Logic in Computer Science, Symposium on (2013)

New Orleans, LA, USA USA

June 25, 2013 to June 28, 2013

ISSN: 1043-6871

ISBN: 978-1-4799-0413-6

pp: 103-112

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/LICS.2013.15

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.

INDEX TERMS

Polynomials, Turing machines, Topology, Computational complexity, Electronic mail, Extraterrestrial measurements, norm, Computable analysis, computational complexity, oracle Turing machine, polynomial time computable functional

CITATION

Hugo Feree,
Mathieu Hoyrup,
Walid Gomaa,
"On the Query Complexity of Real Functionals",

*Logic in Computer Science, Symposium on*, vol. 00, no. , pp. 103-112, 2013, doi:10.1109/LICS.2013.15