Additivity of on-line decision complexity is violated by a linear term in the length of a binary string

Details Additivity of on-line decision complexity is violated by a linear term in the length of a binary string Additivity of on-line decision complexity is violated by a linear term in the length of a binary string

2009-08-31

arxiv.org/abs/0908.4457v1

Computer Science

Information Theory

10 pages

Scientific paper

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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