Computer Science – Computational Complexity
Scientific paper
2006-02-09
Computer Science
Computational Complexity
15 pages
Scientific paper
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.
Doty David
Lutz Jack H.
Nandakumar Satyadev
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