Other Notions of Algorithmic Randomness
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.
KeywordsComputable Function Computable Order Quick Process Algorithmic Randomness Partial Computable Function
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