DC Field | Value | Language |
---|---|---|
dc.contributor.author | Ziegler, Martin | ko |
dc.date.accessioned | 2016-04-12T07:52:03Z | - |
dc.date.available | 2016-04-12T07:52:03Z | - |
dc.date.created | 2015-09-17 | - |
dc.date.created | 2015-09-17 | - |
dc.date.issued | 2007-07 | - |
dc.identifier.citation | THEORY OF COMPUTING SYSTEMS, v.41, no.1, pp.177 - 206 | - |
dc.identifier.issn | 1432-4350 | - |
dc.identifier.uri | http://hdl.handle.net/10203/203397 | - |
dc.description.abstract | By 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.language | English | - |
dc.publisher | SPRINGER | - |
dc.subject | COMPUTABILITY | - |
dc.subject | HIERARCHY | - |
dc.subject | NUMBERS | - |
dc.subject | COMPLEXITY | - |
dc.subject | MACHINES | - |
dc.title | Real hypercomputation and continuity | - |
dc.type | Article | - |
dc.identifier.wosid | 000246522600009 | - |
dc.identifier.scopusid | 2-s2.0-34547190077 | - |
dc.type.rims | ART | - |
dc.citation.volume | 41 | - |
dc.citation.issue | 1 | - |
dc.citation.beginningpage | 177 | - |
dc.citation.endingpage | 206 | - |
dc.citation.publicationname | THEORY OF COMPUTING SYSTEMS | - |
dc.identifier.doi | 10.1007/s00224-006-1343-6 | - |
dc.contributor.localauthor | Ziegler, Martin | - |
dc.type.journalArticle | Article; Proceedings Paper | - |
dc.subject.keywordPlus | COMPUTABILITY | - |
dc.subject.keywordPlus | HIERARCHY | - |
dc.subject.keywordPlus | NUMBERS | - |
dc.subject.keywordPlus | COMPLEXITY | - |
dc.subject.keywordPlus | MACHINES | - |
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