Finite-state dimension and real arithmetic

Authors:
David Doty;Jack H. Lutz;Satyadev Nandakumar
Affiliations:
Department of Computer Science, Iowa State University, Ames, IA 50011, USA;Department of Computer Science, Iowa State University, Ames, IA 50011, USA;Department of Computer Science, Iowa State University, Ames, IA 50011, USA
Venue:
Information and Computation
Year:
2007

Citing 9
Cited 2

An introduction to Kolmogorov complexity and its applications (2nd ed.)

An introduction to Kolmogorov complexity and its applications (2nd ed.)
Note: fractal dimension and logarithmic loss unpredictability

Theoretical Computer Science
Dimension in Complexity Classes

SIAM Journal on Computing
The dimensions of individual strings and sequences

Information and Computation
Finite-state dimension

Theoretical Computer Science
Entropy rates and finite-state dimension

Theoretical Computer Science
Selection Functions that Do Not Preserve Normality

Theory of Computing Systems
Dimensions of Copeland--Erdös sequences

Information and Computation
Effective Strong Dimension in Algorithmic Information and Computational Complexity

SIAM Journal on Computing

Functions that preserve p-randomness

FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Functions that preserve p-randomness

Information and Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

We use entropy rates and Schur concavity to prove that, for every integer k=2, every nonzero rational number q, and every real number @a, the base-k expansions of @a, q+@a, and q@a all have the same finite-state dimension and the same finite-state strong dimension. This extends, and gives a new proof of, Wall's 1949 theorem stating that the sum or product of a nonzero rational number and a Borel normal number is always Borel normal.