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Electronic Colloquium on Computational Complexity

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All reports by Author Peter Ivanov:

TR22-092 | 2nd July 2022
Peter Ivanov, Liam Pavlovic, Emanuele Viola

On correlation bounds against polynomials

We study the fundamental challenge of exhibiting explicit functions that have small correlation with low-degree polynomials over $\mathbb{F}_{2}$. Our main contributions include:

1. In STOC 2020, CHHLZ introduced a new technique to prove correlation bounds. Using their technique they established new correlation bounds for low-degree polynomials. They conjectured that their ... more >>>

TR21-137 | 14th September 2021
Xuangui Huang, Peter Ivanov, Emanuele Viola

Affine extractors and AC0-Parity

Revisions: 1

We study a simple and general template for constructing affine extractors by composing a linear transformation with resilient functions. Using this we show that good affine extractors can be computed by non-explicit circuits of various types, including AC0-Xor circuits: AC0 circuits with a layer of parity gates at the input. ... more >>>

TR21-110 | 22nd July 2021
Jaroslaw Blasiok, Peter Ivanov, Yaonan Jin, Chin Ho Lee, Rocco Servedio, Emanuele Viola

Fourier growth of structured $\mathbb{F}_2$-polynomials and applications

We analyze the Fourier growth, i.e. the $L_1$ Fourier weight at level $k$ (denoted $L_{1,k}$), of various well-studied classes of "structured" $\mathbb{F}_2$-polynomials. This study is motivated by applications in pseudorandomness, in particular recent results and conjectures due to [CHHL19,CHLT19,CGLSS20] which show that upper bounds on Fourier growth (even at ... more >>>

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