Algorithmic randomness and splitting of supermartingales
Information Theory
2008-11-28 v2 math.IT
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.
Cite
@article{arxiv.0807.3156,
title = {Algorithmic randomness and splitting of supermartingales},
author = {Andrej Muchnik},
journal= {arXiv preprint arXiv:0807.3156},
year = {2008}
}
Comments
The same text in English (13 pages) and in Russian (14 pages). Journal version