For a complexity class $C$ and language $L$, a constructive separation of $L \notin C$ gives an efficient algorithm (also called a refuter) to find counterexamples (bad inputs) for every $C$-algorithm attempting to decide $L$. We study the questions: Which lower bounds can be made constructive? What are the consequences ... more >>>

We establish an equivalence between two algorithmic tasks: *derandomization*, the deterministic simulation of probabilistic algorithms; and *refutation*, the deterministic construction of inputs on which a given probabilistic algorithm fails to compute a certain hard function.

We prove that refuting low-space probabilistic streaming algorithms that try to compute functions $f\in\mathcal{FP}$ ... more >>>

This paper studies the \emph{refuter} problems, a family of decision-tree $\mathrm{TFNP}$ problems capturing the metamathematical difficulty of proving proof complexity lower bounds. Suppose $\varphi$ is a hard tautology that does not admit any length-$s$ proof in some proof system $P$. In the corresponding refuter problem, we are given (query ... more >>>