All reports in year 2021:

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TR21-007
| 14th January 2021
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Sai Sandeep#### Almost Optimal Inapproximability of Multidimensional Packing Problems

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TR21-006
| 18th January 2021
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Susanna de Rezende, Jakob NordstrÃ¶m, Marc Vinyals#### How Limited Interaction Hinders Real Communication (and What It Means for Proof and Circuit Complexity)

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TR21-005
| 13th January 2021
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Anindya De, Elchanan Mossel, Joe Neeman#### Robust testing of low-dimensional functions

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TR21-004
| 10th January 2021
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Vishnu Iyer, Avishay Tal, Michael Whitmeyer#### Junta Distance Approximation with Sub-Exponential Queries

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TR21-003
| 6th January 2021
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Lijie Chen, Xin Lyu#### Inverse-Exponential Correlation Bounds and Extremely Rigid Matrices from a New Derandomized XOR Lemma

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TR21-002
| 8th January 2021
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Pooya Hatami, William Hoza, Avishay Tal, Roei Tell#### Fooling Constant-Depth Threshold Circuits

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TR21-001
| 1st January 2021
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Klim Efremenko, Gillat Kol, Dmitry Paramonov, Raghuvansh Saxena#### Computation Over the Noisy Broadcast Channel with Malicious Parties

Sai Sandeep

Multidimensional packing problems generalize the classical packing problems such as Bin Packing, Multiprocessor Scheduling by allowing the jobs to be $d$-dimensional vectors. While the approximability of the scalar problems is well understood, there has been a significant gap between the approximation algorithms and the hardness results for the multidimensional variants. ... more >>>

Susanna de Rezende, Jakob NordstrÃ¶m, Marc Vinyals

We obtain the first true size-space trade-offs for the cutting planes proof system, where the upper bounds hold for size and total space for derivations with constant-size coefficients, and the lower bounds apply to length and formula space (i.e., number of inequalities in memory) even for derivations with exponentially large ... more >>>

Anindya De, Elchanan Mossel, Joe Neeman

A natural problem in high-dimensional inference is to decide if a classifier $f:\mathbb{R}^n \rightarrow \{-1,1\}$ depends on a small number of linear directions of its input data. Call a function $g: \mathbb{R}^n \rightarrow \{-1,1\}$, a linear $k$-junta if it is completely determined by some $k$-dimensional subspace of the input space. ... more >>>

Vishnu Iyer, Avishay Tal, Michael Whitmeyer

Leveraging tools of De, Mossel, and Neeman [FOCS, 2019], we show two different results pertaining to the tolerant testing of juntas. Given black-box access to a Boolean function $f:\{\pm1\}^{n} \to \{\pm1\}$ we give a poly$(k, \frac{1}{\varepsilon})$ query algorithm that distinguishes between functions that are $\gamma$-close to $k$-juntas and $(\gamma+\varepsilon)$-far from ... more >>>

Lijie Chen, Xin Lyu

In this work we prove that there is a function $f \in \textrm{E}^\textrm{NP}$ such that, for every sufficiently large $n$ and $d = \sqrt{n}/\log n$, $f_n$ ($f$ restricted to $n$-bit inputs) cannot be $(1/2 + 2^{-d})$-approximated by $\textrm{F}_2$-polynomials of degree $d$. We also observe that a minor improvement ...
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Pooya Hatami, William Hoza, Avishay Tal, Roei Tell

We present new constructions of pseudorandom generators (PRGs) for two of the most widely-studied non-uniform circuit classes in complexity theory. Our main result is a construction of the first non-trivial PRG for linear threshold (LTF) circuits of arbitrary constant depth and super-linear size. This PRG fools circuits with depth $d\in\mathbb{N}$ ... more >>>

Klim Efremenko, Gillat Kol, Dmitry Paramonov, Raghuvansh Saxena

We study the $n$-party noisy broadcast channel with a constant fraction of malicious parties. Specifically, we assume that each non-malicious party holds an input bit, and communicates with the others in order to learn the input bits of all non-malicious parties. In each communication round, one of the parties broadcasts ... more >>>