Alexander Golovnev, Siyao Guo, Spencer Peters, Noah Stephens-Davidowitz

We study the black-box function inversion problem, which is the problem of finding $x \in [N]$ such that $f(x) = y$, given as input some challenge point $y$ in the image of a function $f : [N] \to [N]$, using $T$ oracle queries to $f$ and preprocessed advice $\sigma \in ... more >>>

Shuichi Hirahara, Rahul Ilango, Ryan Williams

A compression problem is defined with respect to an efficient encoding function $f$; given a string $x$, our task is to find the shortest $y$ such that $f(y) = x$. The obvious brute-force algorithm for solving this compression task on $n$-bit strings runs in time $O(2^{\ell} \cdot t(n))$, where $\ell$ ... more >>>

Noam Mazor, Rafael Pass

The Perebor (Russian for “brute-force search”) conjectures, which date back to the 1950s and 1960s are some of the oldest conjectures in complexity theory. The conjectures are a stronger form of the NP ? = P conjecture (which they predate) and state that for “meta-complexity” problems, such as the Time-bounded ... more >>>

Noam Mazor, Rafael Pass

The relationships between various meta-complexity problems are not well understood in the worst-case regime, including whether the search version is harder than the decision version, whether the hardness scales with the ``threshold", and how the hardness of different meta-complexity problems relate to one another, and to the task of function ... more >>>

Karthik Gajulapalli, Alexander Golovnev, Samuel King

We study the problem of function inversion with preprocessing where, given a function $f : [N] \to [N]$ and a point $y$ in its image, the goal is to find an $x$ such that $f(x) = y$ using at most $T$ oracle queries to $f$ and $S$ bits of preprocessed ... more >>>