The PCP theorem by gap amplification

The PCP theorem [3, 2] says that every language in NP has a witness format that can be checked probabilistically by reading only a constant number of bits from the proof. The celebrated equivalence of this theorem and inapproximability of certain optimization problems, due to [12], has placed the PCP theorem at the heart of the area of inapproximability. In this work we present a new proof of the PCP theorem that draws on this equivalence. We give a combinatorial proof for the NP-hardness of approximating a certain constraint satisfaction problem, which can then be reinterpreted to yield the PCP theorem. Our approach is to consider the unsat value of a constraint system, which is the smallest fraction of unsatisfied constraints, ranging over all possible assignments for the underlying variables. We describe a new combinatorial amplification transformation that doubles the unsat-value of a constraintsystem, with only a linear blowup in the size of the system. The amplification step cau...

• Type: Conference
• Year: 2006
• Where: STOC
• Authors: Irit Dinur
• Keywords: Algorithms, Amplification Lemma, PCP Composition Step, PCP Theorem, STOC 2006