### Abstract

For every integer k ≥ 1, we present a PCP characterization of NP where the verifier uses logarithmic randomness, queries 4k + k^{2} 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 + k^{2}, the same number obtained in [15]. Finally we extend some of the results to larger domains.

Original language | English (US) |
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Title of host publication | Annual Symposium on Foundations of Computer Science - Proceedings |

Pages | 610-619 |

Number of pages | 10 |

State | Published - 2001 |

Event | 42nd Annual Symposium on Foundations of Computer Science - Las Vegas, NV, United States Duration: Oct 14 2001 → Oct 17 2001 |

### Other

Other | 42nd Annual Symposium on Foundations of Computer Science |
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Country | United States |

City | Las Vegas, NV |

Period | 10/14/01 → 10/17/01 |

### ASJC Scopus subject areas

- Hardware and Architecture

### Cite this

*Annual Symposium on Foundations of Computer Science - Proceedings*(pp. 610-619)

**Query efficient PCPs with perfect completeness.** / Håstad, J.; Khot, Subhash.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Annual Symposium on Foundations of Computer Science - Proceedings.*pp. 610-619, 42nd Annual Symposium on Foundations of Computer Science, Las Vegas, NV, United States, 10/14/01.

}

TY - GEN

T1 - Query efficient PCPs with perfect completeness

AU - Håstad, J.

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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UR - http://www.scopus.com/inward/citedby.url?scp=0035175817&partnerID=8YFLogxK

M3 - Conference contribution

SP - 610

EP - 619

BT - Annual Symposium on Foundations of Computer Science - Proceedings

ER -