We show that if a language $\mathcal{L}$ admits a public-coin unambiguous interactive proof (UIP) with round complexity $\ell$, where $a$ bits are communicated per round, then the \emph{batch language} $\mathcal{L}^{\otimes k}$, i.e. the set of $k$-tuples of statements all belonging to $\mathcal{L}$, has an unambiguous interactive proof with round complexity ... more >>>

We present a general framework for derandomizing random linear codes with respect to a broad class of permutation-invariant properties, known as local properties, which encompass several standard notions such as distance, list-decoding, list-recovery, and perfect hashing. Our approach extends the classical Alon-Edmonds-Luby (AEL) construction through a modified formalism of local ... more >>>

We introduce and initiate the study of a new model of reductions called the random noise model. In this model, the truth table $T_f$ of the function $f$ is corrupted on a randomly chosen $\delta$-fraction of instances. A randomized algorithm $\mathcal{A}$ is a $\left(t, \delta, 1-\varepsilon\right)$-recovery reduction for $f$ if:

... more >>>