Finite-State Dimension and Real Arithmetic

We use entropy rates and Schur concavity to prove that, for every integer k 2, every nonzero rational number q, and every real number , the base-k expansions of , q + , and q all have the same finite-state dimension and the same finitestate 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.

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: David Doty, Jack H. Lutz, Satyadev Nandakumar
• Keywords: Borel Normal Number, CORR 2006, Education, Finitestate Strong Dimension, Nonzero Rational Number