We present functions that can be computed in some fixed polynomial time but are hard on average for any algorithm that runs in slightly smaller time, assuming widely-conjectured worst-case hardness for problems from the study of fine-grained complexity. Unconditional constructions of such functions are known from before (Goldmann et al., ... more >>>

In the \emph{conditional disclosure of secrets} problem (Gertner et al., J. Comput. Syst. Sci., 2000) Alice and Bob, who hold inputs $x$ and $y$ respectively, wish to release a common secret $s$ to Carol (who knows both $x$ and $y$) if only if the input $(x,y)$ satisfies some predefined predicate ... more >>>

We define a cutting planes system CP+$\forall$red for quantified Boolean formulas (QBF) and analyse the proof-theoretic strength of this new calculus. While in the propositional case, Cutting Planes is of intermediate strength between resolution and Frege, our findings here show that the situation in QBF is slightly more complex: while ... more >>>