Small PCPs with low query complexity

Most known constructions of probabilistically checkable proofs (PCPs) either blow up the proof size by a large polynomial, or have a high (though constant) query complexity. In this paper we give a transformation with slightly-super-cubic blowup in proof size, with a low query complexity. Specifically, the verifier probes the proof in 16 bits and rejects every proof of a false assertion with probability arbitrarily close to 1/2, while accepting correct proofs of theorems with probability one. The proof is obtained by revisiting known constructions and improving numerous components therein. In the process we abstract a number of new modules that may be of use in other PCP constructions.