Finite-State Dimension and Real Arithmetic

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dc.creatorDoty, David
dc.creatorLutz, Jack H.
dc.creatorNandakumar, Satyadev
dc.date2006-02-09
dc.date.accessioned2026-07-07T08:16:21Z
dc.date.available2026-07-07T08:16:21Z
dc.descriptionWe 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.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/cs/0602032
dc.identifierhttp://arxiv.org/abs/cs/0602032
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/133752
dc.subjectComputational Complexity
dc.subjectInformation Theory
dc.titleFinite-State Dimension and Real Arithmetic
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