We continue the study of the trade-off between the length of PCPs and their query complexity, establishing the following main results (which refer to proofs of satisfiability of c...
Eli Ben-Sasson, Oded Goldreich, Prahladh Harsha, M...
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 c...
Russell Impagliazzo, Valentine Kabanets, Avi Wigde...
The PCP theorem [3, 2] says that every language in NP has a witness format that can be checked probabilistically by reading only a constant number of bits from the proof. The cele...