PPT-Circuit Complexity and Derandomization

Tokyo Institute of Technology Akinori Kawachi Layout Randomized vs Determinsitic Algorithms Primality Test General Framework for Derandomization Circuit Complexity Derandomization. FulfillSustain THE LEADERMID-LOW VOLUME, HIGHER COMPLEXITY +1 877 733 7260 Toll-freePARTEROne Plexus Way www.plexus.com Commercialize Manufacture Product Realization Solutions Boulder, C How to celebrate it, leverage it, and NOT avoid it!. Are YOU sufficiently complex?. Simple = Best. FROM OCCAM’S . RAZOR. COMPLEXITY. Are YOU sufficiently complex?. Simple = Best. Simple but no. Simpler. and . Hierarchy. Concept of Complexity. “whole is more than the sum of its parts”. Holism. new properties not found in subsystems. “mechanistic explanations of emergence rejected”. Weaker view of emergence. Quantum Boolean . Circuits. Vincent . Liew. Generalized-CNOT Circuits. Generalized-CNOT gates have one target, multiple controls. We call a circuit composed of these gates is a . Quantum Boolean Circuit (QBC). Lecture 1: . Intro; Turing machines; . Class P and NP . . . Indian Institute of Science. About the course. Computational complexity attempts . to classify computational . problems. Lecture 1: . Intro; Turing machines; . Class P and NP . . . Indian Institute of Science. About the course. Computational complexity attempts . to classify computational . problems. How Understanding Complexity Promotes Simplicity. Why is writing software hard?. ^. great. http://www.infoq.com/presentations/Simple-Made-Easy. Our duty as software architects is to understand and manage complexity. Algorithms . that Err Extremely Rarely. Oded. . Goldreich. Weizmann Institute of Science. Based on Joint work with . Avi. . Wigderson. Standard . Derandomization. Challenges. Given. a c. ircuit . Theophilus Benson (tbenson@cs.wisc.edu). Aditya Akella (akella@cs.wisc.edu). David A Maltz (dmaltz@microsoft.com). Enterprise Networks. Intricate logical and physical topologies. Diverse network devices. Algorithms . that Err Extremely Rarely. Oded. . Goldreich. Weizmann Institute of Science. Based on Joint work with . Avi. . Wigderson. Standard . Derandomization. Challenges. Given. a c. ircuit . Toniann. . Pitassi. University of Toronto. 2-Party Communication Complexity. [Yao]. 2-party communication: . each party has a dataset. . Goal . is to compute a function f(D. A. ,D. B. ). m. 1. m. 2. What is the best way to measure the time complexity of an algorithm?. - Best-case run time?. - Worst-case run time?. - Average run time?. Which should we try to optimize?. Best-Case Measures. How can we modify almost any algorithm to have a good best-case running time?. Lijie. Chen. MIT. Today’s Topic. Background. . What is Fine-Grained Complexity?. The Methodology of Fine-Grained Complexity. Frontier: Fine-Grained Hardness for Approximation Problems. The Connection. Lijie. Chen. Ryan Williams. Context: The Algorithmic Method for Proving Circuit Lower Bounds. Proving limitations on non-uniform circuits is . extremely. hard.. Prior approaches (. restrictions. , .