Randomness in the sense of Martin-Löf 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 even bits (the first one) and on odd bits (the second one) knowing all the preceding bits.
Problems of Information Transmission – Springer Journals
Published: Apr 30, 2009
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