Online learning and resource-bounded dimension: winnow yields new lower bounds for hard sets

Authors:
John M. Hitchcock
Affiliations:
Department of Computer Science, University of Wyoming
Venue:
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Year:
2006

Citing 19
Cited 1

Distinguishing conjunctive and disjunctive reducibilities by sparse sets

Information and Computation
On polynomial-time bounded truth-table reducibility of NP sets to sparse sets

SIAM Journal on Computing
Relating equivalence and reducibility to sparse sets

SIAM Journal on Computing
Almost everywhere high nonuniform complexity

Journal of Computer and System Sciences
Measure, Stochasticity, and the Density of Hard Languages

SIAM Journal on Computing
Reductions to sets of low information content

Complexity theory
With Quasilinear Queries EXP is not Polynomial Time Turing Reducible to Sparse Sets

SIAM Journal on Computing
The quantitative structure of exponential time

Complexity theory retrospective II
Twelve problems in resource-bounded measure

Current trends in theoretical computer science
The Density of Weakly Complete Problems under Adaptive Reductions

SIAM Journal on Computing
MAX3SAT is exponentially hard to approximate if NP has positive dimension

Theoretical Computer Science
Queries and Concept Learning

Machine Learning
Learning Quickly When Irrelevant Attributes Abound: A New Linear-Threshold Algorithm

Machine Learning
Queries and Concept Learning

Machine Learning
On the Existence of Hard Sparse Sets under Weak Reductions

STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
Six Hypotheses in Search of a Theorem

CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
Dimension in Complexity Classes

SIAM Journal on Computing
Scaled dimension and nonuniform complexity

Journal of Computer and System Sciences
Effective Strong Dimension in Algorithmic Information and Computational Complexity

SIAM Journal on Computing

NE is not NP turing reducible to nonexponentially dense NP sets

LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We establish a relationship between the online mistake-bound model of learning and resource-bounded dimension. This connection is combined with the Winnow algorithm to obtain new results about the density of hard sets under adaptive reductions. This improves previous work of Fu (1995) and Lutz and Zhao (2000), and solves one of Lutz and Mayordomo's “Twelve Problems in Resource-Bounded Measure” (1999).