Solving the conjugacy problem in Garside groups by cyclic sliding

We present a solution to the conjugacy decision problem and the conjugacy search problem in Garside groups, which is theoretically simpler than the usual one, with no loss of efficiency. This is done by replacing the well known cycling and decycling operations by a new one, called cyclic sliding, wh...

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Detalles Bibliográficos
Autores: Gebhardt, Volker, González-Meneses López, Juan
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2010
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/42311
Acceso en línea:http://hdl.handle.net/11441/42311
https://doi.org/10.1016/j.jsc.2010.01.013
Access Level:acceso abierto
Palabra clave:Garside groups
conjugacy
conjugacy problem
cyclic sliding
sliding circuits
complexity analysis
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spelling Solving the conjugacy problem in Garside groups by cyclic slidingGebhardt, VolkerGonzález-Meneses López, JuanGarside groupsconjugacyconjugacy problemcyclic slidingsliding circuitscomplexity analysisWe present a solution to the conjugacy decision problem and the conjugacy search problem in Garside groups, which is theoretically simpler than the usual one, with no loss of efficiency. This is done by replacing the well known cycling and decycling operations by a new one, called cyclic sliding, which appears to be a more natural choice. We give an analysis of the complexity of our algorithm in terms of fundamental operations with simple elements, so our analysis is valid for every Garside group. This paper intends to be self-contained, not requiring any previous knowledge of prior algorithms, and includes all the details for the algorithm to be implemented on a computer.Ministerio de Educación y CienciaFondo Europeo de Desarrollo RegionalElsevierÁlgebraMinisterio de Educación y Ciencia (MEC). EspañaEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)2010info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/42311https://doi.org/10.1016/j.jsc.2010.01.013reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Symbolic Computation, 45 (6), 629-656.MTM2007-66929Amsterdaminfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/423112026-06-17T12:51:07Z
dc.title.none.fl_str_mv Solving the conjugacy problem in Garside groups by cyclic sliding
title Solving the conjugacy problem in Garside groups by cyclic sliding
spellingShingle Solving the conjugacy problem in Garside groups by cyclic sliding
Gebhardt, Volker
Garside groups
conjugacy
conjugacy problem
cyclic sliding
sliding circuits
complexity analysis
title_short Solving the conjugacy problem in Garside groups by cyclic sliding
title_full Solving the conjugacy problem in Garside groups by cyclic sliding
title_fullStr Solving the conjugacy problem in Garside groups by cyclic sliding
title_full_unstemmed Solving the conjugacy problem in Garside groups by cyclic sliding
title_sort Solving the conjugacy problem in Garside groups by cyclic sliding
dc.creator.none.fl_str_mv Gebhardt, Volker
González-Meneses López, Juan
author Gebhardt, Volker
author_facet Gebhardt, Volker
González-Meneses López, Juan
author_role author
author2 González-Meneses López, Juan
author2_role author
dc.contributor.none.fl_str_mv Álgebra
Ministerio de Educación y Ciencia (MEC). España
European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
dc.subject.none.fl_str_mv Garside groups
conjugacy
conjugacy problem
cyclic sliding
sliding circuits
complexity analysis
topic Garside groups
conjugacy
conjugacy problem
cyclic sliding
sliding circuits
complexity analysis
description We present a solution to the conjugacy decision problem and the conjugacy search problem in Garside groups, which is theoretically simpler than the usual one, with no loss of efficiency. This is done by replacing the well known cycling and decycling operations by a new one, called cyclic sliding, which appears to be a more natural choice. We give an analysis of the complexity of our algorithm in terms of fundamental operations with simple elements, so our analysis is valid for every Garside group. This paper intends to be self-contained, not requiring any previous knowledge of prior algorithms, and includes all the details for the algorithm to be implemented on a computer.
publishDate 2010
dc.date.none.fl_str_mv 2010
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/42311
https://doi.org/10.1016/j.jsc.2010.01.013
url http://hdl.handle.net/11441/42311
https://doi.org/10.1016/j.jsc.2010.01.013
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Symbolic Computation, 45 (6), 629-656.
MTM2007-66929
Amsterdam
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.301603

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