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Computation with perturbed dynamical systems

2013-08Journal article Open access
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dc.contributor.authorBournez, Olivier
dc.contributor.authorGraca, Daniel S.
dc.contributor.authorHainry, Emmanuel
dc.date.accessioned2018-12-07T14:52:41Z
dc.date.available2018-12-07T14:52:41Z
dc.date.issued2013-08
dc.description.abstractThis 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.
dc.description.sponsorshipINRIA 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]
dc.description.versioninfo:eu-repo/semantics/publishedVersion
dc.identifier.doi10.1016/j.jcss.2013.01.025
dc.identifier.issn0022-0000
dc.identifier.urihttp://hdl.handle.net/10400.1/11164
dc.language.isoeng
dc.peerreviewedyes
dc.publisherAcademic Press Inc Elsevier Science
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectHybrid systems
dc.subjectTuring-machines
dc.subjectArithmetical hierarchy
dc.subjectNeural-networks
dc.subjectReachable sets
dc.subjectAnalytic-maps
dc.subjectComputability
dc.subjectUndecidability
dc.subjectAchilles
dc.subjectAutomata
dc.titleComputation with perturbed dynamical systems
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage724
oaire.citation.issue5
oaire.citation.startPage714
oaire.citation.titleJournal of Computer and System Sciences
oaire.citation.volume79
person.familyNameBournez
person.familyNameGraça
person.givenNameOlivier
person.givenNameDaniel
person.identifier.ciencia-id2D11-56DE-3F11
person.identifier.orcid0000-0002-9218-1130
person.identifier.orcid0000-0002-0330-833X
person.identifier.ridD-2335-2011
person.identifier.scopus-author-id8882791800
rcaap.rightsopenAccess
rcaap.typearticle
relation.isAuthorOfPublication7813fa45-0e7c-412a-9083-e761008efff5
relation.isAuthorOfPublicationba0c1461-5d2d-4f06-b648-df4a1a505bdf
relation.isAuthorOfPublication.latestForDiscovery7813fa45-0e7c-412a-9083-e761008efff5

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