Computation with perturbed dynamical systems

Detalhes bibliográficos
Autor(a) principal: Bournez, Olivier
Data de Publicação: 2013
Outros Autores: Graca, Daniel S., Hainry, Emmanuel
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.1/11164
Resumo: This paper analyzes the computational power of dynamical systems robust to infinitesimal perturbations. Previous work on the subject has delved on very specific types of systems. Here we obtain results for broader classes of dynamical systems (including those systems defined by Lipschitz/analytic functions). In particular we show that systems robust to infinitesimal perturbations only recognize recursive languages. We also show the converse direction: every recursive language can be robustly recognized by a computable system. By other words we show that robustness is equivalent to decidability. (C) 2013 Elsevier Inc. All rights reserved.
id RCAP_6e3cfb42fec46f30cbec8eddb4cd22ae
oai_identifier_str oai:sapientia.ualg.pt:10400.1/11164
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling Computation with perturbed dynamical systemsHybrid systemsTuring-machinesArithmetical hierarchyNeural-networksReachable setsAnalytic-mapsComputabilityUndecidabilityAchillesAutomataThis paper analyzes the computational power of dynamical systems robust to infinitesimal perturbations. Previous work on the subject has delved on very specific types of systems. Here we obtain results for broader classes of dynamical systems (including those systems defined by Lipschitz/analytic functions). In particular we show that systems robust to infinitesimal perturbations only recognize recursive languages. We also show the converse direction: every recursive language can be robustly recognized by a computable system. By other words we show that robustness is equivalent to decidability. (C) 2013 Elsevier Inc. All rights reserved.INRIA program "Equipe Associee" ComputR; Fundacao para a Ciencia e a Tecnologia; EU FEDER POCTI/POCI via SQIG - Instituto de Telecomunicacoes through the FCT project [PEst-OE/EEI/LA0008/2011]Academic Press Inc Elsevier ScienceSapientiaBournez, OlivierGraca, Daniel S.Hainry, Emmanuel2018-12-07T14:52:41Z2013-082013-08-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/11164eng0022-000010.1016/j.jcss.2013.01.025info: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:RCAAP2023-07-24T10:22:55Zoai:sapientia.ualg.pt:10400.1/11164Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:02:40.879918Repositório 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 Computation with perturbed dynamical systems
title Computation with perturbed dynamical systems
spellingShingle Computation with perturbed dynamical systems
Bournez, Olivier
Hybrid systems
Turing-machines
Arithmetical hierarchy
Neural-networks
Reachable sets
Analytic-maps
Computability
Undecidability
Achilles
Automata
title_short Computation with perturbed dynamical systems
title_full Computation with perturbed dynamical systems
title_fullStr Computation with perturbed dynamical systems
title_full_unstemmed Computation with perturbed dynamical systems
title_sort Computation with perturbed dynamical systems
author Bournez, Olivier
author_facet Bournez, Olivier
Graca, Daniel S.
Hainry, Emmanuel
author_role author
author2 Graca, Daniel S.
Hainry, Emmanuel
author2_role author
author
dc.contributor.none.fl_str_mv Sapientia
dc.contributor.author.fl_str_mv Bournez, Olivier
Graca, Daniel S.
Hainry, Emmanuel
dc.subject.por.fl_str_mv Hybrid systems
Turing-machines
Arithmetical hierarchy
Neural-networks
Reachable sets
Analytic-maps
Computability
Undecidability
Achilles
Automata
topic Hybrid systems
Turing-machines
Arithmetical hierarchy
Neural-networks
Reachable sets
Analytic-maps
Computability
Undecidability
Achilles
Automata
description This paper analyzes the computational power of dynamical systems robust to infinitesimal perturbations. Previous work on the subject has delved on very specific types of systems. Here we obtain results for broader classes of dynamical systems (including those systems defined by Lipschitz/analytic functions). In particular we show that systems robust to infinitesimal perturbations only recognize recursive languages. We also show the converse direction: every recursive language can be robustly recognized by a computable system. By other words we show that robustness is equivalent to decidability. (C) 2013 Elsevier Inc. All rights reserved.
publishDate 2013
dc.date.none.fl_str_mv 2013-08
2013-08-01T00:00:00Z
2018-12-07T14:52:41Z
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/10400.1/11164
url http://hdl.handle.net/10400.1/11164
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0022-0000
10.1016/j.jcss.2013.01.025
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 Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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_ 1799133261578895360

Registros relacionados