Paul Beame, Chris Beck, Russell Impagliazzo

We give the first time-space tradeoff lower bounds for Resolution proofs that apply to superlinear space. In particular, we show that there are formulas of size $N$ that have Resolution refutations of space and size each roughly $N^{\log_2 N}$ (and like all formulas have Resolution refutations of space $N$) for ... more >>>

Henry Corrigan-Gibbs, Dmitry Kogan

We study preprocessing algorithms for the function-inversion problem. In this problem, an algorithm gets oracle access to a function $f\colon[N] \to [N]$ and takes as input $S$ bits of auxiliary information about $f$, along with a point $y \in [N]$. After running for time $T$, the algorithm must output an ... more >>>