文章基本信息

标题：Executions in (Semi-)Integer Petri Nets are Compact Closed Categories
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作者：Fabrizio Genovese ; Jelle Herold
期刊名称：Electronic Proceedings in Theoretical Computer Science
电子版ISSN：2075-2180
出版年度：2019
卷号：287
页码：127-144
DOI：10.4204/EPTCS.287.7
语种：English
出版社：Open Publishing Association
摘要：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.