Upper set monoids and length preserving morphisms

Length preserving morphisms and inverse of substitutions are two well-studied operations on regular languages. Their connection with varieties generated by power monoids was established independently by Reutenauer and Straubing in 1979. More recently, an ordered version of this theory was proposed b...

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Detalles Bibliográficos
Autores: Cano Gómez, Antonio, Pin, Jean-Eric
Tipo de recurso: artículo
Fecha de publicación:2012
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/37245
Acceso en línea:https://riunet.upv.es/handle/10251/37245
Access Level:acceso abierto
Palabra clave:Varieties
Semigroups
Languages
LENGUAJES Y SISTEMAS INFORMATICOS
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spelling Upper set monoids and length preserving morphismsCano Gómez, AntonioPin, Jean-EricVarietiesSemigroupsLanguagesLENGUAJES Y SISTEMAS INFORMATICOSLength preserving morphisms and inverse of substitutions are two well-studied operations on regular languages. Their connection with varieties generated by power monoids was established independently by Reutenauer and Straubing in 1979. More recently, an ordered version of this theory was proposed by Polák and by the authors. In this paper, we present an improved version of these results and obtain the following consequences. Given a variety of finite ordered monoids V, let P ¿V be the variety of finite ordered monoids generated by the upper set monoids of members of V. Then P ¿(P ¿V)=P ¿V. This contrasts with the known results for the unordered case: the operator PV corresponding to power monoids satisfies P 3V=P 4V, but the varieties V, PV, P 2V and P 3V can be distinct. © 2011 Elsevier B.V.Work supported by the integrated action Picasso 19245ZC and by the AuthoMathA Programme of the European Science Foundation. The first author was supported by the project Tecnicas de Inferencia Gramatical y aplicacion al procesamiento de biosecuencias (TIN2007-60769) supported by the Spanish Ministry of Education and Sciences. The second author was supported by the project ANR 2010 BLAN 0202 02 FREC.ElsevierMinisterio de Educación y CienciaAgence Nationale de la Recherche, FranciaMinisterio de Ciencia e InnovaciónRepositorio Institucional de la Universitat Politècnica de València Riunet20122012-05-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/37245reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgence Nationale de la Recherche, Francia https://doi.org/10.13039/501100001665 ANR-10-BLAN-0202 Frontiers of recognizabilityMinisterio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 HF2008-0009 HF2008-0009Ministerio de Educación y Ciencia https://doi.org/10.13039/501100008743 TIN2007-60769 TECNICAS DE INFERENCIA GRAMATICAL Y APLICACION AL PROCESAMIENTO DE BIOSECUENCIASopen accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/372452026-06-13T07:49:27Z
dc.title.none.fl_str_mv Upper set monoids and length preserving morphisms
title Upper set monoids and length preserving morphisms
spellingShingle Upper set monoids and length preserving morphisms
Cano Gómez, Antonio
Varieties
Semigroups
Languages
LENGUAJES Y SISTEMAS INFORMATICOS
title_short Upper set monoids and length preserving morphisms
title_full Upper set monoids and length preserving morphisms
title_fullStr Upper set monoids and length preserving morphisms
title_full_unstemmed Upper set monoids and length preserving morphisms
title_sort Upper set monoids and length preserving morphisms
dc.creator.none.fl_str_mv Cano Gómez, Antonio
Pin, Jean-Eric
author Cano Gómez, Antonio
author_facet Cano Gómez, Antonio
Pin, Jean-Eric
author_role author
author2 Pin, Jean-Eric
author2_role author
dc.contributor.none.fl_str_mv Ministerio de Educación y Ciencia
Agence Nationale de la Recherche, Francia
Ministerio de Ciencia e Innovación
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Varieties
Semigroups
Languages
LENGUAJES Y SISTEMAS INFORMATICOS
topic Varieties
Semigroups
Languages
LENGUAJES Y SISTEMAS INFORMATICOS
description Length preserving morphisms and inverse of substitutions are two well-studied operations on regular languages. Their connection with varieties generated by power monoids was established independently by Reutenauer and Straubing in 1979. More recently, an ordered version of this theory was proposed by Polák and by the authors. In this paper, we present an improved version of these results and obtain the following consequences. Given a variety of finite ordered monoids V, let P ¿V be the variety of finite ordered monoids generated by the upper set monoids of members of V. Then P ¿(P ¿V)=P ¿V. This contrasts with the known results for the unordered case: the operator PV corresponding to power monoids satisfies P 3V=P 4V, but the varieties V, PV, P 2V and P 3V can be distinct. © 2011 Elsevier B.V.
publishDate 2012
dc.date.none.fl_str_mv 2012
2012-05-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/37245
url https://riunet.upv.es/handle/10251/37245
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agence Nationale de la Recherche, Francia https://doi.org/10.13039/501100001665 ANR-10-BLAN-0202 Frontiers of recognizability
Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 HF2008-0009 HF2008-0009
Ministerio de Educación y Ciencia https://doi.org/10.13039/501100008743 TIN2007-60769 TECNICAS DE INFERENCIA GRAMATICAL Y APLICACION AL PROCESAMIENTO DE BIOSECUENCIAS
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
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
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
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:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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