In recent work by Chattopadhyay et al.[CHHL19,CHLT19], the authors exhibit a simple and flexible construction of pseudorandom generators for classes of Boolean functions that satisfy $L_1$ Fourier bounds. [CHHL19] show that if a class satisfies such tail bounds at all levels, this implies a PRG whose seed length depends on ... more >>>

We prove that parallel repetition of the (3-player) GHZ game reduces the value of the game polynomially fast to 0. That is, the value of the GHZ game repeated in parallel $t$ times is at most $t^{-\Omega(1)}$. Previously, only a bound of $\approx \frac{1}{\alpha(t)}$, where $\alpha$ is the inverse Ackermann ... more >>>

We study parity decision trees for Boolean functions. The motivation of our study is the log-rank conjecture for XOR functions and its connection to Fourier analysis and parity decision tree complexity. Our contributions are as follows. Let $f : \mathbb{F}_2^n \to \{-1, 1\}$ be a Boolean function with Fourier support ... more >>>