| Abstract |
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For every integer k \geqslant 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^{ - k^2 + 1}. In particular, the verifier achieves optimal amortized query complexity of 1+ \delta for arbitrarily small constant ¦\delta > 0. Such a characterization was already proved by Samorodnitsky and Trevisan [15], 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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 Additional Information
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Citation:
J. Hastad, S. Khot,
"Query Efficient PCPs with Perfect Completeness,"
focs,
p. 610,
42nd IEEE symposium on Foundations of Computer Science (FOCS’01),
2001
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