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TR22-073
| 18th May 2022
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Itay Kalev, Amnon Ta-Shma#### Unbalanced Expanders from Multiplicity Codes

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TR22-072
| 15th May 2022
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Halley Goldberg, Valentine Kabanets, Zhenjian Lu, Igor Oliveira#### Probabilistic Kolmogorov Complexity with Applications to Average-Case Complexity

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TR22-071
| 13th May 2022
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Arkadev Chattopadhyay, Utsab Ghosal, Partha Mukhopadhyay#### Robustly Separating the Arithmetic Monotone Hierarchy Via Graph Inner-Product

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Itay Kalev, Amnon Ta-Shma

In 2007 Guruswami, Umans and Vadhan gave an explicit construction of a lossless condenser based on Parvaresh-Vardy codes. This lossless condenser is a basic building block in many constructions, and, in particular, is behind the state of the art extractor constructions.

We give an alternative construction that is based on ... more >>>

Halley Goldberg, Valentine Kabanets, Zhenjian Lu, Igor Oliveira

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 >>>

Arkadev Chattopadhyay, Utsab Ghosal, Partha Mukhopadhyay

We establish an $\epsilon$-sensitive hierarchy separation for monotone arithmetic computations. The notion of $\epsilon$-sensitive monotone lower bounds was recently introduced by Hrubes [Computational Complexity'20]. We show the following:

(1) There exists a monotone polynomial over $n$ variables in VNP that cannot be computed by $2^{o(n)}$ size monotone ...
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