The current proof of the PCP Theorem (i.e., NP = PCP(log, O(1))) is very complicated. One source of difficulty is the technically involved analysis of low-degree tests. Here, we r...
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...
A PCP is a proof system for NP in which the proof can be checked by a probabilistic verifier. The verifier is only allowed to read a very small portion of the proof, and in return ...
The aim of this note is to point out some combinatorial applications of a lemma of Scarf, proved first in the context of game theory. The usefulness of the lemma in combinatorics...
We prove a version of the derandomized Direct Product lemma for deterministic space-bounded algorithms. Suppose a Boolean function g : {0, 1}n {0, 1} cannot be computed on more th...