We study interactive proofs when the prover and the verifier access the same underlying data through independent noisy views. The noise is \emph{persistent} for each party: each location is corrupted once, and repeated queries to the same location return the same corrupted value. We introduce two models in this setting: ... more >>>

We prove that the XOR of $k$ majorities on disjoint blocks of \(\ell\) bits has correlation at most \((2d/\sqrt{\ell})^k\) with every degree-\(d\) polynomial over \(\mathbb F_2\). By known techniques, this implies pseudorandom generators with polylogarithmic seed length for low-degree polynomials over $\mathbb F_2$ and for alternating circuits with parity ... more >>>

We introduce a variant of a polynomial family called $\TQBFfamily$ obtained from `arithmetization' of the popular $\PSPACE$-complete problem - $\TQBF$. This polynomial family has several nice characteristics such as: $\TQBFfamily \in \VPSPACE_b$, where $\VPSPACEb$ is the `bounded' algebraic version of $\PSPACE$, it is \emph{self-testable}, it captures the computational power of ... more >>>