Source: J. Symbolic Logic
Volume 78, Issue 2
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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