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Electronic Colloquium on Computational Complexity

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Reports tagged with symmetry of information:
TR04-031 | 22nd March 2004
Troy Lee, Andrei Romashchenko

On Polynomially Time Bounded Symmetry of Information

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 >>>

TR22-007 | 14th January 2022
Halley Goldberg, Valentine Kabanets

A Simpler Proof of the Worst-Case to Average-Case Reduction for Polynomial Hierarchy via Symmetry of Information

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 >>>

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