Symmetry of Information (SoI) is a fundamental result in Kolmogorov complexity stating that for all $n$-bit strings $x$ and $y$, $K(x,y) = K(y) + K(x \mid y)$ up to an additive error of $O(\log n)$ [ZL70]. In contrast, understanding whether SoI holds for time-bounded Kolmogorov complexity measures is closely related ... more >>>

We show an unconditional classical oracle separation between the class of languages that can be verified using a quantum proof (QMA) and the class of languages that can be verified with a classical proof (QCMA). Compared to the recent work of Bostanci, Haferkamp, Nirkhe, and Zhandry (STOC 2026), our proof ... more >>>

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 >>>