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Algorithmic Probability

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

Abstract

P.S. Laplace (1749–1827) pointed out the following reason why intuitively, a regular outcome of a random event is unlikely:

“We arrange in our thought all possible events in various classes; and we regard as extraordinary those classes which include a very small number. In the game of heads and tails, if heads comes up a hundred times in a row then this appears to us extraordinary, because the almost infinite number of combinations that can arise in a hundred throws are divided in regular sequences, or those in which we observe a rule that is easy to grasp, and in irregular sequences, that are incomparably more numerous.” [Laplace]

Keywords

Infinite Sequence Code Word Kolmogorov Complexity Computable Measure Fair Coin 
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.

Copyright information

© Springer Science + Business Media, LLC 2008

Authors and Affiliations

  1. 1.Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada
  2. 2.Centrum voor Wiskunde en InformaticaAmsterdamThe Netherlands

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