Unlike in TFNP, for which there is an abundance of problems capturing natural existence principles which are incomparable (in the black-box setting), Kleinberg et al. [KKMP21] observed that many of the natural problems considered so far in the second level of the total function polynomial hierarchy (TF$\Sigma_2$) reduce to the ... more >>>

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 >>>