A Strange Application of Kolmogorov Complexity

  • Authors:

  • D. Hammer;A. Shen

  • Affiliations:

  • Technische Universität Berlin, FB Mathematik, Sekr. MA 8-1, Straβ e des 17. Juni 135, 10623 Berlin, Germany hammer@math.tu-berlin.de , Germany;Institute of Problems of Information Transmission, 57th Moscow School, Moscow Mathematics Institute, Moscow, Russia shen@main.mccme.rssi.ru, Russia

  • Venue:
  • Theory of Computing Systems
  • Year:
  • 1998

Quantified Score

Hi-index 0.00

Visualization

Abstract

This paper deals with two similar inequalities:[Figure not available: see fulltext.][Figure not available: see fulltext.]where K denotes simple Kolmogorov entropy (i.e., the very first version of Kolmogorov complexity having been introduced by Kolmogorov himself) and KP denotes prefix entropy (self-delimiting complexity by the terminology of Li and Vitanyi [1]). It turns out that from (1) the following well-known geometric fact can be inferred:[Figure not available: see fulltext.]where V is a set in three-dimensional space, Sxy , Syz , Sxz are its three two-dimensional projections, and |W| is the volume (or the area) of W . Inequality (2), in its turn, is a corollary of the well-known Cauchy--Schwarz inequality. So the connection between geometry and Kolmogorov complexity works in both directions.