Some collapsing operations for 2-dimensional precubical sets
Autor(a) principal: | |
---|---|
Data de Publicação: | 2012 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/1822/21116 |
Resumo: | In this paper, we consider 2-dimensional precubical sets, which can be used to model systems of two concurrently executing processes. From the point of view of concurrency theory, two precubical sets can be considered equivalent if their geometric realizations have the same directed homotopy type relative to the extremal elements in the sense of P. Bubenik.We give easily verifiable conditions under which it is possible to reduce a 2-dimensional precubical set to an equivalent smaller one by collapsing an edge or eliminating a square and one or two free faces. We also look at some simple standard examples in order to illustrate how our results can be used to construct small models of 2-dimensional precubical sets. |
id |
RCAP_9194f6bb4ae74959720f7e65691b910d |
---|---|
oai_identifier_str |
oai:repositorium.sdum.uminho.pt:1822/21116 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
Some collapsing operations for 2-dimensional precubical setsCubical setsd-spacesFundamental bipartite graphFundamental categoryTrace spacesDirected homotopy theoryConcurrency theoryScience & TechnologyIn this paper, we consider 2-dimensional precubical sets, which can be used to model systems of two concurrently executing processes. From the point of view of concurrency theory, two precubical sets can be considered equivalent if their geometric realizations have the same directed homotopy type relative to the extremal elements in the sense of P. Bubenik.We give easily verifiable conditions under which it is possible to reduce a 2-dimensional precubical set to an equivalent smaller one by collapsing an edge or eliminating a square and one or two free faces. We also look at some simple standard examples in order to illustrate how our results can be used to construct small models of 2-dimensional precubical sets.This research has been supported by FEDER funds through "Programa Operacional Factores de Competitividade-COMPETE" and by FCT-Fundacao para a Ciencia e a Tecnologia through projects Est-C/MAT/UI0013/2011 and PTDC/MAT/0938317/2008.SpringerUniversidade do MinhoKahl, Thomas2012-06-052012-06-05T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/21116eng2193-840710.1007/s40062-012-0010-7http://link.springer.com/article/10.1007%2Fs40062-012-0010-7info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:15:50Zoai:repositorium.sdum.uminho.pt:1822/21116Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:08:22.096670Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Some collapsing operations for 2-dimensional precubical sets |
title |
Some collapsing operations for 2-dimensional precubical sets |
spellingShingle |
Some collapsing operations for 2-dimensional precubical sets Kahl, Thomas Cubical sets d-spaces Fundamental bipartite graph Fundamental category Trace spaces Directed homotopy theory Concurrency theory Science & Technology |
title_short |
Some collapsing operations for 2-dimensional precubical sets |
title_full |
Some collapsing operations for 2-dimensional precubical sets |
title_fullStr |
Some collapsing operations for 2-dimensional precubical sets |
title_full_unstemmed |
Some collapsing operations for 2-dimensional precubical sets |
title_sort |
Some collapsing operations for 2-dimensional precubical sets |
author |
Kahl, Thomas |
author_facet |
Kahl, Thomas |
author_role |
author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Kahl, Thomas |
dc.subject.por.fl_str_mv |
Cubical sets d-spaces Fundamental bipartite graph Fundamental category Trace spaces Directed homotopy theory Concurrency theory Science & Technology |
topic |
Cubical sets d-spaces Fundamental bipartite graph Fundamental category Trace spaces Directed homotopy theory Concurrency theory Science & Technology |
description |
In this paper, we consider 2-dimensional precubical sets, which can be used to model systems of two concurrently executing processes. From the point of view of concurrency theory, two precubical sets can be considered equivalent if their geometric realizations have the same directed homotopy type relative to the extremal elements in the sense of P. Bubenik.We give easily verifiable conditions under which it is possible to reduce a 2-dimensional precubical set to an equivalent smaller one by collapsing an edge or eliminating a square and one or two free faces. We also look at some simple standard examples in order to illustrate how our results can be used to construct small models of 2-dimensional precubical sets. |
publishDate |
2012 |
dc.date.none.fl_str_mv |
2012-06-05 2012-06-05T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/1822/21116 |
url |
http://hdl.handle.net/1822/21116 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
2193-8407 10.1007/s40062-012-0010-7 http://link.springer.com/article/10.1007%2Fs40062-012-0010-7 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Springer |
publisher.none.fl_str_mv |
Springer |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
|
_version_ |
1799132505579716608 |