Some properties of antistochastic strings

TL;DR

This paper explores the properties of antistochastic strings, showing they can be reconstructed from any part using short programs, and discusses implications for list decoding and the symmetry of information in total conditional complexity.

Contribution

It introduces the concept that absolutely non-stochastic strings are holographic, enabling their reconstruction from any part, and examines related implications in information theory.

Findings

Absolutely non-stochastic strings are holographic.

Reconstruction of strings from any part using short programs.

Symmetry of information fails for total conditional complexity.

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.