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Monotonous betting strategies in warped casinos

Suppose that the outcomes of a roulette table are not entirely random, in the sense that there exists a successful betting strategy. Is there a successful 'separable' strategy, in the sense that it does not use the winnings from betting on red in …

Equivalences between learning of data and probability distributions, and their applications

Algorithmic learning theory traditionally studies the learnability of effective infinite binary sequences (reals), while recent work by Vitányi and Chater has adapted this framework to the study of learnability of effective probability distributions …

Optimal asymptotic bounds on the oracle use in computations from Chaitin's Omega

We characterise the asymptotic upper bounds on the use of Chaitin's Ω in oracle computations of halting probabilities (i.e. c.e. reals). We show that the following two conditions are equivalent for any computable function h such that h(n)−n is …