The parallel repetition conjecture (PRC) of Feige and Lovasz says that the
error probability of a two prover one round interactive protocol repeated $n$
times in parallel is exponentially small in $n$.
We show that the PRC is true in the case when
the bipartite graph of dependence between ... more >>>

We present constant-round interactive proof systems for sufficiently uniform versions of AC0[2] and NC1.
Both proof systems are doubly-efficient, and offer a better trade-off between the round complexity and the total communication than
the work of Reingold, Rothblum, and Rothblum (STOC, 2016).
Our proof system for AC0[2] supports a more ... more >>>

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 >>>

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 >>>