Some Properties of Antistochastic Strings
Antistochastic strings are those strings that do not have any reasonable statistical explanation. We establish the follow property of such strings: every antistochastic string x is “holographic” in the sense that it can be restored by a short program from any of its part whose length equals the Kolmogorov complexity of x. Further we will show how it can be used for list decoding from erasing and prove that Symmetry of Information fails for total conditional complexity.
KeywordsKolmogorov complexity Algorithmic statistics Stochastic strings Total conditional complexity Symmetry of Information
I would like to thank Alexander Shen and Nikolay Vereshchagin for useful discussions, advises and remarks.
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