InforLorV4, Main, Exploration, bibRecord, 001146

On the query complexity of real functionals

Identifieur interne : 001146 ( Main/Exploration ); précédent : 001145; suivant : 001147

On the query complexity of real functionals

Auteurs : Hugo Férée [France] ; Mathieu Hoyrup [France] ; Walid Gomaa [Égypte]

Source :

RBID : Hal:hal-00773653

Abstract

Recently Kawamura and Cook developed a framework to define the computational complexity of operators arising in analysis. Our goal is to understand the effects of complexity restrictions on the analytical properties of the operator. We focus on the case of norms over C[0,1] and introduce the notion of dependence of a norm on a point and relate it to the query complexity of the norm. We show that the dependence of almost every point is of the order of the query complexity of the norm. A norm with small complexity depends on a few points but, as compensation, highly depends on them. We characterize the functionals that are computable using one oracle call only and discuss the uniformity of that characterization.

Url:

https://hal.inria.fr/hal-00773653

DOI: 10.1109/LICS.2013.15

Affiliations:

Links toward previous steps (curation, corpus...)

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to stream Hal, to step Curation: 003856
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Le document en format XML

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<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-211562" status="VALID"><orgName>Department of Computer and Systems Engineering [Alexandria]</orgName>
<desc><address><country key="EG"></country>
</address>
</desc>
<listRelation><relation active="#struct-301450" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-301450" type="direct"><org type="institution" xml:id="struct-301450" status="VALID"><orgName>Université d'Alexandrie</orgName>
<desc><address><country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>Égypte</country>
</affiliation>
</author>
</analytic>
<idno type="DOI">10.1109/LICS.2013.15</idno>
</biblStruct>
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<profileDesc><textClass></textClass>
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<front><div type="abstract" xml:lang="en">Recently Kawamura and Cook developed a framework to define the computational complexity of operators arising in analysis. Our goal is to understand the effects of complexity restrictions on the analytical properties of the operator. We focus on the case of norms over C[0,1] and introduce the notion of dependence of a norm on a point and relate it to the query complexity of the norm. We show that the dependence of almost every point is of the order of the query complexity of the norm. A norm with small complexity depends on a few points but, as compensation, highly depends on them. We characterize the functionals that are computable using one oracle call only and discuss the uniformity of that characterization.</div>
</front>
</TEI>
<affiliations><list><country><li>France</li>
<li>Égypte</li>
</country>
<region><li>Grand Est</li>
<li>Lorraine (région)</li>
</region>
<settlement><li>Metz</li>
<li>Nancy</li>
</settlement>
<orgName><li>Université de Lorraine</li>
</orgName>
</list>
<tree><country name="France"><region name="Grand Est"><name sortKey="Feree, Hugo" sort="Feree, Hugo" uniqKey="Feree H" first="Hugo" last="Férée">Hugo Férée</name>
</region>
<name sortKey="Hoyrup, Mathieu" sort="Hoyrup, Mathieu" uniqKey="Hoyrup M" first="Mathieu" last="Hoyrup">Mathieu Hoyrup</name>
</country>
<country name="Égypte"><noRegion><name sortKey="Gomaa, Walid" sort="Gomaa, Walid" uniqKey="Gomaa W" first="Walid" last="Gomaa">Walid Gomaa</name>
</noRegion>
</country>
</tree>
</affiliations>
</record>

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On the query complexity of real functionals

On the query complexity of real functionals

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