BU CS 332 – Theory of Computation Lecture 20: • More on NP Reading: Sipser Ch 7.3-7.5 Mark Bun April 13, 2020 Goals of complexity theory Ultimate goal: Classify problems according to their feasibility and inherent computational difficulty P ≈ Decision problems which can be solved efficiently Can we exhibit general classes of problems which […]
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BU CS 332 – Theory of Computation Lecture 21: • NP-Completeness • Cook-Levin Theorem • Reductions Mark Bun April 15, 2020 Reading: Sipser Ch 7.3-7.5 Last time: Two equivalent definitions of NP 1) NP is the class of languages decidable in polynomial time on a nondeterministic TM NP = ⋃∞ NTIME(𝑛𝑛𝑘𝑘) 𝑘𝑘=1 2) A polynomial-time
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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
The Unbounded-Error Communication Complexity of Symmetric Functions∗ ALEXANDER A. SHERSTOV† Abstract We prove an essentially tight lower bound on the unbounded-error communication complexity of every symmetric function, i.e., f (x, y) = D(|x ∧ y|), where D: {0,1,…,n} → {0,1} is a given predicate and x, y range over {0, 1}n . Specifically, we show
Prof. Mark Bun CAS CS 591 B: Communication Complexity Lecture Notes 5: Discrepancy Fall 2019 Reading. • Rao-Yehudayoff Chapter 5 Last time we saw how Yao’s Principle could be used (in principle) to lower bound the random- ized communication complexity of a function by exhibiting a distribution under which it has high distributional complexity. Namely,
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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
CS 591 B1: Communication Complexity, Fall 2019 Problem Set 2 Due: 5:00PM, Friday, October 25, 2019. Homework Policies: • Submit your completed assignment by email to mbun[at]bu[dot]edu. Please include the string “CS591PS2” somewhere in your subject line. • Solutions must be typeset, e.g., using LATEX or Microsoft Word. • To help your instructor calibrate the
COMP760, SUMMARY OF LECTURE 17. HAMED HATAMI 1. How to do compression? In this lecture we will discuss how to compress a protocol with low information cost, but possibly very high communication cost, to a protocol with low communication cost. It will be important to understand how much information is revealed at every step of
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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
Prof. Mark Bun CAS CS 591 B: Communication Complexity Lecture Notes 12: One-way communication, streaming Fall 2019 Reading. • Rao-Yehudayo Chapter 10, Roughgarden Chapters 1 & 2 We’ll start looking in depth at an application of communication complexity to lower bounds for streaming algorithms. The data stream model is motivated by applications to analyzing massive
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