The “direct product code” of a function f gives its values on all k-tuples (f(x1), . . . , f(xk)).
This basic construct underlies “hardness amplification” in cryptography, circuit complexity and
PCPs. Goldreich and Safra [GS00] pioneered its local testing and its PCP application. A recent
result by Dinur and ... more >>>

We solve the derandomized direct product testing question in the low acceptance regime, by constructing new high dimensional expanders that have no small connected covers. We show that our complexes have swap cocycle expansion, which allows us to deduce the agreement theorem by relying on previous work.

Derandomized direct product ... more >>>