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Other Notions of Algorithmic Randomness

  • Rodney G. Downey
  • Denis R. Hirschfeldt
Chapter
Part of the Theory and Applications of Computability book series (THEOAPPLCOM)

Abstract

In [348, 349], Schnorr analyzed his characterization of 1-randomness in terms of c.e. martingales (Theorem 6.3.4). He argued that this result demonstrates a failure of 1-randomness to capture the intuition behind Martin-Löf`s original definition, because effective randomness should be concerned with defeating computable betting strategies rather than computably enumerable ones, as the latter are fundamentally asymmetric, in the same way that a c.e. set is semi-decidable rather than decidable.

Keywords

Computable Function Computable Order Quick Process Algorithmic Randomness Partial Computable Function 
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.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.School of Mathematics, Statistics and Operations ResearchVictoria University of WellingtonWellingtonNew Zealand
  2. 2.Department of MathematicsUniversity of ChicagoChicagoUSA

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