Finite-State Dimension and Real Arithmetic

  • David Doty
  • Jack H. Lutz
  • Satyadev Nandakumar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4051)

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 α, the base-k expansions of α, q + α, and 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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • David Doty
    • 1
  • Jack H. Lutz
    • 1
  • Satyadev Nandakumar
    • 1
  1. 1.Department of Computer ScienceIowa State UniversityAmesUSA

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