Small PCPs with low query complexity

Most known constructions of probabilistically checkable proofs (PCPs) eithe r blow up the proof size by a large polynomial, or have a high (though cons tant) query complexity. In this paper we give a transformation with slightl y-super-cubic blowup in proof size, with a low query complexity. Specifical ly, the verifier probes the proof in 16 bits and rejects every proof of a f alse assertion with probability arbitrarily close to 1/2, while accepting c orrect proofs of theorems with probability one. The proof is obtained by re visiting 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.