Cited By
View all- Newton PRichelson SWilson CSaha BServedio R(2023)A High Dimensional Goldreich-Levin TheoremProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585224(1463-1474)Online publication date: 2-Jun-2023
Low-degree test with polynomially small error
Pages 531 - 582
Abstract
A long line of work in Theoretical Computer Science shows that a function is close to a low-degree polynomial iff it is locally close to a low-degree polynomial. This is known as low-degree testing and is the core of the algebraic approach to construction of PCP. We obtain a low-degree test whose error, i.e., the probability it accepts a function that does not correspond to a low-degree polynomial, is polynomially smaller than existing low-degree tests. A key tool in our analysis is an analysis of the sampling properties of the incidence graph of degree-k curves and kź-tuples of points in a finite space $${\mathbb{F}^m}$$Fm. We show that the Sliding Scale Conjecture in PCP, namely the conjecture that there are PCP verifiers whose error is exponentially small in their randomness, would follow from a derandomization of our low-degree test.
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- Low-degree test with polynomially small error
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Published: 01 September 2017
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View all- Newton PRichelson SWilson CSaha BServedio R(2023)A High Dimensional Goldreich-Levin TheoremProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585224(1463-1474)Online publication date: 2-Jun-2023