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On the query complexity of real functionals

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.
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Contributor : Mathieu Hoyrup Connect in order to contact the contributor
Submitted on : Monday, January 14, 2013 - 2:32:02 PM
Last modification on : Saturday, October 16, 2021 - 11:26:05 AM
Long-term archiving on: : Monday, April 15, 2013 - 4:02:07 AM


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Hugo Férée, Mathieu Hoyrup, Walid Gomaa. On the query complexity of real functionals. LICS - 28th ACM/IEEE Symposium on Logic in Computer Science, Jun 2013, New Orleans, United States. pp.103-112, ⟨10.1109/LICS.2013.15⟩. ⟨hal-00773653⟩



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