NDLI: The PCP theorem by gap amplification

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The PCP theorem by gap amplification

Content Provider	ACM Digital Library
Author	Dinur, Irit
Abstract	We present a new proof of the PCP theorem that is based on a combinatorial amplification lemma. The unsat value of a set of constraints C = $(c_{1},.,c_{n}),$ denoted UNSAT(C), 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 constraint-system, with only a linear blowup in the size of the system. The amplification step causes an increase in alphabet-size that is corrected by a PCP composition step. Iterative application of these two steps yields a proof for the PCP theorem.The amplification lemma relies on a new notion of "graph powering" that can be applied to systems of constraints. This powering amplifies the unsat-value of a constraint system provided that the underlying graph structure is an expander.We also apply the amplification lemma to construct PCPs and locally-testable codes whose length is linear up to a polylog factor, and whose correctness can be probabilistically verified by making a constant number of queries. Namely, we prove SAT ∈ $PCP_{1/2,1}[log_{2}(n$ • poly log n),O(1)].
Starting Page	241
Ending Page	250
Page Count	10
File Format	PDF
ISBN	1595931341
DOI	10.1145/1132516.1132553
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2006-05-21
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Pcp Gap amplification
Content Type	Text
Resource Type	Article

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