CS 880 : Advanced Complexity Theory 2 / 29 / 2008 Lecture 15 : Hardness Amplification within NP
نویسندگان
چکیده
In the last lecture, we introduced the general idea of boosting the hardness of a function by taking k independent copies of the function and aggregating them using another function h. We obtained the following result:
منابع مشابه
Cs 880: Advanced Complexity Theory Lecture 13: Average-case Hardness 1 Worst-case vs. Average-case Complexity
In this lecture and the next two lectures we study hardness amplification, in which the goal is to take a mildly average-case hard function from some class and construct another function in that class that is very average-case hard. Today we prove a lemma that roughly states that every average-case hard function has a set of inputs that encapsulates the hardness of that function in a certain se...
متن کاملCS 880: Advanced Complexity Theory Final Project: Hardness Amplification within NP
We survey the current status of the problem of Hardness amplification within NP, reviewing known results and evaluating various approaches for improving on them. We also prove that under some stronger assumptions, we can amplify the hardness to (12 − 1/2).
متن کاملCS 880 : Advanced Complexity Theory 2 / 11 / 2008 Lecture 8 : Active Learning
Last time we studied computational learning theory and saw how harmonic analysis could be used to design and analyze efficient learning algorithms with respect to the uniform distribution. We developed a generic passive learning algorithm for concepts whose Fourier spectrum is concentrated on a known set, and applied it to decision trees. We also started developing an approach for the case wher...
متن کاملCS 880 : Advanced Complexity Theory 2 / 20 / 2008 Lecture 12 : Social Choice Theory
At the end of the last lecture we briefly introduced our first application of harmonic analysis to social choice theory. Today we go over this in detail and look at a second application. We saw last time that there exists a certain coalition that makes up a very small fraction, namely o(1) of the number of voters, that can ensure that the result of a ”two party election” is forced to their pref...
متن کاملCS 880 : Advanced Complexity Theory 2 / 15 / 2008 Lecture 10 : Hypercontractivity
the inequality follows from Hölder’s inequality: E [ fg] ≤ ∥f ∥∥ p ∥g ∥∥ q , if 1p + 1 q = 1 with p, q ≥ 1. If α = ±1 then (1) fails unless p = q or f is constant in absolute value. This follows because (T±1f)(x) = f(±x), where −x denotes x with all its bits flipped, and because the only functions f for which ∥f ∥∥ p = ∥f ∥∥ q for p 6= q are those that are constant in absolute value. In proving...
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 2008