Checking computations in polylogarithmic time
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
The PCP theorem by gap amplification
Journal of the ACM (JACM)
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We show an alternative implementation of the gap amplification step in Dinur's [4] recent proof of the PCP theorem. We construct a product Gt of a constraint graph G, so that if every assignment in G leaves an ε-fraction of the edges unsatisfied, then in Gt every assignment leaves an Ω(tε)-fraction of the edges unsatisfied, that is, it amplifies the gap by a factor Ω(t). The corresponding result in [4] showed that one could amplify the gap by a factor $\Omega(\sqrt{t})$. More than this small quantitative improvement, the main contribution of this work is in the analysis. Our construction uses random walks on expander graphs with exponentially distributed length. By this we ensure that some random variables arising in the proof are automatically independent, and avoid some technical difficulties.