Bisimulations for non-deterministic labelled Markov processes

Autores
D'argenio, Pedro Ruben; Sanchez Terraf, Pedro Octavio; Wolovick, Nicolás
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We extend the theory of labelled Markov processes to include internal non-determinism, which is a fundamental concept for the further development of a process theory with abstraction on non-deterministic continuous probabilistic systems. We define non-deterministic labelled Markov processes (NLMP) and provide three definitions of bisimulations: a bisimulation following a traditional characterisation; a state-based bisimulation tailored to our 'measurable' non-determinism; and an event-based bisimulation. We show the relations between them, including the fact that the largest state bisimulation is also an event bisimulation. We also introduce a variation of the Hennessy-Milner logic that characterises event bisimulation and is sound with respect to the other bisimulations for an arbitrary NLMP. This logic, however, is infinitary as it contains a denumerable. We then introduce a finitary sublogic that characterises all bisimulations for an image finite NLMP whose underlying measure space is also analytic. Hence, in this setting, all the notions of bisimulation we consider turn out to be equal. Finally, we show that all these bisimulation notions are different in the general case. The counterexamples that separate them turn out to be non-probabilistic NLMPs.
Fil: D'argenio, Pedro Ruben. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Fil: Sanchez Terraf, Pedro Octavio. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Fil: Wolovick, Nicolás. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Materia
PROCESS SEMANTICS
CONTINUOUS PROBABILITY
BISIMULATION
MEASURE THEORY
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:11336/197265
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Bisimulations for non-deterministic labelled Markov processesD'argenio, Pedro RubenSanchez Terraf, Pedro OctavioWolovick, NicolásPROCESS SEMANTICSCONTINUOUS PROBABILITYBISIMULATIONMEASURE THEORYhttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1We extend the theory of labelled Markov processes to include internal non-determinism, which is a fundamental concept for the further development of a process theory with abstraction on non-deterministic continuous probabilistic systems. We define non-deterministic labelled Markov processes (NLMP) and provide three definitions of bisimulations: a bisimulation following a traditional characterisation; a state-based bisimulation tailored to our 'measurable' non-determinism; and an event-based bisimulation. We show the relations between them, including the fact that the largest state bisimulation is also an event bisimulation. We also introduce a variation of the Hennessy-Milner logic that characterises event bisimulation and is sound with respect to the other bisimulations for an arbitrary NLMP. This logic, however, is infinitary as it contains a denumerable. We then introduce a finitary sublogic that characterises all bisimulations for an image finite NLMP whose underlying measure space is also analytic. Hence, in this setting, all the notions of bisimulation we consider turn out to be equal. Finally, we show that all these bisimulation notions are different in the general case. The counterexamples that separate them turn out to be non-probabilistic NLMPs.Fil: D'argenio, Pedro Ruben. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Sanchez Terraf, Pedro Octavio. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Wolovick, Nicolás. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaCambridge University Press2012-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/197265D'argenio, Pedro Ruben; Sanchez Terraf, Pedro Octavio; Wolovick, Nicolás; Bisimulations for non-deterministic labelled Markov processes; Cambridge University Press; Mathematical Structures In Computer Science; 22; 1; 2-2012; 43-680960-1295CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8459011info:eu-repo/semantics/altIdentifier/doi/10.1017/S0960129511000454info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:50:10Zoai:ri.conicet.gov.ar:11336/197265instacron: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:34982025-09-03 09:50:10.794CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Bisimulations for non-deterministic labelled Markov processes
title Bisimulations for non-deterministic labelled Markov processes
spellingShingle Bisimulations for non-deterministic labelled Markov processes
D'argenio, Pedro Ruben
PROCESS SEMANTICS
CONTINUOUS PROBABILITY
BISIMULATION
MEASURE THEORY
title_short Bisimulations for non-deterministic labelled Markov processes
