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Petri nets based on Lawvere theories

Published online by Cambridge University Press:  09 November 2020

Jade MasterOpen the ORCID record for Jade Master[Opens in a new window]
Jade Master*
Affiliation:
University of California Riverside, Department of Mathematics, Riverside, CA USA
*
Email: jmast003@ucr.edu
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Abstract

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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.

Keywords

Petri netsLawvere theoryCategory theoryoperational semantics

Information

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 30 , Issue 7 , August 2020, pp. 833 - 864
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Creative Commons
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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