Algebrization: A New Barrier in Complexity Theory Scott Aaronson∗ Avi Wigderson† MIT Institute for Advanced Study Abstract Any proof of P ̸= NP will have to overcome two barriers: relativization and natural proofs. Yet over the last decade, we have seen circuit lower bounds (for example, that PP does not have linear-size circuits) that overcome […]
LATEX Tutorials A PRIMER Indian TEX Users Group Trivandrum, India 2003 September LATEX TUTORIALS — A PRIMER Indian TEX Users Group EDITOR: E. Krishnan COVER: G. S. Krishna Copyright ⃝c 2002, 2003 Indian TEX Users Group Floor III, SJP Buildings, Cotton Hills Trivandrum 695014, India http://www.tug.org.in Permission is granted to copy, distribute and/or modify this
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PROPERTY TESTING LOWER BOUNDS VIA COMMUNICATION COMPLEXITY Eric Blais, Joshua Brody, and Kevin Matulef February 21, 2012 Abstract. We develop a new technique for proving lower bounds in property testing, by showing a strong connection between testing and communication complexity. We give a simple scheme for reducing com- munication problems to testing problems, thus allowing
CS 591 B1: Communication Complexity, Fall 2019 Course Project Guidelines The course project is an opportunity to perform an in-depth exploration of a topic in communication complexity that interests you. The goals are to gain experience • Independently reading and synthesizing research papers, • Presenting research papers to an audience of your peers, and •
LATEX Tutorials A PRIMER Indian TEX Users Group Trivandrum, India 2003 September LATEX TUTORIALS — A PRIMER Indian TEX Users Group EDITOR: E. Krishnan COVER: G. S. Krishna Copyright ⃝c 2002, 2003 Indian TEX Users Group Floor III, SJP Buildings, Cotton Hills Trivandrum 695014, India http://www.tug.org.in Permission is granted to copy, distribute and/or modify this
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Foundations and Trends⃝R in Theoretical Computer Science Vol. 4, Nos. 1–2 (2008) 1–155 ⃝c 2009 S. V. Lokam DOI: 10.1561/0400000011 Complexity Lower Bounds using Linear Algebra By Satyanarayana V. Lokam Contents 1 Introduction 2 1.1 Scope 2 1.2 Matrix Rigidity 3 1.3 Spectral Techniques 4 1.4 Sign-Rank 5 1.5 Communication Complexity 6 1.6 Graph Complexity
Lower Bounds in Communication Complexity: A Survey Troy Lee Adi Shraibman Columbia University Weizmann Institute Abstract We survey lower bounds in communication complexity. Our focus is on lower bounds that work by first representing the communication complexity measure in Euclidean space. That is to say, the first step in these lower bound techniques is to
Beyond Set Disjointness: The Communication Complexity of Finding the Intersection Joshua Brody Amit Chakrabarti Ranganath Kondapally Swarthmore College Dartmouth College Dartmouth College brody@cs.swarthmore.edu ac@cs.dartmouth.edu rangak@cs.dartmouth.edu ABSTRACT David P. Woodruff IBM Almaden dpwoodru@us.ibm.com Grigory Yaroslavtsev Brown University, ICERM grigory@grigory.us 1. INTRODUCTION Communication complexity [Yao79] quantifies the com- munication necessary for two or more players to compute
Communication Complexity (for Algorithm Designers) Tim Roughgarden ⃝c Tim Roughgarden 2015 Preface The best algorithm designers prove both possibility and impossibility results — both upper and lower bounds. For example, every serious computer scientist knows a collection of canonical NP-complete problems and how to reduce them to other problems of interest. Communication complexity offers a
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