Some properties of antistochastic strings

Abstract

Antistochastic strings are those strings that lack any reasonable statistical explanations. We establish the follow property of such strings: every absolutely non-stochastic string $x$ is "holographic" in the sense that it can be restored by a short program from any 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 for prove that symmetry of information fails for total conditional complexity.