The design of a parallel algorithm to solve the word problem for the free partially commutative groups

We develop a parallel algorithm to solve the word problem for free partially commutative groups. These groups were introduced by C. Wrathall to generalize free groups. We represent the elements of these groups as a certain type of acyclic labeled graphs called dependency graphs. These graphs were in...

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Detalles Bibliográficos
Autor: Gabarró Vallès, Joaquim|||0000-0003-3771-2813
Tipo de recurso: informe técnico
Fecha de publicación:1991
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/330529
Acceso en línea:https://hdl.handle.net/2117/330529
Access Level:acceso abierto
Palabra clave:Parallel algorithms
Word problems (Mathematics)
PRAMS
Data parallel algorithms
Modular design
Trace theory
Free groups
Free partially commutative groups
Word problems
Parallel complexity classes
NC*
NL*
ACo
Complete problems
Algorismes paral·lels
Paraules, Problemes de (Matemàtica)
Àrees temàtiques de la UPC::Informàtica
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repository_id_str
spelling The design of a parallel algorithm to solve the word problem for the free partially commutative groupsGabarró Vallès, Joaquim|||0000-0003-3771-2813Parallel algorithmsWord problems (Mathematics)PRAMSData parallel algorithmsModular designTrace theoryFree groupsFree partially commutative groupsWord problemsParallel complexity classesNC*NL*ACoComplete problemsAlgorismes paral·lelsParaules, Problemes de (Matemàtica)Àrees temàtiques de la UPC::InformàticaWe develop a parallel algorithm to solve the word problem for free partially commutative groups. These groups were introduced by C. Wrathall to generalize free groups. We represent the elements of these groups as a certain type of acyclic labeled graphs called dependency graphs. These graphs were introduced by A Maxurkiewicz to model concurrent systems. First we study the parallel complexity of some basic problems arising in the study of dependency graphs. Such as correctness, isomorphism and relations with traces. Parallel algorithms are developed to solve all of them. Second we consider the combinatorial properties of free partially commutative groups. To do this we associate to every group a rewriting system over dependency graphs. Finally we apply all these ideas to solve in parallel the word problem. Special emphasis is given in the design of the algorithms. The modular approach is widely used to obtain readable programs. It seems that many of the structuring techniques developed in sequential programming can be used directly in the PRAM context.19911991-10-1520202020-10-21reporthttp://purl.org/coar/resource_type/c_93fcVoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/reportapplication/pdfhttps://hdl.handle.net/2117/330529reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3305292026-05-27T15:37:01Z
dc.title.none.fl_str_mv The design of a parallel algorithm to solve the word problem for the free partially commutative groups
title The design of a parallel algorithm to solve the word problem for the free partially commutative groups
spellingShingle The design of a parallel algorithm to solve the word problem for the free partially commutative groups
Gabarró Vallès, Joaquim|||0000-0003-3771-2813
Parallel algorithms
Word problems (Mathematics)
PRAMS
Data parallel algorithms
Modular design
Trace theory
Free groups
Free partially commutative groups
Word problems
Parallel complexity classes
NC*
NL*
ACo
Complete problems
Algorismes paral·lels
Paraules, Problemes de (Matemàtica)
Àrees temàtiques de la UPC::Informàtica
title_short The design of a parallel algorithm to solve the word problem for the free partially commutative groups
title_full The design of a parallel algorithm to solve the word problem for the free partially commutative groups
title_fullStr The design of a parallel algorithm to solve the word problem for the free partially commutative groups
title_full_unstemmed The design of a parallel algorithm to solve the word problem for the free partially commutative groups
title_sort The design of a parallel algorithm to solve the word problem for the free partially commutative groups
dc.creator.none.fl_str_mv Gabarró Vallès, Joaquim|||0000-0003-3771-2813
author Gabarró Vallès, Joaquim|||0000-0003-3771-2813
author_facet Gabarró Vallès, Joaquim|||0000-0003-3771-2813
author_role author
dc.subject.none.fl_str_mv Parallel algorithms
Word problems (Mathematics)
PRAMS
Data parallel algorithms
Modular design
Trace theory
Free groups
Free partially commutative groups
Word problems
Parallel complexity classes
NC*
NL*
ACo
Complete problems
Algorismes paral·lels
Paraules, Problemes de (Matemàtica)
Àrees temàtiques de la UPC::Informàtica
topic Parallel algorithms
Word problems (Mathematics)
PRAMS
Data parallel algorithms
Modular design
Trace theory
Free groups
Free partially commutative groups
Word problems
Parallel complexity classes
NC*
NL*
ACo
Complete problems
Algorismes paral·lels
Paraules, Problemes de (Matemàtica)
Àrees temàtiques de la UPC::Informàtica
description We develop a parallel algorithm to solve the word problem for free partially commutative groups. These groups were introduced by C. Wrathall to generalize free groups. We represent the elements of these groups as a certain type of acyclic labeled graphs called dependency graphs. These graphs were introduced by A Maxurkiewicz to model concurrent systems. First we study the parallel complexity of some basic problems arising in the study of dependency graphs. Such as correctness, isomorphism and relations with traces. Parallel algorithms are developed to solve all of them. Second we consider the combinatorial properties of free partially commutative groups. To do this we associate to every group a rewriting system over dependency graphs. Finally we apply all these ideas to solve in parallel the word problem. Special emphasis is given in the design of the algorithms. The modular approach is widely used to obtain readable programs. It seems that many of the structuring techniques developed in sequential programming can be used directly in the PRAM context.
publishDate 1991
dc.date.none.fl_str_mv 1991
1991-10-15
2020
2020-10-21
dc.type.none.fl_str_mv report
http://purl.org/coar/resource_type/c_93fc
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/report
format report
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/330529
url https://hdl.handle.net/2117/330529
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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