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1 results

  • Petri nets based on Lawvere theories

  • Jade Master
  • Journal:
    Mathematical Structures in Computer Science / Volume 30 / Issue 7 / August 2020
    Published online by Cambridge University Press:
    09 November 2020, pp. 833-864
    • Article
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  • We 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.