Iterated periodicity over finite aperiodic semigroups

Detalhes bibliográficos
Autor(a) principal: Almeida, Jorge
Data de Publicação: 2014
Outros Autores: Costa, José Carlos, Zeitoun, Marc
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/15034
Resumo: This paper provides a characterization of pseudowords over the pseudovariety of all finite aperiodic semigroups that can be described from the free generators using only the operations of multiplication and omega-power. A necessary and sufficient condition for this property to hold turns out to be given by the conjunction of two rather simple finiteness conditions: the nonexistence of infinite anti-chains of factors and the rationality of the language of McCammond normal forms of omega-terms that define factors of the given pseudoword. The relationship between pseudowords with this property and arbitrary pseudowords is also investigated.
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spelling Iterated periodicity over finite aperiodic semigroupsAperiodic semigroupFree profinitePseudowordomega-termMcCammond normal formRational languageAnti-chainSemigroupoidScience & TechnologyThis paper provides a characterization of pseudowords over the pseudovariety of all finite aperiodic semigroups that can be described from the free generators using only the operations of multiplication and omega-power. A necessary and sufficient condition for this property to hold turns out to be given by the conjunction of two rather simple finiteness conditions: the nonexistence of infinite anti-chains of factors and the rationality of the language of McCammond normal forms of omega-terms that define factors of the given pseudoword. The relationship between pseudowords with this property and arbitrary pseudowords is also investigated.Projeto PTDC/MAT/65481/2006 financiado em parte pelo European Community Fund FEDERPrograma AutoMathA da European Science Fundation (ESF)Projeto Egide-Grices 11113YMFundação para a Ciência e a Tecnologia (FCT)ElsevierUniversidade do MinhoAlmeida, JorgeCosta, José CarlosZeitoun, Marc20142014-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/15034eng0195-669810.1016/j.ejc.2013.07.011info: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:RCAAP2023-07-21T12:40:06Zoai:repositorium.sdum.uminho.pt:1822/15034Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:36:50.511147Repositório 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 Iterated periodicity over finite aperiodic semigroups
title Iterated periodicity over finite aperiodic semigroups
spellingShingle Iterated periodicity over finite aperiodic semigroups
Almeida, Jorge
Aperiodic semigroup
Free profinite
Pseudoword
omega-term
McCammond normal form
Rational language
Anti-chain
Semigroupoid
Science & Technology
title_short Iterated periodicity over finite aperiodic semigroups
title_full Iterated periodicity over finite aperiodic semigroups
title_fullStr Iterated periodicity over finite aperiodic semigroups
title_full_unstemmed Iterated periodicity over finite aperiodic semigroups
title_sort Iterated periodicity over finite aperiodic semigroups
author Almeida, Jorge
author_facet Almeida, Jorge
Costa, José Carlos
Zeitoun, Marc
author_role author
author2 Costa, José Carlos
Zeitoun, Marc
author2_role author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Almeida, Jorge
Costa, José Carlos
Zeitoun, Marc
dc.subject.por.fl_str_mv Aperiodic semigroup
Free profinite
Pseudoword
omega-term
McCammond normal form
Rational language
Anti-chain
Semigroupoid
Science & Technology
topic Aperiodic semigroup
Free profinite
Pseudoword
omega-term
McCammond normal form
Rational language
Anti-chain
Semigroupoid
Science & Technology
description This paper provides a characterization of pseudowords over the pseudovariety of all finite aperiodic semigroups that can be described from the free generators using only the operations of multiplication and omega-power. A necessary and sufficient condition for this property to hold turns out to be given by the conjunction of two rather simple finiteness conditions: the nonexistence of infinite anti-chains of factors and the rationality of the language of McCammond normal forms of omega-terms that define factors of the given pseudoword. The relationship between pseudowords with this property and arbitrary pseudowords is also investigated.
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-01-01T00:00:00Z
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/1822/15034
url http://hdl.handle.net/1822/15034
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0195-6698
10.1016/j.ejc.2013.07.011
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 Elsevier
publisher.none.fl_str_mv Elsevier
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
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