We unconditionally prove there exists a promise problem in promise ZSUBEXP that cannot be solved in promise RP.
The proof technique builds upon Kabanets' easy witness method [Kab01] as implemented by Impagliazzo et. al [IKW02], with a separate diagonalization carried out on each of the two alternatives in the ... more >>>

We consider the following question: using a source of labeled data and interaction with an untrusted prover, what is the complexity of verifying that a given hypothesis is "approximately correct"? We study interactive proof systems for PAC verification, where a verifier that interacts with a prover is required to accept ... more >>>

Proving super-logarithmic data structure lower bounds in the static \emph{group model} has been a fundamental challenge in computational geometry since the early 80's. We prove a polynomial ($n^{\Omega(1)}$) lower bound for an explicit range counting problem of $n^3$ convex polygons in $\R^2$ (each with $n^{\tilde{O}(1)}$ facets/semialgebraic-complexity), against linear storage arithmetic ... more >>>