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Probabilistic Algorithmic Randomness

Published online by Cambridge University Press:  12 March 2014

Sam Buss and
Mia Minnes
Sam Buss
Affiliation:
Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112, USA, E-mail:sbuss@math.ucsd.edu, E-mail:minnes@math.ucsd.edu
Mia Minnes
Affiliation:
Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112, USA, E-mail:sbuss@math.ucsd.edu, E-mail:minnes@math.ucsd.edu
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Abstract

We introduce martingales defined by probabilistic strategies, in which randomness is used to decide whether to bet. We show that different criteria for the success of computable probabilistic strategies can be used to characterize ML-randomness, computable randomness, and partial computable randomness. Our characterization of ML-randomness partially addresses a critique of Schnorr by formulating ML randomness in terms of a computable process rather than a computably enumerable function.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 2 , June 2013, pp. 579 - 601
Copyright
Copyright © Association for Symbolic Logic 2013

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References

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