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TR21-170 | 25th November 2021
Reyad Abed Elrazik, Robert Robere, Assaf Schuster, Gal Yehuda

#### Pseudorandom Self-Reductions for NP-Complete Problems

A language $L$ is random-self-reducible if deciding membership in $L$ can be reduced (in polynomial time) to deciding membership in $L$ for uniformly random instances. It is known that several "number theoretic" languages (such as computing the permanent of a matrix) admit random self-reductions. Feigenbaum and Fortnow showed that NP-complete ... more >>>

TR21-169 | 24th November 2021
Mitali Bafna, Max Hopkins, Tali Kaufman, Shachar Lovett

#### Hypercontractivity on High Dimensional Expanders: a Local-to-Global Approach for Higher Moments

Hypercontractivity is one of the most powerful tools in Boolean function analysis. Originally studied over the discrete hypercube, recent years have seen increasing interest in extensions to settings like the $p$-biased cube, slice, or Grassmannian, where variants of hypercontractivity have found a number of breakthrough applications including the resolution of ... more >>>

TR21-168 | 17th November 2021
Tom Gur, Noam Lifshitz, Siqi Liu

#### Hypercontractivity on High Dimensional Expanders: Approximate Efron-Stein Decompositions for $\epsilon$-Product Spaces

Revisions: 1

We prove hypercontractive inequalities on high dimensional expanders. As in the settings of the p-biased hypercube, the symmetric group, and the Grassmann scheme, our inequalities are effective for global functions, which are functions that are not significantly affected by a restriction of a small set of coordinates. As applications, we ... more >>>

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