All reports by Author Pei Wu:

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TR20-128
| 3rd September 2020
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Alexander A. Sherstov, Andrey Storozhenko, Pei Wu#### An Optimal Separation of Randomized and Quantum Query Complexity

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TR19-003
| 2nd January 2019
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Alexander A. Sherstov, Pei Wu#### Near-Optimal Lower Bounds on the Threshold Degree and Sign-Rank of AC^0

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TR17-079
| 1st May 2017
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Alexander A. Sherstov, Pei Wu#### Optimal Interactive Coding for Insertions, Deletions, and Substitutions

Alexander A. Sherstov, Andrey Storozhenko, Pei Wu

We prove that for every decision tree, the absolute values of the Fourier coefficients of given order $\ell\geq1$ sum to at most $c^{\ell}\sqrt{{d\choose\ell}(1+\log n)^{\ell-1}},$ where $n$ is the number of variables, $d$ is the tree depth, and $c>0$ is an absolute constant. This bound is essentially tight and settles a ... more >>>

Alexander A. Sherstov, Pei Wu

The threshold degree of a Boolean function $f\colon\{0,1\}^n\to\{0,1\}$ is the minimum degree of a real polynomial $p$ that represents $f$ in sign: $\mathrm{sgn}\; p(x)=(-1)^{f(x)}.$ A related notion is sign-rank, defined for a Boolean matrix $F=[F_{ij}]$ as the minimum rank of a real matrix $M$ with $\mathrm{sgn}\; M_{ij}=(-1)^{F_{ij}}$. Determining the maximum ... more >>>

Alexander A. Sherstov, Pei Wu

Interactive coding, pioneered by Schulman (FOCS 1992, STOC 1993), is concerned with making communication protocols resilient to adversarial noise. The canonical model allows the adversary to alter a small constant fraction of symbols, chosen at the adversary's discretion, as they pass through the communication channel. Braverman, Gelles, Mao, and Ostrovsky ... more >>>