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Open Petri nets

Published online by Cambridge University Press:  07 April 2020

John C. Baez Open the ORCID record for John C. Baez [Opens in a new window]  and
Jade Master Open the ORCID record for Jade Master [Opens in a new window]
John C. Baez*
Affiliation:
Department of Mathematics, University of California, Riverside, CA92521, USA
Jade Master*
Affiliation:
Department of Mathematics, University of California, Riverside, CA92521, USA
*
*Corresponding author. Emails: baez@math.ucr.edu; jadeedenstarmaster@gmail.com
*Corresponding author. Emails: baez@math.ucr.edu; jadeedenstarmaster@gmail.com
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Abstract

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The reachability semantics for Petri nets can be studied using open Petri nets. For us, an “open” Petri net is one with certain places designated as inputs and outputs via a cospan of sets. We can compose open Petri nets by gluing the outputs of one to the inputs of another. Open Petri nets can be treated as morphisms of a category Open(Petri), which becomes symmetric monoidal under disjoint union. However, since the composite of open Petri nets is defined only up to isomorphism, it is better to treat them as morphisms of a symmetric monoidal double category ${\mathbb O}$pen(Petri). We describe two forms of semantics for open Petri nets using symmetric monoidal double functors out of ${\mathbb O}$pen(Petri). The first, an operational semantics, gives for each open Petri net a category whose morphisms are the processes that this net can carry out. This is done in a compositional way, so that these categories can be computed on smaller subnets and then glued together. The second, a reachability semantics, simply says which markings of the outputs can be reached from a given marking of the inputs.

Keywords

Double categoryopen systemoperational semanticsPetri netreachability

Information

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 30 , Issue 3 , March 2020 , pp. 314 - 341
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - SA
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike licence (http://creativecommons.org/licenses/by-nc-sa/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the same Creative Commons licence is included and the original work is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use.
Copyright
© The Author(s) 2020. Published by Cambridge University Press

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