Chain rule for Kolmogorov complexity: Difference between revisions

Revision as of 18:30, 8 January 2009

Revision as of 01:59, 11 February 2009

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The [[chain rule]] for [[Kolmogorov complexity]] is an analogue of the chain rule for [[Information entropy]], which states:

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That is, the combined [[randomness]] of two sequences ''X'' and ''Y'' is the sum of the randomness of ''X'' plus whatever randomness is left in ''Y'' once we know ''X''.

This follows immediately from the definitions of [[conditional entropy|conditional]] and [[joint entropy]] fact from [[probability theory]] that the [[joint probability]] is the product of the [[marginal probability|marginal]] and [[conditional probability]]: