Executions in (Semi-)Integer Petri Nets are Compact Closed Categories

Fabrizio Genovese
(Statebox)
Jelle Herold
(Statebox)

In this work, we analyse Petri nets where places are allowed to have a negative number of tokens. For each net we build its correspondent category of executions, which is compact closed, and prove that this procedure is functorial. We moreover exhibit a procedure to recover the original net from its category of executions, show that it is again functorial, and that this gives rise to an adjoint pair. Finally, we use compact closeness to infer that allowing negative tokens in a Petri net makes the causal relations between transition firings non-trivial, and we use this to model interesting phenomena in economics and computer science.

In Peter Selinger and Giulio Chiribella: Proceedings of the 15th International Conference on Quantum Physics and Logic (QPL 2018), Halifax, Canada, 3-7th June 2018, Electronic Proceedings in Theoretical Computer Science 287, pp. 127–144.
Published: 31st January 2019.

ArXived at: http://dx.doi.org/10.4204/EPTCS.287.7 bibtex PDF
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