Other Notions of Algorithmic Randomness

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


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.


Computable Function Computable Order Quick Process Algorithmic Randomness Partial Computable Function 
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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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