Algorithmic randomness and splitting of supermartingales

Details Algorithmic randomness and splitting of supermartingales Algorithmic randomness and splitting of supermartingales

2008-07-21

arxiv.org/abs/0807.3156v2

Computer Science

Information Theory

The same text in English (13 pages) and in Russian (14 pages). Journal version

Scientific paper

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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