Advertisement

The Incompressibility Method

  • Ming Li
  • Paul Vitányi
Part of the Texts and Monographs in Computer Science book series (MCS)

Abstract

The incompressibility of random objects yields a simple but powerful proof technique. The incompressibility method is a general purpose tool and should be compared with the pidgeon hole principle or the probabilistic method. Whereas the older methods generally show the existence of an object with the required properties, the incompressibility argument shows that almost all objects have the required property. This follows immediately from the fact that the argument is typically used on a Kolmogorov random object. Since such objects are effectively undistinguishable, the proof holds for all such objects. Each class of objects has an abundance of relatively Kolmogorov random objects. In fact, they have probability about 1.

Keywords

Entropy Compressibility Sorting Rosen Prefix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Ming Li
    • 1
  • Paul Vitányi
    • 2
  1. 1.Department of Computer ScienceUniversity of WaterlooWaterlooCanada
  2. 2.Centrum voor Wiskunde en InformaticaAmsterdamThe Netherlands

Personalised recommendations