Quantitative Hennessy-Milner theorems via notions of density
Autor(a) principal: | |
---|---|
Data de Publicação: | 2023 |
Outros Autores: | , , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10773/37968 |
Resumo: | The classical Hennessy-Milner theorem is an important tool in the analysis of concurrent processes; it guarantees that any two non-bisimilar states in finitely branching labelled transition systems can be distinguished by a modal formula. Numerous variants of this theorem have since been established for a wide range of logics and system types, including quantitative versions where lower bounds on behavioural distance (e.g. in weighted, metric, or probabilistic transition systems) are witnessed by quantitative modal formulas. Both the qualitative and the quantitative versions have been accommodated within the framework of coalgebraic logic, with distances taking values in quantales, subject to certain restrictions, such as being so-called value quantales. While previous quantitative coalgebraic Hennessy-Milner theorems apply only to liftings of set functors to (pseudo)metric spaces, in the present work we provide a quantitative coalgebraic Hennessy-Milner theorem that applies more widely to functors native to metric spaces; notably, we thus cover, for the first time, the well-known Hennessy-Milner theorem for continuous probabilistic transition systems, where transitions are given by Borel measures on metric spaces, as an instance of such a general result. In the process, we also relax the restrictions imposed on the quantale, and additionally parametrize the technical account over notions of closure and, hence, density, providing associated variants of the Stone-Weierstraß theorem; this allows us to cover, for instance, behavioural ultrametrics. |
id |
RCAP_0ca0732adb760fbce544d10f87c2148e |
---|---|
oai_identifier_str |
oai:ria.ua.pt:10773/37968 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
Quantitative Hennessy-Milner theorems via notions of densityBehavioural distancesCoalgebraCharacteristic modal logicsDensityHennessy-Milner theoremsQuantale-enriched categoriesStone-Weierstraß theoremsThe classical Hennessy-Milner theorem is an important tool in the analysis of concurrent processes; it guarantees that any two non-bisimilar states in finitely branching labelled transition systems can be distinguished by a modal formula. Numerous variants of this theorem have since been established for a wide range of logics and system types, including quantitative versions where lower bounds on behavioural distance (e.g. in weighted, metric, or probabilistic transition systems) are witnessed by quantitative modal formulas. Both the qualitative and the quantitative versions have been accommodated within the framework of coalgebraic logic, with distances taking values in quantales, subject to certain restrictions, such as being so-called value quantales. While previous quantitative coalgebraic Hennessy-Milner theorems apply only to liftings of set functors to (pseudo)metric spaces, in the present work we provide a quantitative coalgebraic Hennessy-Milner theorem that applies more widely to functors native to metric spaces; notably, we thus cover, for the first time, the well-known Hennessy-Milner theorem for continuous probabilistic transition systems, where transitions are given by Borel measures on metric spaces, as an instance of such a general result. In the process, we also relax the restrictions imposed on the quantale, and additionally parametrize the technical account over notions of closure and, hence, density, providing associated variants of the Stone-Weierstraß theorem; this allows us to cover, for instance, behavioural ultrametrics.Schloss Dagstuhl - Leibniz-Zentrum für Informatik2023-06-07T14:59:20Z2023-01-01T00:00:00Z2023info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/37968eng10.4230/LIPIcs.CSL.2023.22Forster, JonasGoncharov, SergeyHofmann, DirkNora, PedroSchröder, LutzWild, Paulinfo: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:RCAAP2024-02-22T12:11:55Zoai:ria.ua.pt:10773/37968Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:07:53.946398Repositório 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 |
Quantitative Hennessy-Milner theorems via notions of density |
title |
Quantitative Hennessy-Milner theorems via notions of density |
spellingShingle |
Quantitative Hennessy-Milner theorems via notions of density Forster, Jonas Behavioural distances Coalgebra Characteristic modal logics Density Hennessy-Milner theorems Quantale-enriched categories Stone-Weierstraß theorems |
title_short |
Quantitative Hennessy-Milner theorems via notions of density |
title_full |
Quantitative Hennessy-Milner theorems via notions of density |
title_fullStr |
Quantitative Hennessy-Milner theorems via notions of density |
title_full_unstemmed |
Quantitative Hennessy-Milner theorems via notions of density |
title_sort |
Quantitative Hennessy-Milner theorems via notions of density |
author |
Forster, Jonas |
author_facet |
Forster, Jonas Goncharov, Sergey Hofmann, Dirk Nora, Pedro Schröder, Lutz Wild, Paul |
author_role |
author |
author2 |
Goncharov, Sergey Hofmann, Dirk Nora, Pedro Schröder, Lutz Wild, Paul |
author2_role |
author author author author author |
dc.contributor.author.fl_str_mv |
Forster, Jonas Goncharov, Sergey Hofmann, Dirk Nora, Pedro Schröder, Lutz Wild, Paul |
dc.subject.por.fl_str_mv |
Behavioural distances Coalgebra Characteristic modal logics Density Hennessy-Milner theorems Quantale-enriched categories Stone-Weierstraß theorems |
topic |
Behavioural distances Coalgebra Characteristic modal logics Density Hennessy-Milner theorems Quantale-enriched categories Stone-Weierstraß theorems |
description |
The classical Hennessy-Milner theorem is an important tool in the analysis of concurrent processes; it guarantees that any two non-bisimilar states in finitely branching labelled transition systems can be distinguished by a modal formula. Numerous variants of this theorem have since been established for a wide range of logics and system types, including quantitative versions where lower bounds on behavioural distance (e.g. in weighted, metric, or probabilistic transition systems) are witnessed by quantitative modal formulas. Both the qualitative and the quantitative versions have been accommodated within the framework of coalgebraic logic, with distances taking values in quantales, subject to certain restrictions, such as being so-called value quantales. While previous quantitative coalgebraic Hennessy-Milner theorems apply only to liftings of set functors to (pseudo)metric spaces, in the present work we provide a quantitative coalgebraic Hennessy-Milner theorem that applies more widely to functors native to metric spaces; notably, we thus cover, for the first time, the well-known Hennessy-Milner theorem for continuous probabilistic transition systems, where transitions are given by Borel measures on metric spaces, as an instance of such a general result. In the process, we also relax the restrictions imposed on the quantale, and additionally parametrize the technical account over notions of closure and, hence, density, providing associated variants of the Stone-Weierstraß theorem; this allows us to cover, for instance, behavioural ultrametrics. |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-06-07T14:59:20Z 2023-01-01T00:00:00Z 2023 |
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 |
http://hdl.handle.net/10773/37968 |
url |
http://hdl.handle.net/10773/37968 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.4230/LIPIcs.CSL.2023.22 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
publisher.none.fl_str_mv |
Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
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 |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
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 |
repository.mail.fl_str_mv |
|
_version_ |
1799137733127438336 |