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This is the first comprehensive exposition of basic lower-bounds arguments, reviewing gems discovered in the past two decades right up to results from the last year. Covers a wide spectrum of models: circuits, formulas, communication protocols, branching programs.

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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.

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Part I Basics.- Part II Communication Complexity.- Part III Circuit Complexity.- Part IV Bounded Depth Circuits.- Part V Branching Programs.- Part VI Fragments of Proof Complexity.- A Epilog.- B Mathematical Background.- References.- Index.

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http://www.thi.informatik.uni-frankfurt.de/~jukna/

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