4 edition of Lower bounds on communication complexity in VLSI found in the catalog.
by Courant Institute of Mathematical Sciences, New York University in New York
Written in English
|Statement||by Richard Cole, Alan Siegel.|
|Series||Ultracomputer note -- 90|
|The Physical Object|
|Number of Pages||23|
This book surveys the mathematical theory of communication complexity, concentrating on the question of how much communication is necessary for any particular computing process. Applications of the theory include computer networks, VLSI circuits and data structures. Lower bound techniques for VLSI algorithms. Trends, Techniques, and Problems in Theoretical Computer Science, () Complexity classes in communication complexity by:
The Communication Complexity of Relations Multiparty Communication Complexity Variable Partition Models Networks, Communication, and VLSI Decision Trees and Data Structures Boolean Circuit Depth More Boolean Circuit Lower Bounds Time and Space Randomness . Communication Complexity Introduction: Motivated by VLSI applications, research in communication complexity has so far mainly focused on lower bounds for protocols computing specific functions. In this paper we take a look at communication complexity from the point of view of (“machine based”) complexity theory.
Applications for proving lower bounds for VLSI chips, decision trees, and data structures. Communication complexity of relations, application for lower bounds for monotone circuits depth and formulae size. Lower bounds for AC0 circuits. Requirements: The course is an elective course for graduate students. Avi Wigderson Mathematics and Computation Draft: Ma Acknowledgments In this book I tried to present some of the knowledge and understanding I acquired in my four decades in the eld. The main source of this knowledge was the Theory of Computation commu-nity, which has been my academic and social home throughout this period.
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Lower Bounds in Communication Complexity: A Survey Troy Lee Columbia University Adi Shraibman Weizmann Institute. VLSI design, proof complexity, and streaming algorithms, is norm is very useful for showing communication complexity lower bounds, and develop some more exotic norms as well.
We discuss this step in each. Excerpt from Lower Bounds on Communication Complexity in Vlsi We analyze a family of problems governing the vlsi complexity of broadcasting 8 bits of information in time T (s B) to each of N processors located along the perimeter of a two dimensional broadcast by: 1.
The communication complexity of a function f(x;y) measures the num-ber of bits that two players, one who knows xand the other who knows y, must exchange to determine the aluev f(x;y). Communication com-plexity is a fundamental measure of complexity of functions.
Lower bounds on this measure lead to lower bounds on many other measures. TY - BOOK. T1 - Lower bounds on communication complexity in VLSI. AU - Cole, Richard. AU - Siegel, Alan. PY - Y1 - M3 - Other report.
T3 - Technical Report No. BT - Lower bounds on communication complexity in VLSI. PB - Courant Institute, NYU. ER -Cited by: 1. Lower Bounds in Communication Complexity is an ideal primer for anyone with an interest in this current and popular topic.
Cited By S. K, Laekhanukit B and Manurangsi P () On the Parameterized Complexity of Approximating Dominating Set, Journal of the ACM. The applicability of communication complexity to other areas, including circuit and formula complexity, VLSI design, Lower bounds on communication complexity in VLSI book complexity, and streaming algorithms, has meant that it has attracted a lot of interest.
Lower Bounds in Communication Complexity focuses on showing lower bounds on the communication complexity of explicit by: Increased use of Very Large Scale Integration (VLSI) for the fabrication of digital circuits has led to increased interest in complexity results on the inherent VLSI difficulty of various problems.
Lower bounds have been obtained for problems such as integer multiplication [1,2], matrix multiplication , sorting , and discrete Fourier transform , all within VLSI models similar to one.
Communication Complexity studies how many bits ALICE and BOB have to exchange to computer a function. Questinos of this sort are interesting in and of themselves AND also because they help proof lower Bounds on models of computation like circuits and decision trees.
THIS book is readable and gives you all the basics that you by: The applicability of communication complexity to other areas, including circuit and formula complexity, VLSI design, proof complexity, and streaming algorithms, has meant it has attracted a lot of interest.
Lower Bounds in Communication Complexity focuses on showing lower bounds on the communication complexity of explicit by: Variation ranks of communication matrices and lower bounds for depth two circuits having symmetric gates with unbounded fan-in. In Proc. 32nd IEEE Symposium on Foundations of Computer Science, pages –, Cited by: 5.
The basic hierarchy of S-communication complexity, exponential gap between deterministic and nondeterministic S-communication complexity, and further basic results concerning the properties of S-communication complexity are established.
New, linear lower bounds on S-communication complexity for the recognition of specific languages are by: 1. the eld of communication complexity. Our focus is on lower bounds that work by rst representing the communication complexity measure in Euclidean space.
That is to say, the rst step in these lower bound techniques is to nd a geometric complexity measure, such as rank or trace norm, that serves as a lower bound to the underlying communica-tion Cited by: Lower bounds in communication complexity can be used to prove lower bounds in decision tree complexity, VLSI circuits, data structures, streaming algorithms, space–time tradeoffs for Turing machines and more.
See also. Gap-Hamming problem; Notes. Communication complexity has provided upper and lower bounds for the complexity of many fundamental communication problems.
It has clarified the role which communication plays in distributed and parallel computation as well as in the performance of VLSI circuits. Communication complexity lower bounds in the two-party model can be used to prove time lower bounds for more complicated (multiparty) networks.
Roughly speaking, the method consists of two stages. First, we partition the network into two “large” parts such that the number of edges connecting the two parts (sometimes called the bandwidth. () Lower bounds for one-way probabilistic communication complexity and their application to space complexity.
Theoretical Computer ScienceCited by: In VLSI, communication constraints dictate lower bounds on the performance of chips.
we obtain some upper and lower bounds on communication complexity. The upper bounds which we obtained for Author: Dömötör Pálvölgyi. In the two-party case, there is a lower bound on quantum communication complexity in terms of a norm 2, which is known to subsume nearly all other tech- niques in the literature.
communication complexity. In this lecture we’ll see two more ways we can prove these lower bounds: the Rectangle Size Method and the Rank Method. Both of these are stronger than the fooling set method. We’ll show (n) lower bounds for the dot product function with both methods while the fooling set method can only give (log(n)).
lower bounds for one-tape TMs using communication complexity. This lecture is based on Chapters 8 and 12 of Kushilevtiz and Nisan’s book on Communication Complexity [KN97]. T p A lower bounds for VLSI We begin with the T p A lower bound for VLSI chips due to Thompson [Tho79], one of the earliest motivations for communication complexity.
Furthermore, lowerbounds on communication complexity have uses in a variety of areas, including lowerbounds for parallel and VLSI computation, circuit lowerbounds, polyhedral theory, data structure lower-bounds, etc. We give a very rudimentary introduction to this area; an excellent and detailed treatment can be found in the book by Kushilevitz.prove lower bounds on communication complexity, there are numerous techniques (Kushilevitz & Nisan, ).
However, for the purposes of this paper, we will only need one: that of a fooling set. This technique ac-tually proves lower bounds even on nondeterministic communication complexity (and thus also on random-ized communication complexity).Communication Complexity is a computational model introduced by Yao in .
Since then, many papers have been written about it, more likely because of its consequences in applications, including VLSI theory, and because it is more tractable than computational complexity, it is easier to prove lower bounds. It also has a very simple.