Automaton semigroups: New constructions results and examples of non-automaton semigroups
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://doi.org/10.1016/j.tcs.2017.02.003 |
Resumo: | FCT exploratory project IF/01622/2013/CP1161/CT0001. FCT fellowship (IF/01622/2013/CP1161/CT0001). |
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7160 |
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Automaton semigroups: New constructions results and examples of non-automaton semigroupsAutomaton semigroupConstructionsFree productSmall extensionsWreath productTheoretical Computer ScienceComputer Science(all)FCT exploratory project IF/01622/2013/CP1161/CT0001. FCT fellowship (IF/01622/2013/CP1161/CT0001).This paper studies the class of automaton semigroups from two perspectives: closure under constructions, and examples of semigroups that are not automaton semigroups. We prove that (semigroup) free products of finite semigroups always arise as automaton semigroups, and that the class of automaton monoids is closed under forming wreath products with finite monoids. We also consider closure under certain kinds of Rees matrix constructions, strong semilattices, and small extensions. Finally, we prove that no subsemigroup of (N,+) arises as an automaton semigroup. (Previously, (N,+) itself was the unique example of a semigroup having the ‘general’ properties of automaton semigroups (such as residual finiteness, solvable word problem, etc.) but that was known not to arise as an automaton semigroup.)CMA - Centro de Matemática e AplicaçõesRUNBrough, TaraCain, Alan J.2019-07-12T22:28:30Z2017-04-252017-04-25T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article15application/pdfhttps://doi.org/10.1016/j.tcs.2017.02.003eng0304-3975PURE: 3804936http://www.scopus.com/inward/record.url?scp=85015758537&partnerID=8YFLogxKhttps://doi.org/10.1016/j.tcs.2017.02.003info: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:RCAAP2024-03-11T04:34:28Zoai:run.unl.pt:10362/75289Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:35:30.429313Repositório 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 |
Automaton semigroups: New constructions results and examples of non-automaton semigroups |
title |
Automaton semigroups: New constructions results and examples of non-automaton semigroups |
spellingShingle |
Automaton semigroups: New constructions results and examples of non-automaton semigroups Brough, Tara Automaton semigroup Constructions Free product Small extensions Wreath product Theoretical Computer Science Computer Science(all) |
title_short |
Automaton semigroups: New constructions results and examples of non-automaton semigroups |
title_full |
Automaton semigroups: New constructions results and examples of non-automaton semigroups |
title_fullStr |
Automaton semigroups: New constructions results and examples of non-automaton semigroups |
title_full_unstemmed |
Automaton semigroups: New constructions results and examples of non-automaton semigroups |
title_sort |
Automaton semigroups: New constructions results and examples of non-automaton semigroups |
author |
Brough, Tara |
author_facet |
Brough, Tara Cain, Alan J. |
author_role |
author |
author2 |
Cain, Alan J. |
author2_role |
author |
dc.contributor.none.fl_str_mv |
CMA - Centro de Matemática e Aplicações RUN |
dc.contributor.author.fl_str_mv |
Brough, Tara Cain, Alan J. |
dc.subject.por.fl_str_mv |
Automaton semigroup Constructions Free product Small extensions Wreath product Theoretical Computer Science Computer Science(all) |
topic |
Automaton semigroup Constructions Free product Small extensions Wreath product Theoretical Computer Science Computer Science(all) |
description |
FCT exploratory project IF/01622/2013/CP1161/CT0001. FCT fellowship (IF/01622/2013/CP1161/CT0001). |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-04-25 2017-04-25T00:00:00Z 2019-07-12T22:28:30Z |
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 |
https://doi.org/10.1016/j.tcs.2017.02.003 |
url |
https://doi.org/10.1016/j.tcs.2017.02.003 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0304-3975 PURE: 3804936 http://www.scopus.com/inward/record.url?scp=85015758537&partnerID=8YFLogxK https://doi.org/10.1016/j.tcs.2017.02.003 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
15 application/pdf |
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 |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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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 |
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1799137976118149120 |