Finite-State Dimension and Real Arithmetic
计算复杂性
2007-07-13 v1 信息论
math.IT
摘要
We use entropy rates and Schur concavity to prove that, for every integer k >= 2, every nonzero rational number q, and every real number alpha, the base-k expansions of alpha, q+alpha, and q*alpha 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.
引用
@article{arxiv.cs/0602032,
title = {Finite-State Dimension and Real Arithmetic},
author = {David Doty and Jack H. Lutz and Satyadev Nandakumar},
journal= {arXiv preprint arXiv:cs/0602032},
year = {2007}
}
备注
15 pages