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Electronic Colloquium on Computational Complexity

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TR21-102 | 13th July 2021
Siddharth Iyer, Anup Rao, Victor Reis, Thomas Rothvoss, Amir Yehudayoff

Tight bounds on the Fourier growth of bounded functions on the hypercube

Revisions: 1

We give tight bounds on the degree $\ell$ homogenous parts $f_\ell$ of a bounded function $f$ on the cube. We show that if $f: \{\pm 1\}^n \rightarrow [-1,1]$ has degree $d$, then $\| f_\ell \|_\infty$ is bounded by $d^\ell/\ell!$, and $\| \hat{f}_\ell \|_1$ is bounded by $d^\ell e^{{\ell+1 \choose 2}} ... more >>>


TR21-101 | 13th July 2021
Uma Girish, Justin Holmgren, Kunal Mittal, Ran Raz, Wei Zhan

A Parallel Repetition Theorem for the GHZ Game: A Simpler Proof

Revisions: 1

We give a new proof of the fact that the parallel repetition of the (3-player) GHZ game reduces the value of the game to zero polynomially quickly. That is, we show that the value of the $n$-fold GHZ game is at most $n^{-\Omega(1)}$. This was first established by Holmgren and ... more >>>


TR21-100 | 11th July 2021
Christian Ikenmeyer, Balagopal Komarath, Nitin Saurabh

Karchmer-Wigderson Games for Hazard-free Computation

Revisions: 1

We present a Karchmer-Wigderson game to study the complexity of hazard-free formulas. This new game is both a generalization of the monotone Karchmer-Wigderson game and an analog of the classical Boolean Karchmer-Wigderson game. Therefore, it acts as a bridge between the existing monotone and general games.

Using this game, we ... more >>>



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