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A. Chernov, A. Shen, N. Vereshchagin, V. Vovk (2008)
Proc. 19th Int. Conf. on Algorithmic Learning Theory (ALT 2008), Budapest, Hungary, 2008
V. Uspenskii, Alexei Semenov, A. Shen (1990)
Can an individual sequence of zeros and ones be random? Russian Math
A. Chernov, A. Shen, N. Vereshchagin, V. Vovk (2008)
On-Line Probability, Complexity and Randomness
M. Lambalgen (1987)
Von Mises' Definition of Random Sequences ReconsideredJ. Symb. Log., 52
V Uspenskii, A Semenov, A Shen' (1990)
Can an individual sequence of zeros and ones be random?Russian Mathematical Surveys, 45
V.A. Uspensky, A.L. Semenov, A.Kh. Shen’ (1990)
Can an Individual Sequence of Zeros and Ones Be Random?Uspekhi Mat. Nauk, 45
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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