Complexity and Randomness in Group Theory

Complexity and Randomness in Group Theory
Author: Frédérique Bassino
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 412
Release: 2020-06-08
Genre: Mathematics
ISBN: 3110667525

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Groups and Model Theory

Groups and Model Theory
Author: Olga Kharlampovich
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 244
Release: 2021-05-10
Genre: Mathematics
ISBN: 3110719711

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This monograph provides an overview of developments in group theory motivated by model theory by key international researchers in the field. Topics covered include: stable groups and generalizations, model theory of nonabelian free groups and of rigid solvable groups, pseudofinite groups, approximate groups, topological dynamics, groups interpreting the arithmetic. The book is intended for mathematicians and graduate students in group theory and model theory. The book follows the course of the GAGTA (Geometric and Asymptotic Group Theory with Applications) conference series. The first book, "Complexity and Randomness in Group Theory. GAGTA book 1," can be found here: http://www.degruyter.com/books/978-3-11-066491-1 .

The Complexity Theory Companion

The Complexity Theory Companion
Author: Lane Hemaspaandra
Publisher: Springer Science & Business Media
Total Pages: 396
Release: 2001-12-01
Genre: Computers
ISBN: 9783540674191

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Here is an accessible, algorithmically oriented guide to some of the most interesting techniques of complexity theory. The book shows that simple algorithms are at the heart of complexity theory. The book is organized by technique rather than by topic. Each chapter focuses on one technique: what it is, and what results and applications it yields.

Kolmogorov Complexity and Algorithmic Randomness

Kolmogorov Complexity and Algorithmic Randomness
Author: A. Shen
Publisher: American Mathematical Soc.
Total Pages: 534
Release: 2017-11-02
Genre: Computers
ISBN: 1470431823

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Looking at a sequence of zeros and ones, we often feel that it is not random, that is, it is not plausible as an outcome of fair coin tossing. Why? The answer is provided by algorithmic information theory: because the sequence is compressible, that is, it has small complexity or, equivalently, can be produced by a short program. This idea, going back to Solomonoff, Kolmogorov, Chaitin, Levin, and others, is now the starting point of algorithmic information theory. The first part of this book is a textbook-style exposition of the basic notions of complexity and randomness; the second part covers some recent work done by participants of the “Kolmogorov seminar” in Moscow (started by Kolmogorov himself in the 1980s) and their colleagues. This book contains numerous exercises (embedded in the text) that will help readers to grasp the material.

Computational Complexity

Computational Complexity
Author: Sanjeev Arora
Publisher: Cambridge University Press
Total Pages: 609
Release: 2009-04-20
Genre: Computers
ISBN: 0521424267

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New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Computational and Statistical Group Theory

Computational and Statistical Group Theory
Author: Robert H. Gilman
Publisher: American Mathematical Soc.
Total Pages: 138
Release: 2002
Genre: Mathematics
ISBN: 0821831585

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This book gives a nice overview of the diversity of current trends in computational and statistical group theory. It presents the latest research and a number of specific topics, such as growth, black box groups, measures on groups, product replacement algorithms, quantum automata, and more. It includes contributions by speakers at AMS Special Sessions at The University of Nevada (Las Vegas) and the Stevens Institute of Technology (Hoboken, NJ). It is suitable for graduate students and research mathematicians interested in group theory.

Algorithmic Problems of Group Theory, Their Complexity, and Applications to Cryptography

Algorithmic Problems of Group Theory, Their Complexity, and Applications to Cryptography
Author: Delaram Kahrobaei
Publisher: American Mathematical Soc.
Total Pages: 136
Release: 2015-02-25
Genre: Business & Economics
ISBN: 0821898590

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This volume contains the proceedings of the AMS Special Session on Algorithmic Problems of Group Theory and Their Complexity, held January 9-10, 2013 in San Diego, CA and the AMS Special Session on Algorithmic Problems of Group Theory and Applications to Information Security, held April 6-7, 2013 at Boston College, Chestnut Hill, MA. Over the past few years the field of group-based cryptography has attracted attention from both group theorists and cryptographers. The new techniques inspired by algorithmic problems in non-commutative group theory and their complexity have offered promising ideas for developing new cryptographic protocols. The papers in this volume cover algorithmic group theory and applications to cryptography.

Complexity

Complexity
Author: M. Mitchell Waldrop
Publisher: Open Road Media
Total Pages: 492
Release: 2019-10-01
Genre: Science
ISBN: 150405914X

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“If you liked Chaos, you’ll love Complexity. Waldrop creates the most exciting intellectual adventure story of the year” (The Washington Post). In a rarified world of scientific research, a revolution has been brewing. Its activists are not anarchists, but rather Nobel Laureates in physics and economics and pony-tailed graduates, mathematicians, and computer scientists from all over the world. They have formed an iconoclastic think-tank and their radical idea is to create a new science: complexity. They want to know how a primordial soup of simple molecules managed to turn itself into the first living cell—and what the origin of life some four billion years ago can tell us about the process of technological innovation today. This book is their story—the story of how they have tried to forge what they like to call the science of the twenty-first century. “Lucidly shows physicists, biologists, computer scientists and economists swapping metaphors and reveling in the sense that epochal discoveries are just around the corner . . . [Waldrop] has a special talent for relaying the exhilaration of moments of intellectual insight.” —The New York Times Book Review “Where I enjoyed the book was when it dove into the actual question of complexity, talking about complex systems in economics, biology, genetics, computer modeling, and so on. Snippets of rare beauty here and there almost took your breath away.” —Medium “[Waldrop] provides a good grounding of what may indeed be the first flowering of a new science.” —Publishers Weekly

Non-commutative Cryptography and Complexity of Group-theoretic Problems

Non-commutative Cryptography and Complexity of Group-theoretic Problems
Author: Alexei G. Myasnikov
Publisher: American Mathematical Soc.
Total Pages: 402
Release: 2011
Genre: Computers
ISBN: 0821853600

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Examines the relationship between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It explores how non-commutative (infinite) groups can be used in public key cryptography. It also shows that there is remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory.