Advanced Complexity Theory Fall 2012 Lecture 15 — November 1 , 2012
نویسنده
چکیده
Q: Why are we using circuit lower bounds here, as opposed to a claim such as E ̸⊆ P for example? A: The proof of the Nisan-Wigderson pseudorandom generator relies on nonuniformity, by showing that distinguishing a pseudorandom generator implies a circuit for solving a hard problem – this reduction involves hardwiring advice into a circuit in order to solve the hard problem. A contradiction requires that the hard problem has circuit lower bounds.
منابع مشابه
CS5236 – Advanced Automata Theory
Advanced Automata Theory is a lecture which will first review the basics of formal languages and automata theory and then give insight into specific topics from the theory of automata theory. In computer science, automata are an important tool for many theoretical results and various types of automata have been used to characterise complexity classes. The lecture will give a deeper understandin...
متن کامل5 . Applications to streaming
In this lecture, we will see applications of communication complexity to proving lower bounds for streaming algorithms. Towards the end of the lecture, we will introduce combinatorial auctions, and we will see applications of communication complexity to auctions in the next lecture. The references for this lecture include Lecture 7 of Troy Lee’s course on communication complexity [Lee10], Lectu...
متن کاملSemidefinite and Second Order Cone Programming Seminar Fall 2012 Lecture 2
1 Overview We had a general overview of semidefinite programming(SDP) in lecture 1, starting from this lecture we will be jumping into the theory. Some topics we will discuss in the next few lectures include: the duality theory, notion of complementary slackness, at least one polynomial time algorithm of solving SDP and application in integer programming and combinatorial optimization. Througho...
متن کاملUniversal homogeneous structures ( lecture notes )
We present category-theoretic framework for universal homogeneous structures, with selected applications. Most of the material had been presented as a series of lectures for graduate students at Department of Mathematics, University of Silesia in Katowice, Poland (21 – 23 November 2012).
متن کامل18.405J S16 Lecture 1: PH Time-Space Tradeoffs
The main result of this lecture is that NTIME(n) has algorithms which do not run in time n1.2 and use n0.2 space. We begin by reviewing some major open problems in complexity theory and describing how this result fits into those open problems. We define the classes in basic complexity theory and the Polynomial Hierarchy. Then we prove the main theorem by using 2 claims. The method we use is an ...
متن کامل