Boolean Function Complexity

doi:10.1017/CBO9780511526633

By considering the size of the logical network needed to perform a given computational task, the intrinsic difficulty of that task can be examined. Boolean function complexity, the combinatorial study of such networks, is a subject that started back in the 1950s and has today become one of the most challenging and vigorous areas of theoretical computer science. The papers in this book stem from the London Mathematical Society Symposium on Boolean Function Complexity held at Durham University in July 1990. The range of topics covered will be of interest to the newcomer to the field as well as the expert, and overall the papers are representative of the research presented at the Symposium. Anyone with an interest in Boolean Function complexity will find that this book is a necessary purchase.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Preface
pp vii-vii
- By Mike Paterson, University of Warwick Coventry, England
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List of Participants
pp viii-x
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Relationships Between Monotone and Non-Monotone Network Complexity
pp 1-24
- By Paul E. Dunne
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On Read-Once Boolean Functions
pp 25-34
- By Ilan Newman
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Boolean Function Complexity: a Lattice-Theoretic Perspective
pp 35-56
- By W. Meurig Beynon
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Monotone Complexity
pp 57-75
- By Michelangelo Grigni, Michael Sipser
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On Submodular Complexity Measures
pp 76-83
- By A.A. Razborov
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Why is Boolean Complexity Theory so Difficult?
pp 84-94
- By Leslie G. Valiant
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The Multiplicative Complexity of Boolean Quadratic Forms, a Survey
pp 95-108
- By Roland Mirwald, Claus P. Schnorr
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Some Problems Involving Razborov-Smolensky Polynomials
pp 109-128
- By David A. Mix Barrington
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Symmetry Functions in AC° can be Computed in Constant Depth with Very Small Size
pp 129-139
- By Ingo Wegener, Norbert Wurm, Sang-Zin Yi
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Boolean Complexity and Probabilistic Constructions
pp 140-164
- By Miklós Ajtai
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Networks Computing Boolean Functions for Multiple Input Values
pp 165-173
- By Dietmar Uhlig
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Optimal Carry Save Networks
pp 174-201
- By Michael S. Paterson, Nicholas Pippenger, Uri Zwick
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Boolean Function Complexity

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-vii

List of Participants
pp viii-x

Relationships Between Monotone and Non-Monotone Network Complexity
pp 1-24

On Read-Once Boolean Functions
pp 25-34

Boolean Function Complexity: a Lattice-Theoretic Perspective
pp 35-56

Monotone Complexity
pp 57-75

On Submodular Complexity Measures
pp 76-83

Why is Boolean Complexity Theory so Difficult?
pp 84-94

The Multiplicative Complexity of Boolean Quadratic Forms, a Survey
pp 95-108

Some Problems Involving Razborov-Smolensky Polynomials
pp 109-128

Symmetry Functions in AC° can be Computed in Constant Depth with Very Small Size
pp 129-139

Boolean Complexity and Probabilistic Constructions
pp 140-164

Networks Computing Boolean Functions for Multiple Input Values
pp 165-173

Optimal Carry Save Networks
pp 174-201

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Boolean Function Complexity

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