Abstract:
We show a construction of a PCP with both sub-constant error and almost-linear size. Specifically, for some constant alpha in (0,1), we construct a PCP verifier for checking satisfiability of Boolean formulas that on input of size n uses log n + O((log n)^{1-alpha}) random bits to query a constant number of places in a proof of size n 2^{O((log n)^{1-alpha})} over symbols consisting of O((log n)^{1-alpha}) bits and achieves error 2^{-Omega((log n)^{alpha})}. The construction is by a new randomness-efficient version of the aggregation through curves technique. Its main ingredients are a recent low degree test with both sub-constant error and almost-linear size and a new method for constructing a short list of balanced curves.