Paper Accepted at QPL 2018
You can read the paper here and see the talk by Fabrizio and Jelle at the upcoming QPL 2018 which will take place in Halifax, Canada.
Abstract: 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 that a procedure to recover the original net from its category of executions exists, 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.