Journal of Symbolic Logic

Probabilistic algorithmic randomness

Sam Buss and Mia Minnes

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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.

Article information

Source
J. Symbolic Logic Volume 78, Issue 2 (2013), 579-601.

Dates
First available in Project Euclid: 15 May 2013

Permanent link to this document
http://projecteuclid.org/euclid.jsl/1368627066

Digital Object Identifier
doi:10.2178/jsl.7802130

Zentralblatt MATH identifier
06180300

Mathematical Reviews number (MathSciNet)
MR3145197

Citation

Buss, Sam; Minnes, Mia. Probabilistic algorithmic randomness. J. Symbolic Logic 78 (2013), no. 2, 579--601. doi:10.2178/jsl.7802130. http://projecteuclid.org/euclid.jsl/1368627066.


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