Oscillation in the Initial Segment Complexity of Random Reals


We study oscillation in the prefix-free complexity of initial segments of 1-random reals. For upward oscillations, we prove that P n∈ω 2 −g(n) diverges iff (∃∞n) K(X n) > n+g(n) for every 1-random X ∈ 2ω . For downward oscillations, we characterize the functions g such that (∃∞n) K(X n) < n+g(n) for almost every X ∈ 2ω . The proof of this result uses an… (More)


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