Resource-bounded strong dimension versus resource-bounded category

Authors:
John M. Hitchcock;A. Pavan
Affiliations:
Department of Computer Science, University of Wyoming, 1000 E. University Ave., Laramie, WY 82071, USA;Department of Computer Science, Iowa State University, Ames, IA 50011, USA
Venue:
Information Processing Letters
Year:
2005

Citing 8
Cited 2

Category and measure in complexity classes

SIAM Journal on Computing
Almost everywhere high nonuniform complexity

Journal of Computer and System Sciences
Almost every set in exponential time is P-bi-immune

Theoretical Computer Science
Resource-bounded genericity

Computability, enumerability, unsolvability
Genericity and measure for exponential time

MFCS '94 Selected papers from the 19th international symposium on Mathematical foundations of computer science
Dimension in Complexity Classes

SIAM Journal on Computing
A note on dimensions of polynomial size circuits

Theoretical Computer Science
Effective Strong Dimension in Algorithmic Information and Computational Complexity

SIAM Journal on Computing

Extracting Kolmogorov complexity with applications to dimension zero-one laws

Information and Computation
Extracting kolmogorov complexity with applications to dimension zero-one laws

ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I

Quantified Score

Hi-index	0.89

Visualization

Abstract

Classically it is known that any set with packing dimension less than 1 is meager in the sense of Baire category. We establish a resource-bounded extension: if a class X has @D-strong dimension less than 1, then X is @D-meager. This has the applications of explaining some of Lutz's simultaneous @D-meager, @D-measure 0 results and providing a new proof of a Gu's strong dimension result on infinitely-often classes.