Algorithmic randomness and splitting of supermartingales

Published 21 Jul 2008 in cs.IT and math.IT | (0807.3156v2)

Abstract: Randomness in the sense of Martin-L\"of can be defined in terms of lower semicomputable supermartingales. We show that such a supermartingale cannot be replaced by a pair of supermartingales that bet only on the even bits (the first one) and on the odd bits (the second one) knowing all preceding bits.

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