Large alphabets and incompressibility

  • Authors:
  • Travis Gagie

  • Affiliations:
  • Department of Computer Science, University of Toronto, Canada

  • Venue:
  • Information Processing Letters
  • Year:
  • 2006

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Abstract

We briefly survey some concepts related to empirical entropy--normal numbers, de Bruijn sequences and Markov processes-- and investigate how well it approximates Kolmogorov complexity. Our results suggest lth-order empirical entropy stops being a reasonable complexity metric for almost all strings of length m over alphabets of size n about when nl surpasses m.