Complexity theory of real functions
Complexity theory of real functions
Complexity and real computation
Complexity and real computation
Computable analysis: an introduction
Computable analysis: an introduction
Complexity theory for operators in analysis
Proceedings of the forty-second ACM symposium on Theory of computing
Lipschitz Continuous Ordinary Differential Equations are Polynomial-Space Complete
Computational Complexity - Selected papers from the 24th Annual IEEE Conference on Computational Complexity (CCC 2009)
On the Kolmogorov complexity of continuous real functions
CiE'11 Proceedings of the 7th conference on Models of computation in context: computability in Europe
Computational complexity of smooth differential equations
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
| Hi-index | 0.00 |
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.