Lecture 10 : Low degree testing
نویسندگان
چکیده
Theorem 1. Let p be a prime power, d and m be any positive integers such that d < p/2, and ∈ (0, 1) be a parameter. Then, there is a randomized algorithm A, which when given access to a function f : Fp → Fp, runs in time Poly(log p,m, d, 1 ) and satisfies the following. 1. If f is a polynomial of degree at most d, then Pr[A accepts] = 1. 2. If f is -far from every polynomial of degree at most d, then Pr[A rejects] ≥ 0.9.
منابع مشابه
Limits of Approximation Algorithms 18 Mar , 2010 ( TIFR ) Lec . 7 : Low degree testing ( Part I )
In this lecture1, we will give a local algorithm to test whether a given function is close to a low degree polynomial, i.e. check whether the function f : Fm → F (given as a truth-table) is close to the evaluation of some multi-variate polynomial of low degree without reading all of f . This problem is refered to as the “low-degree testing”. The main references for this lecture include Lecture ...
متن کاملLec . 9 : PCPs Constructions via low degree polynomials
In today’s lecture 1, we will see how we can use the results on low-degree testing (which we discussed in detail in the earlier lectures) to construct PCPs. Towards this end, we will first show how local checkers for low-degreeness can be extended to check if a given function is a low-degree polynomial that vanishes on a pre-specified subcube. We will then “arithmetize” the NP-complete problem ...
متن کاملGestational diabetes mellitus
Introduction: Gestational diabetes mellitus (GDM) is defined as any degree of glucose intolerance with onset or first recognition during pregnancy. The prevalence range from 1 to 14% of all pregnancies, depending on the population studied and the diagnostic tests employed. Risk assessment for GDM should be undertaken at the prenatal visit. Women with clinical characteristics of GDM should und...
متن کاملLecture 3 : The Sum Check Protocol
i.e., a PCP Theorem with a poly-logarithmic number of queries. For this lecture we use a simplified version of the low degree testing assumption. This simplified version is in fact over-simplified, and, as is, false. However, we use it as a place holder for the more intricate version of the assumption that is both correct and sufficient for our needs. More details about the assumptions are in t...
متن کاملLecture Notes on Testing Graph Properties in the Bounded-Degree Graph Model
1. Presenting lower and upper bounds on the complexity of testing Bipartitness; specifically, we present a poly(1/ǫ) · Õ( √ k)-time tester, and an Ω √ k) lower bound on the query complexity of any tester for Bipartitness. 2. Reviewing a quasi-poly(1/ǫ)-time tester for Planarity. The result extends to testing any minor-closed property (i.e., a graph property that is preserved under the omission ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017