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International Colloquium on Automata, Languages, and Programming

ICALP 2006: Automata, Languages and Programming pp 537–547Cite as

Finite-State Dimension and Real Arithmetic

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,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 qα 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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Author information

Authors and Affiliations

  1. Department of Computer Science, Iowa State University, Ames, IA, 50011, USA

    David Doty, Jack H. Lutz & Satyadev Nandakumar

Authors
  1. David Doty
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  2. Jack H. Lutz
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  3. Satyadev Nandakumar
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Università Ca’ Foscari, Venice

    Michele Bugliesi

  2. Interdisciplinary Institute for BroadBand Technology (IBBT), Belgium

    Bart Preneel

  3. ECS, University of Southampton, UK

    Vladimiro Sassone

  4. FB Informatik, Univ. Dortmund, LS2, 44221, Dortmund, Germany

    Ingo Wegener

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© 2006 Springer-Verlag Berlin Heidelberg

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Doty, D., Lutz, J.H., Nandakumar, S. (2006). Finite-State Dimension and Real Arithmetic. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11786986_47

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  • DOI: https://doi.org/10.1007/11786986_47

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35904-3

  • Online ISBN: 978-3-540-35905-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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