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Electronic Colloquium on Computational Complexity

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All reports by Author Halley Goldberg:

TR22-072 | 15th May 2022
Halley Goldberg, Valentine Kabanets, Zhenjian Lu, Igor Oliveira

Probabilistic Kolmogorov Complexity with Applications to Average-Case Complexity

Understanding the relationship between the worst-case and average-case complexities of $\mathrm{NP}$ and of other subclasses of $\mathrm{PH}$ is a long-standing problem in complexity theory. Over the last few years, much progress has been achieved in this front through the investigation of meta-complexity: the complexity of problems that refer to the ... 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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