Additivity of on-line decision complexity is violated by a linear term in the length of a binary string
Information Theory
2009-09-01 v1 math.IT
Abstract
We show that there are infinitely many binary strings z, such that the sum of the on-line decision complexity of predicting the even bits of z given the previous uneven bits, and the decision complexity of predicting the uneven bits given the previous event bits, exceeds the Kolmogorov complexity of z by a linear term in the length of z.
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Cite
@article{arxiv.0908.4457,
title = {Additivity of on-line decision complexity is violated by a linear term in the length of a binary string},
author = {Bruno Bauwens},
journal= {arXiv preprint arXiv:0908.4457},
year = {2009}
}
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10 pages