Bisimilarity is not borel

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 ove...

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Author: Sanchez Terraf, Pedro Octavio
Format: article
Status:Published version
Publication Date:2017
Country:Argentina
Institution:Consejo Nacional de Investigaciones Científicas y Técnicas
Repository:CONICET Digital (CONICET)
Language:English
OAI Identifier:oai:ri.conicet.gov.ar:11336/135326
Online Access:http://hdl.handle.net/11336/135326
Access Level:Open access
Keyword:MEASURABLE LABELLED TRANSITION SYSTEM
NON-DETERMINISTIC LABELLED MARKOV PROCESS
MODAL LOGIC
BOREL HIERARCHY
https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.1
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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 Técnicas2024-05-08T13:49:05Zoai: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:34982024-05-08 13:49:05.3CONICET 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
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
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
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
topic MEASURABLE LABELLED TRANSITION SYSTEM
NON-DETERMINISTIC LABELLED MARKOV PROCESS
MODAL LOGIC
BOREL HIERARCHY
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
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
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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_ 1799195323465203712
score 15,812429

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