Real hypercomputation and continuity

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dc.contributor.authorZiegler, Martinko
dc.date.accessioned2016-04-12T07:52:03Z-
dc.date.available2016-04-12T07:52:03Z-
dc.date.created2015-09-17-
dc.date.created2015-09-17-
dc.date.issued2007-07-
dc.identifier.citationTHEORY OF COMPUTING SYSTEMS, v.41, no.1, pp.177 - 206-
dc.identifier.issn1432-4350-
dc.identifier.urihttp://hdl.handle.net/10203/203397-
dc.description.abstractBy the sometimes so-called Main Theorem of Recursive Analysis, every computable real function is necessarily continuous. We wonder whether and which kinds of hype rcomputation allow for the effective evaluation of also discontinuous f: R ->-> R. More precisely the present work considers the following three superTuring notions of real function computability: - lativized computation; specifically given oracle access to the Halting Problem 0' or its jump 0"; - encoding input x epsilon R and/or output y = f (x) in weaker ways also related to the Arithmetic Hierarchy; - nondeterministic computation. It turns out that any f: R ->-> R computable in the first or second sense is still necessarily continuous whereas the third type of hypercomputation provides the required power to evaluate for instance the discontinuous Heaviside function.-
dc.languageEnglish-
dc.publisherSPRINGER-
dc.subjectCOMPUTABILITY-
dc.subjectHIERARCHY-
dc.subjectNUMBERS-
dc.subjectCOMPLEXITY-
dc.subjectMACHINES-
dc.titleReal hypercomputation and continuity-
dc.typeArticle-
dc.identifier.wosid000246522600009-
dc.identifier.scopusid2-s2.0-34547190077-
dc.type.rimsART-
dc.citation.volume41-
dc.citation.issue1-
dc.citation.beginningpage177-
dc.citation.endingpage206-
dc.citation.publicationnameTHEORY OF COMPUTING SYSTEMS-
dc.identifier.doi10.1007/s00224-006-1343-6-
dc.contributor.localauthorZiegler, Martin-
dc.type.journalArticleArticle; Proceedings Paper-
dc.subject.keywordPlusCOMPUTABILITY-
dc.subject.keywordPlusHIERARCHY-
dc.subject.keywordPlusNUMBERS-
dc.subject.keywordPlusCOMPLEXITY-
dc.subject.keywordPlusMACHINES-
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