Scaled dimension and nonuniform complexity
Journal of Computer and System Sciences
SIGACT news complexity theory column 48
ACM SIGACT News
Journal of Computer and System Sciences - Special issue on COLT 2002
Entropy rates and finite-state dimension
Theoretical Computer Science
The arithmetical complexity of dimension and randomness
ACM Transactions on Computational Logic (TOCL)
Theoretical Computer Science
Generic density and small span theorem
Information and Computation
Scaled dimension and nonuniform complexity
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
A zero-one SUBEXP-dimension law for BPP
Information Processing Letters
Two open problems on effective dimension
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Generic density and small span theorem
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
| Hi-index | 0.00 |
Abstract: In this paper we investigate effective versions of Hausdorff dimension which have been recently introduced by Lutz. We focus on dimension in the class E of sets computable in linear exponential time. We determine the dimension of various classes related to fundamental structural properties including different types of autoreducibility and immunity. By a new general invariance theorem for resource-bounded dimension we show that the class of p-m- complete sets for E has dimension 1 in E . Moreover, we show that there are p-m-lower spans in E of dimension {\cal H} (\beta )for any rational \beta between 0 and 1 ,where {\cal H}(\beta) is the binary entropy function. This leads to a new general completeness notion for E that properly extends Lutz's concept of weak completeness. Finally we characterize resource-bounded dimension in terms of martingales with restricted betting ratios and in terms of prediction functions.