title_full Bisimulations for non-deterministic labelled Markov processes
title_fullStr Bisimulations for non-deterministic labelled Markov processes
title_full_unstemmed Bisimulations for non-deterministic labelled Markov processes
title_sort Bisimulations for non-deterministic labelled Markov processes
dc.creator.none.fl_str_mv D'argenio, Pedro Ruben
Sanchez Terraf, Pedro Octavio
Wolovick, Nicolás
author D'argenio, Pedro Ruben
author_facet D'argenio, Pedro Ruben
Sanchez Terraf, Pedro Octavio
Wolovick, Nicolás
author_role author
author2 Sanchez Terraf, Pedro Octavio
Wolovick, Nicolás
author2_role author
author
dc.subject.none.fl_str_mv PROCESS SEMANTICS
CONTINUOUS PROBABILITY
BISIMULATION
MEASURE THEORY
topic PROCESS SEMANTICS
CONTINUOUS PROBABILITY
BISIMULATION
MEASURE THEORY
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We extend the theory of labelled Markov processes to include internal non-determinism, which is a fundamental concept for the further development of a process theory with abstraction on non-deterministic continuous probabilistic systems. We define non-deterministic labelled Markov processes (NLMP) and provide three definitions of bisimulations: a bisimulation following a traditional characterisation; a state-based bisimulation tailored to our 'measurable' non-determinism; and an event-based bisimulation. We show the relations between them, including the fact that the largest state bisimulation is also an event bisimulation. We also introduce a variation of the Hennessy-Milner logic that characterises event bisimulation and is sound with respect to the other bisimulations for an arbitrary NLMP. This logic, however, is infinitary as it contains a denumerable. We then introduce a finitary sublogic that characterises all bisimulations for an image finite NLMP whose underlying measure space is also analytic. Hence, in this setting, all the notions of bisimulation we consider turn out to be equal. Finally, we show that all these bisimulation notions are different in the general case. The counterexamples that separate them turn out to be non-probabilistic NLMPs.
Fil: D'argenio, Pedro Ruben. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Fil: Sanchez Terraf, Pedro Octavio. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Fil: Wolovick, Nicolás. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
description We extend the theory of labelled Markov processes to include internal non-determinism, which is a fundamental concept for the further development of a process theory with abstraction on non-deterministic continuous probabilistic systems. We define non-deterministic labelled Markov processes (NLMP) and provide three definitions of bisimulations: a bisimulation following a traditional characterisation; a state-based bisimulation tailored to our 'measurable' non-determinism; and an event-based bisimulation. We show the relations between them, including the fact that the largest state bisimulation is also an event bisimulation. We also introduce a variation of the Hennessy-Milner logic that characterises event bisimulation and is sound with respect to the other bisimulations for an arbitrary NLMP. This logic, however, is infinitary as it contains a denumerable. We then introduce a finitary sublogic that characterises all bisimulations for an image finite NLMP whose underlying measure space is also analytic. Hence, in this setting, all the notions of bisimulation we consider turn out to be equal. Finally, we show that all these bisimulation notions are different in the general case. The counterexamples that separate them turn out to be non-probabilistic NLMPs.
publishDate 2012
dc.date.none.fl_str_mv 2012-02
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/11336/197265
D'argenio, Pedro Ruben; Sanchez Terraf, Pedro Octavio; Wolovick, Nicolás; Bisimulations for non-deterministic labelled Markov processes; Cambridge University Press; Mathematical Structures In Computer Science; 22; 1; 2-2012; 43-68
0960-1295
CONICET Digital
CONICET
url http://hdl.handle.net/11336/197265
identifier_str_mv D'argenio, Pedro Ruben; Sanchez Terraf, Pedro Octavio; Wolovick, Nicolás; Bisimulations for non-deterministic labelled Markov processes; Cambridge University Press; Mathematical Structures In Computer Science; 22; 1; 2-2012; 43-68
0960-1295
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8459011
info:eu-repo/semantics/altIdentifier/doi/10.1017/S0960129511000454
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/pdf
application/pdf
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
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score 13.13397

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