Analog Computers and the Iteration Functional
Autor(a) principal: | |
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Data de Publicação: | 1998 |
Outros Autores: | , |
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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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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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 |
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 |
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1799134258511478784 |