Bisimilarity is not borel

Autores
Sanchez Terraf, Pedro Octavio
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We prove that the relation of bisimilarity between countable labelled transition systems (LTS) is Σ1 1-complete (hence not Borel), by reducing the set of non-well orders over the natural numbers continuously to it. This has an impact on the theory of probabilistic and non-deterministic processes over uncountable spaces, since logical characterizations of bisimilarity (as, for instance, those based on the unique structure theorem for analytic spaces) require a countable logic whose formulas have measurable semantics. Our reduction shows that such a logic does not exist in the case of image-infinite processes.
Fil: Sanchez Terraf, Pedro Octavio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina
Materia
MEASURABLE LABELLED TRANSITION SYSTEM
NON-DETERMINISTIC LABELLED MARKOV PROCESS
MODAL LOGIC
BOREL HIERARCHY
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/135326
Acceder
id CONICETDig_7db1ea25e49ef81ababd4833e2f84a02
oai_identifier_str oai:ri.conicet.gov.ar:11336/135326
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Bisimilarity is not borelSanchez Terraf, Pedro OctavioMEASURABLE LABELLED TRANSITION SYSTEMNON-DETERMINISTIC LABELLED MARKOV PROCESSMODAL LOGICBOREL HIERARCHYhttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We prove that the relation of bisimilarity between countable labelled transition systems (LTS) is Σ1 1-complete (hence not Borel), by reducing the set of non-well orders over the natural numbers continuously to it. This has an impact on the theory of probabilistic and non-deterministic processes over uncountable spaces, since logical characterizations of bisimilarity (as, for instance, those based on the unique structure theorem for analytic spaces) require a countable logic whose formulas have measurable semantics. Our reduction shows that such a logic does not exist in the case of image-infinite processes.Fil: Sanchez Terraf, Pedro Octavio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; ArgentinaCambridge University Press2017-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/135326Sanchez Terraf, Pedro Octavio; Bisimilarity is not borel; Cambridge University Press; Mathematical Structures In Computer Science; 27; 7; 10-2017; 1265-12840960-12951469-8072CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1017/S0960129515000535info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/mathematical-structures-in-computer-science/article/bisimilarity-is-not-borel/D307FCD95EB5B75B1A299F131134FEB5info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:23:01Zoai:ri.conicet.gov.ar:11336/135326instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:23:01.518CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Bisimilarity is not borel
title Bisimilarity is not borel
spellingShingle Bisimilarity is not borel
Sanchez Terraf, Pedro Octavio
MEASURABLE LABELLED TRANSITION SYSTEM
NON-DETERMINISTIC LABELLED MARKOV PROCESS
MODAL LOGIC
BOREL HIERARCHY
title_short Bisimilarity is not borel
title_full Bisimilarity is not borel
title_fullStr Bisimilarity is not borel
title_full_unstemmed Bisimilarity is not borel
title_sort Bisimilarity is not borel
dc.creator.none.fl_str_mv Sanchez Terraf, Pedro Octavio
author Sanchez Terraf, Pedro Octavio
author_facet Sanchez Terraf, Pedro Octavio
author_role author
dc.subject.none.fl_str_mv MEASURABLE LABELLED TRANSITION SYSTEM
NON-DETERMINISTIC LABELLED MARKOV PROCESS
MODAL LOGIC
BOREL HIERARCHY
topic MEASURABLE LABELLED TRANSITION SYSTEM
NON-DETERMINISTIC LABELLED MARKOV PROCESS
MODAL LOGIC
BOREL HIERARCHY
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We prove that the relation of bisimilarity between countable labelled transition systems (LTS) is Σ1 1-complete (hence not Borel), by reducing the set of non-well orders over the natural numbers continuously to it. This has an impact on the theory of probabilistic and non-deterministic processes over uncountable spaces, since logical characterizations of bisimilarity (as, for instance, those based on the unique structure theorem for analytic spaces) require a countable logic whose formulas have measurable semantics. Our reduction shows that such a logic does not exist in the case of image-infinite processes.
Fil: Sanchez Terraf, Pedro Octavio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina
description We prove that the relation of bisimilarity between countable labelled transition systems (LTS) is Σ1 1-complete (hence not Borel), by reducing the set of non-well orders over the natural numbers continuously to it. This has an impact on the theory of probabilistic and non-deterministic processes over uncountable spaces, since logical characterizations of bisimilarity (as, for instance, those based on the unique structure theorem for analytic spaces) require a countable logic whose formulas have measurable semantics. Our reduction shows that such a logic does not exist in the case of image-infinite processes.
publishDate 2017
dc.date.none.fl_str_mv 2017-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/135326
Sanchez Terraf, Pedro Octavio; Bisimilarity is not borel; Cambridge University Press; Mathematical Structures In Computer Science; 27; 7; 10-2017; 1265-1284
0960-1295
1469-8072
CONICET Digital
CONICET
url http://hdl.handle.net/11336/135326
identifier_str_mv Sanchez Terraf, Pedro Octavio; Bisimilarity is not borel; Cambridge University Press; Mathematical Structures In Computer Science; 27; 7; 10-2017; 1265-1284
0960-1295
1469-8072
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1017/S0960129515000535
info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/mathematical-structures-in-computer-science/article/bisimilarity-is-not-borel/D307FCD95EB5B75B1A299F131134FEB5
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/zip
application/pdf
dc.publisher.none.fl_str_mv Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1846781754561527808
score 12.982451

Publicaciones similares