Meta-complexity investigates the complexity of computational problems and tasks that are themselves about computations and their complexity. Understanding whether such problems can capture the hardness of $\mathrm{NP}$ is a central research direction. A longstanding open problem in this area is to establish the $\mathrm{NP}$-hardness of $\mathrm{MINKT}$ [Ko91], the problem of ... more >>>

We revisit the question of whether worst-case hardness of the time-bounded Kolmogorov complexity problem, $\KpolyA$---that is, determining whether a string is ``structured" (i.e., $K^t(x) n - \log n$)---characterizes OWF,
but with either of the following caveats (1) considering a non-standard notion of \emph{probabilistic $K^t$}, as opposed to the ... more >>>

We consider interactive proofs for the promise problem, called $\epsilon$-FARNESS, in which the yes-instances are pairs of distributions over $[n]$ that are $\epsilon$-far from one another, and the no-instances are pairs of identical distributions.
For any $t\leq n^{2/3}$, we obtain an interactive proof in which the verifier has sample complexity ... more >>>