Analog Computers and the Iteration Functional

Detalhes bibliográficos
Autor(a) principal: Campagnolo, Manuel Lameiras
Data de Publicação: 1998
Outros Autores: Moore, Cristopher, Costa, José Félix
Tipo de documento: Relatório
Idioma: por
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10451/14111
Resumo: In this paper we extend the class of differentially algebraic functions computed by Shannon's General Purpose Analog Computer (GPAC). We relax Pour-El's definition of GPAC to obtain new operators and we use recursion theory on the reals to define a new class of analog computable functions. We show that a function F(t,x) which simulates t time-steps of a Turing machine on input x, and more generally a functional that allows us to define the t'th iterate of a definable function, are definable in this system. Therefore, functions like Gamma which are not generable by GPAC become computable in this extension
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spelling Analog Computers and the Iteration FunctionalAnalog computationrecursion theorycomputable functionsuniversal computationIn this paper we extend the class of differentially algebraic functions computed by Shannon's General Purpose Analog Computer (GPAC). We relax Pour-El's definition of GPAC to obtain new operators and we use recursion theory on the reals to define a new class of analog computable functions. We show that a function F(t,x) which simulates t time-steps of a Turing machine on input x, and more generally a functional that allows us to define the t'th iterate of a definable function, are definable in this system. Therefore, functions like Gamma which are not generable by GPAC become computable in this extensionDepartment of Informatics, University of LisbonRepositório da Universidade de LisboaCampagnolo, Manuel LameirasMoore, CristopherCosta, José Félix2009-02-10T13:11:58Z1998-121998-12-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/reportapplication/octet-streamhttp://hdl.handle.net/10451/14111porinfo: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:RCAAP2023-11-08T15:59:42Zoai:repositorio.ul.pt:10451/14111Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:35:57.971743Repositório 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 Analog Computers and the Iteration Functional
title Analog Computers and the Iteration Functional
spellingShingle Analog Computers and the Iteration Functional
Campagnolo, Manuel Lameiras
Analog computation
recursion theory
computable functions
universal computation
title_short Analog Computers and the Iteration Functional
title_full Analog Computers and the Iteration Functional
title_fullStr Analog Computers and the Iteration Functional
title_full_unstemmed Analog Computers and the Iteration Functional
title_sort Analog Computers and the Iteration Functional
author Campagnolo, Manuel Lameiras
author_facet Campagnolo, Manuel Lameiras
Moore, Cristopher
Costa, José Félix
author_role author
author2 Moore, Cristopher
Costa, José Félix
author2_role author
author
dc.contributor.none.fl_str_mv Repositório da Universidade de Lisboa
dc.contributor.author.fl_str_mv Campagnolo, Manuel Lameiras
Moore, Cristopher
Costa, José Félix
dc.subject.por.fl_str_mv Analog computation
recursion theory
computable functions
universal computation
topic Analog computation
recursion theory
computable functions
universal computation
description In this paper we extend the class of differentially algebraic functions computed by Shannon's General Purpose Analog Computer (GPAC). We relax Pour-El's definition of GPAC to obtain new operators and we use recursion theory on the reals to define a new class of analog computable functions. We show that a function F(t,x) which simulates t time-steps of a Turing machine on input x, and more generally a functional that allows us to define the t'th iterate of a definable function, are definable in this system. Therefore, functions like Gamma which are not generable by GPAC become computable in this extension
publishDate 1998
dc.date.none.fl_str_mv 1998-12
1998-12-01T00:00:00Z
2009-02-10T13:11:58Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/report
format report
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10451/14111
url http://hdl.handle.net/10451/14111
dc.language.iso.fl_str_mv por
language por
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/octet-stream
dc.publisher.none.fl_str_mv Department of Informatics, University of Lisbon
publisher.none.fl_str_mv Department of Informatics, University of Lisbon
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
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instacron_str RCAAP
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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
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