Lower Bounds in Communication Complexity

Front Cover
Now Publishers Inc, 2009 - Computers - 152 pages
In the thirty years since its inception, communication complexity has become a vital area of theoretical computer science. 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 functions. It treats different variants of communication complexity, including randomized, quantum, and multiparty models. Many tools have been developed for this purpose from a diverse set of fields including linear algebra, Fourier analysis, and information theory. As is often the case in complexity theory, demonstrating a lower bound is usually the more difficult task. Lower Bounds in Communication Complexity describes a three-step approach for the development and application of these techniques. This approach can be applied in much the same way for different models, be they randomized, quantum, or multiparty. Lower Bounds in Communication Complexity is an ideal primer for anyone with an interest in this current and popular topic.
 

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Contents

Introduction
1
Deterministic Communication Complexity
13
Nondeterministic Communication Complexity
33
Randomized Communication Complexity
43
Quantum Communication Complexity
65
The Role of Duality in Proving Lower Bounds
77
Choosing a Witness
87
Multiparty Communication Complexity
109
Upper Bounds on Multiparty Communication
125
Acknowledgments
133
Copyright

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