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2006
ACM

The PCP theorem by gap amplification

11 years 13 hour ago
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...
Irit Dinur
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2006
Where STOC
Authors Irit Dinur
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