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

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

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...

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Bibliographic Details
Main Authors: Fabrizio Genovese, Jelle Herold
Format: Article
Language:English
Published: Open Publishing Association 2019-01-01
Series:Electronic Proceedings in Theoretical Computer Science
Online Access:http://arxiv.org/pdf/1805.05988v3
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spelling doaj-b2dcb051ae044cd7a24b424315bd4a872020-11-25T02:19:32ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802019-01-01287Proc. QPL 201812714410.4204/EPTCS.287.7:28Executions in (Semi-)Integer Petri Nets are Compact Closed CategoriesFabrizio Genovese0Jelle Herold1 Statebox 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.http://arxiv.org/pdf/1805.05988v3
collection DOAJ
language English
format Article
sources DOAJ
author Fabrizio Genovese
Jelle Herold
spellingShingle Fabrizio Genovese
Jelle Herold
Executions in (Semi-)Integer Petri Nets are Compact Closed Categories
Electronic Proceedings in Theoretical Computer Science
author_facet Fabrizio Genovese
Jelle Herold
author_sort Fabrizio Genovese
title Executions in (Semi-)Integer Petri Nets are Compact Closed Categories
title_short Executions in (Semi-)Integer Petri Nets are Compact Closed Categories
title_full Executions in (Semi-)Integer Petri Nets are Compact Closed Categories
title_fullStr Executions in (Semi-)Integer Petri Nets are Compact Closed Categories
title_full_unstemmed Executions in (Semi-)Integer Petri Nets are Compact Closed Categories
title_sort executions in (semi-)integer petri nets are compact closed categories
publisher Open Publishing Association
series Electronic Proceedings in Theoretical Computer Science
issn 2075-2180
publishDate 2019-01-01
description 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.
url http://arxiv.org/pdf/1805.05988v3
work_keys_str_mv AT fabriziogenovese executionsinsemiintegerpetrinetsarecompactclosedcategories
AT jelleherold executionsinsemiintegerpetrinetsarecompactclosedcategories
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