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Speedability of computably approximable reals and their approximations
George Barmpalias, Nan Fang, Wolfgang Merkle +1
An approximation of a real is a sequence of rational numbers that converges to the real. An approximation is left-c.e. if it is computable and nondecreasing and is d.c.e. if it is…
Monotonous betting strategies in warped casinos
George Barmpalias, Nan Fang, Andrew Lewis-Pye
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…
Equivalences between learning of data and probability distributions, and their applications
George Barmpalias, Nan Fang, Frank Stephan
Algorithmic learning theory traditionally studies the learnability of effective infinite binary sequences (reals), while recent work by [Vitanyi and Chater, 2017] and [Bienvenu et…
Optimal asymptotic bounds on the oracle use in computations from Chaitin's Omega
George Barmpalias, Nan Fang, Andrew Lewis-Pye
Chaitin's number Omega is the halting probability of a universal prefix-free machine, and although it depends on the underlying enumeration of prefix-free machines, it is always Tu…