Query efficient PCPs with perfect completeness

J. Håstad, Subhash Khot

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish (US)
Title of host publicationAnnual Symposium on Foundations of Computer Science - Proceedings
Pages610-619
Number of pages10
StatePublished - 2001
Event42nd Annual Symposium on Foundations of Computer Science - Las Vegas, NV, United States
Duration: Oct 14 2001Oct 17 2001

Other

Other42nd Annual Symposium on Foundations of Computer Science
CountryUnited States
CityLas Vegas, NV
Period10/14/0110/17/01

ASJC Scopus subject areas

  • Hardware and Architecture

Cite this

Håstad, J., & Khot, S. (2001). Query efficient PCPs with perfect completeness. In Annual Symposium on Foundations of Computer Science - Proceedings (pp. 610-619)

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

Annual Symposium on Foundations of Computer Science - Proceedings. 2001. p. 610-619.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Håstad, J & Khot, S 2001, Query efficient PCPs with perfect completeness. in 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.
Håstad J, Khot S. Query efficient PCPs with perfect completeness. In Annual Symposium on Foundations of Computer Science - Proceedings. 2001. p. 610-619
Håstad, J. ; Khot, Subhash. / Query efficient PCPs with perfect completeness. Annual Symposium on Foundations of Computer Science - Proceedings. 2001. pp. 610-619
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