We give new algorithms for tree evaluation (S. Cook et. al. TOCT 2012) in the catalytic-computing model (Buhrman et. al. STOC 2014). Two existing approaches aim to solve tree evaluation in low space: on the one hand, J. Cook and Mertz (STOC 2024) give an algorithm for TreeEval running in ... more >>>

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 >>>