We prove that for any 3-player game $\mathcal G$, whose query distribution has the same support as the GHZ game (i.e., all $x,y,z\in \{0,1\}$ satisfying $x+y+z=0\pmod{2}$), the value of the $n$-fold parallel repetition of $\mathcal G$ decays exponentially fast: \[ \text{val}(\mathcal G^{\otimes n}) \leq \exp(-n^c)\] for all sufficiently large $n$, ... more >>>

We show that for any unsatisfiable CNF formula $\varphi$ that requires resolution refutation width at least $w$, and for any $1$-stifling gadget $g$ (for example, $g=MAJ_3$), (1) every resolution-over-parities (Res($\oplus$)) refutation of the lifted formula $\varphi \circ g$ of size at most $S$ has depth at least $\Omega(w^2/\log S)$; (2) ... more >>>

The hardness vs. randomness paradigm aims to construct pseudorandom generators (PRGs) based on complexity theoretic hardness assumptions. A seminal result in this area is a PRG construction by \cite{NW,IW97}.
A sequence of works \cite{KvM,SU01,Umans02,SU05} generalized the result of \cite{NW,IW97} to nondeterministic circuits. More specifically, they showed that if $\E=\DTIME(2^{O(n)})$ requires ... more >>>