eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-08-11
34:1
34:14
10.4230/LIPIcs.APPROX/RANDOM.2020.34
article
Revisiting Alphabet Reduction in Dinur’s PCP
Guruswami, Venkatesan
1
https://orcid.org/0000-0001-7926-3396
Opršal, Jakub
2
https://orcid.org/0000-0003-1245-3456
Sandeep, Sai
1
Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA
Computer Science Department, Durham University, UK
Dinur’s celebrated proof of the PCP theorem alternates two main steps in several iterations: gap amplification to increase the soundness gap by a large constant factor (at the expense of much larger alphabet size), and a composition step that brings back the alphabet size to an absolute constant (at the expense of a fixed constant factor loss in the soundness gap). We note that the gap amplification can produce a Label Cover CSP. This allows us to reduce the alphabet size via a direct long-code based reduction from Label Cover to a Boolean CSP. Our composition step thus bypasses the concept of Assignment Testers from Dinur’s proof, and we believe it is more intuitive - it is just a gadget reduction. The analysis also uses only elementary facts (Parseval’s identity) about Fourier Transforms over the hypercube.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol176-approx-random2020/LIPIcs.APPROX-RANDOM.2020.34/LIPIcs.APPROX-RANDOM.2020.34.pdf
PCP theorem
CSP
discrete Fourier analysis
label cover
long code