We consider interactive proofs for the promise problem, called $\epsilon$-FARNESS, in which the yes-instances are pairs of distributions over $[n]$ that are $\epsilon$-far from one another, and the no-instances are pairs of identical distributions.
For any $t\leq n^{2/3}$, we obtain an interactive proof in which the verifier has sample complexity ... more >>>

Interactive proofs of proximity for distributions, introduced by Chiesa and Gur (ITCS18) and extensively studied recently by Herman and Rothblum (STOC22, FOCS23, FOCS24}, offer a way of verifying properties of distributions using less samples than required to test these properties.

We say that such an interactive proof system is {\sf ... more >>>

We revisit the setting of Interactive Proof Systems for Distribution Testing, introduced by Chiesa and Gur (2018), showing that a simple twist on the task requirements may lead to dramatic improvements, allowing verifiers with constant sample complexity.

We define and investigate the multi-prover and zero-knowledge versions of these interactive proof ... more >>>