Interactive proofs of proximity (IPPs) offer ultra-fast
approximate verification of assertions regarding their input,
where ultra-fast means that only a small portion of the input is read
and approximate verification is analogous to the notion of
approximate decision that underlies property testing.
Specifically, in an IPP, the prover can make ... more >>>

Suppose Alice has collected a small number of samples from an unknown distribution, and would like to learn about the distribution. Bob, an untrusted data analyst, claims that he ran a sophisticated data analysis on the distribution, and makes assertions about its properties. Can Alice efficiently verify Bob's claims using ... more >>>

We initiate a study of doubly-efficient interactive proofs of proximity, while focusing on properties that can be tested within query-complexity that is significantly sub-linear, and seeking interactive proofs of proximity in which

1. The query-complexity of verification is significantly smaller than the query-complexity of testing.

2. The query-complexity of the ... more >>>

Interactive proofs of proximity (IPPs) are a relaxation of interactive proofs, analogous to property testing, in which soundness is required to hold only for inputs that are far from the property being verified. In such proof systems, the verifier has oracle access to the input, and it engages in two ... more >>>

A property of functions is called location-invariant (or symmetric) if it can be characterized in terms of the frequencies in which each value occurs in the function, regardless of the locations in which each value occurs.
It is known that the (query) complexity of testing location-invariant properties of functions ... more >>>

Suppose that an untrusted analyst claims that it ran a distribution tester and determined that an unknown distribution has a certain property. Can the untrusted analyst prove that its assertion is correct to a verifier that does not have sufficient samples and computational resources to run the tester on its ... more >>>

Interactive proofs of proximity (IPPs) are a relaxation of interactive proofs, analogous to property testing, in which soundness is required to hold only for inputs that are $\epsilon$-far from the property being verified, where $\epsilon>0$ is a proximity parameter. In such proof systems, the verifier has oracle access to the ... 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 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 >>>