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Query efficient PCPs with perfect completeness
KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.ORCID iD: 0000-0002-5379-345X
2005 (English)In: Theory of Computing, ISSN 1557-2862, Vol. 1, 119-149 p.Article in journal (Refereed) Published
Abstract [en]

For every integer k >0, and an arbitrarily small constante> 0, we present a PCP characterization of NP where the verifier uses logarithmic randomness, non-adaptively queries 4 k +k2 bits in the proof, accepts a correct proof with probability 1, i. e., it has perfect completeness, and accepts any supposed proof of a false statement with probability at most 2 −k2 +e. In particular, the verifier achieves optimal amortized query complexity of 1 +dfor arbitrarily small constantd> 0. Such a characterization was already proved by Samorodnitsky and Trevisan (STOC 2000), 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 2 k +k2 , equal to the number obtained by Samorodnitsky and Trevisan. Finally we extend some of the results to PCPs over non-Boolean alphabets.

Place, publisher, year, edition, pages
2005. Vol. 1, 119-149 p.
Keyword [en]
Computational complexity, approximation algorithms, probabilistically checkable proofs, PCP, inapproximability, amortized query bits, perfect completeness, amortized query bits
National Category
Computer and Information Science
URN: urn:nbn:se:kth:diva-62993DOI: 10.4086/toc.2005.v001a007OAI: diva2:481473
QC 20120123Available from: 2012-01-21 Created: 2012-01-21 Last updated: 2012-01-23Bibliographically approved

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