Journal of Symbolic Logic

Probabilistic algorithmic randomness

Sam Buss and Mia Minnes

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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.

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

First available in Project Euclid: 15 May 2013

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

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