Lower Bounds in Communication Complexity PDF Download
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Author: Troy Lee
Publisher: Now Publishers Inc
ISBN: 1601982585
Category : Computers
Languages : en
Pages : 152
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Book Description
The communication complexity of a function f(x, y) measures the number of bits that two players, one who knows x and the other who knows y, must exchange to determine the value f(x, y). Communication complexity is a fundamental measure of complexity of functions. Lower bounds on this measure lead to lower bounds on many other measures of computational complexity. This monograph surveys lower bounds in the field of 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 find a geometric complexity measure, such as rank or trace norm, that serves as a lower bound to the underlying communication complexity measure. Lower bounds on this geometric complexity measure are then found using algebraic and geometric tools.
Author: Troy Lee
Publisher: Now Publishers Inc
ISBN: 1601982585
Category : Computers
Languages : en
Pages : 152
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Book Description
The communication complexity of a function f(x, y) measures the number of bits that two players, one who knows x and the other who knows y, must exchange to determine the value f(x, y). Communication complexity is a fundamental measure of complexity of functions. Lower bounds on this measure lead to lower bounds on many other measures of computational complexity. This monograph surveys lower bounds in the field of 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 find a geometric complexity measure, such as rank or trace norm, that serves as a lower bound to the underlying communication complexity measure. Lower bounds on this geometric complexity measure are then found using algebraic and geometric tools.
Author: Eyal Kushilevitz
Publisher: Cambridge University Press
ISBN: 052102983X
Category : Computers
Languages : en
Pages : 209
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Book Description
Surveys the mathematical theory and applications such as computer networks, VLSI circuits, and data structures.
Author: Tim Roughgarden
Publisher: Foundations and Trends (R) in Theoretical Computer Science
ISBN: 9781680831146
Category :
Languages : en
Pages : 206
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Book Description
This book deals mostly with impossibility results - lower bounds on what can be accomplished by algorithms. However, the perspective is unapologetically that of an algorithm designer. The reader will learn lower bound technology on a "need-to-know" basis, guided by fundamental algorithmic problems that we care about.
Author: Satyanarayana V. Lokam
Publisher: Now Publishers Inc
ISBN: 1601982429
Category : Computers
Languages : en
Pages : 177
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Book Description
We survey several techniques for proving lower bounds in Boolean, algebraic, and communication complexity based on certain linear algebraic approaches. The common theme among these approaches is to study robustness measures of matrix rank that capture the complexity in a given model. Suitably strong lower bounds on such robustness functions of explicit matrices lead to important consequences in the corresponding circuit or communication models. Many of the linear algebraic problems arising from these approaches are independently interesting mathematical challenges.
Author: Anup Rao
Publisher: Cambridge University Press
ISBN: 1108776019
Category : Computers
Languages : en
Pages : 271
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Book Description
Communication complexity is the mathematical study of scenarios where several parties need to communicate to achieve a common goal, a situation that naturally appears during computation. This introduction presents the most recent developments in an accessible form, providing the language to unify several disjoint research subareas. Written as a guide for a graduate course on communication complexity, it will interest a broad audience in computer science, from advanced undergraduates to researchers in areas ranging from theory to algorithm design to distributed computing. The first part presents basic theory in a clear and illustrative way, offering beginners an entry into the field. The second part describes applications including circuit complexity, proof complexity, streaming algorithms, extension complexity of polytopes, and distributed computing. Proofs throughout the text use ideas from a wide range of mathematics, including geometry, algebra, and probability. Each chapter contains numerous examples, figures, and exercises to aid understanding.
Author: Oded Goldreich
Publisher: Springer Nature
ISBN: 3030436624
Category : Computers
Languages : en
Pages : 391
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Book Description
This volume contains a collection of studies in the areas of complexity theory and property testing. The 21 pieces of scientific work included were conducted at different times, mostly during the last decade. Although most of these works have been cited in the literature, none of them was formally published before. Within complexity theory the topics include constant-depth Boolean circuits, explicit construction of expander graphs, interactive proof systems, monotone formulae for majority, probabilistically checkable proofs (PCPs), pseudorandomness, worst-case to average-case reductions, and zero-knowledge proofs. Within property testing the topics include distribution testing, linearity testing, lower bounds on the query complexity (of property testing), testing graph properties, and tolerant testing. A common theme in this collection is the interplay between randomness and computation.
Author: Stasys Jukna
Publisher: Springer Science & Business Media
ISBN: 3642245080
Category : Mathematics
Languages : en
Pages : 618
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Book Description
Boolean circuit complexity is the combinatorics of computer science and involves many intriguing problems that are easy to state and explain, even for the layman. This book is a comprehensive description of basic lower bound arguments, covering many of the gems of this “complexity Waterloo” that have been discovered over the past several decades, right up to results from the last year or two. Many open problems, marked as Research Problems, are mentioned along the way. The problems are mainly of combinatorial flavor but their solutions could have great consequences in circuit complexity and computer science. The book will be of interest to graduate students and researchers in the fields of computer science and discrete mathematics.
Author: Sanjeev Arora
Publisher: Cambridge University Press
ISBN: 0521424267
Category : Computers
Languages : en
Pages : 609
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Book Description
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Author: Colin P. Williams
Publisher: Springer
ISBN: 3540492089
Category : Computers
Languages : en
Pages : 490
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Book Description
This book contains selected papers presented at the First NASA International Conference on Quantum Computing and Quantum Communications, QCQC'98, held in Palm Springs, California, USA in February 1998. As the record of the first large-scale meeting entirely devoted to quantum computing and communications, this book is a unique survey of the state-of-the-art in the area. The 43 carefully reviewed papers are organized in topical sections on entanglement and quantum algorithms, quantum cryptography, quantum copying and quantum information theory, quantum error correction and fault-tolerant quantum computing, and embodiments of quantum computers.
Author: Johan Håstad
Publisher: MIT Press (MA)
ISBN:
Category : Computers
Languages : en
Pages : 110
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Book Description
Proving lower bounds on the amount of resources needed to compute specific functions is one of the most active branches of theoretical computer science. Significant progress has been made recently in proving lower bounds in two restricted models of Boolean circuits. One is the model of small depth circuits, and in this book Johan Torkel Hastad has developed very powerful techniques for proving exponential lower bounds on the size of small depth circuits' computing functions. The techniques described in Computational Limitations for Small Depth Circuitscan be used to demonstrate almost optimal lower bounds on the size of small depth circuits computing several different functions, such as parity and majority. The main tool used in the proof of the lower bounds is a lemma, stating that any AND of small fanout OR gates can be converted into an OR of small fanout AND gates with high probability when random values are substituted for the variables. Hastad also applies this tool to relativized complexity, and discusses in great detail the computation of parity and majority in small depth circuits. Contents:Introduction. Small Depth Circuits. Outline of Lower Bound Proofs. Main Lemma. Lower Bounds for Small Depth Circuits. Functions Requiring Depth k to Have Small Circuits. Applications to Relativized Complexity. How Well Can We Compute Parity in Small Depth? Is Majority Harder than Parity? Conclusions. John Hastad is a postdoctoral fellow in the Department of Mathematics at MIT Computational Limitations of Small Depth Circuitsis a winner of the 1986 ACM Doctoral Dissertation Award.
