TY - JOUR

T1 - Query efficient PCPs with perfect completeness

AU - Håstad, Johan

AU - Khot, Subhash

PY - 2001

Y1 - 2001

N2 - For every integer k ≥ 1, we present a PCP characterization of NP where the verifier uses logarithmic randomness, queries 4k + k2 bits in the proof, accepts a correct proof with probability 1 (i.e. it is has perfect completeness) and accepts any supposed proof of a false statement with probability at most 2-k2+1. In particular, the verifier achieves optimal amortized query complexity of 1 + δ for arbitrarily small constant δ > 0. Such a characterization was already proved by Samorodnitsky and Trevisan, but their verifier loses perfect completeness and their proof makes an essential use of this feature. By using an adaptive verifier we can decrease the number of query bits to 2k + k2, the same number obtained in [15]. Finally we extend some of the results to larger domains.

AB - For every integer k ≥ 1, we present a PCP characterization of NP where the verifier uses logarithmic randomness, queries 4k + k2 bits in the proof, accepts a correct proof with probability 1 (i.e. it is has perfect completeness) and accepts any supposed proof of a false statement with probability at most 2-k2+1. In particular, the verifier achieves optimal amortized query complexity of 1 + δ for arbitrarily small constant δ > 0. Such a characterization was already proved by Samorodnitsky and Trevisan, but their verifier loses perfect completeness and their proof makes an essential use of this feature. By using an adaptive verifier we can decrease the number of query bits to 2k + k2, the same number obtained in [15]. Finally we extend some of the results to larger domains.

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U2 - 10.1109/SFCS.2001.959937

DO - 10.1109/SFCS.2001.959937

M3 - Article

AN - SCOPUS:0035175817

SN - 0272-5428

SP - 610

EP - 619

JO - Annual Symposium on Foundations of Computer Science - Proceedings

JF - Annual Symposium on Foundations of Computer Science - Proceedings

ER -