISSN: | 1469-8072 0960-1295 |
| DOI: | 10.1017/s0960129520000262 |
| Popis: | 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, pre-nets, integer nets, and elementary net systems. 32 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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