Troy Lee, Andrei Romashchenko

The information contained in a string $x$ about a string $y$

is defined as the difference between the Kolmogorov complexity

of $y$ and the conditional Kolmogorov complexity of $y$ given $x$,

i.e., $I(x:y)=\C(y)-\C(y|x)$. From the well-known Kolmogorov--Levin Theorem it follows that $I(x:y)$ is symmetric up to a small ...
more >>>

Halley Goldberg, Valentine Kabanets

We give a simplified proof of Hirahara's STOC'21 result showing that $DistPH \subseteq AvgP$ would imply $PH \subseteq DTIME[2^{O(n/\log n)}]$. The argument relies on a proof of the new result: Symmetry of Information for time-bounded Kolmogorov complexity under the assumption that $NP$ is easy on average, which is interesting in ... more >>>