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 corrects proofs of theorems with probability one. The proof is obtained by revisiting known constructions and g numerous components therein. In the process we abstract a number of new modules that may be of use in other PCP constructions. Keywords. NP completeness, probabilistic proof systems, holographic proofs. Subject classification. 68Q15

• Type: Conference
• Year: 2001
• Where: STACS
• Authors: Prahladh Harsha, Madhu Sudan
• Keywords: Probabilistically Checkable Proofs, Proof Size, Query Complexity, STACS 2001, Theoretical Computer Science