Introduction to the Theory of Complexity

Introduction to the Theory of Complexity
Author: Daniel Pierre Bovet
Publisher: Prentice Hall PTR
Total Pages: 304
Release: 1994
Genre: Computers
ISBN:

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Using a balanced approach that is partly algorithmic and partly structuralist, this book systematically reviews the most significant results obtained in the study of computational complexity theory. Features over 120 worked examples, over 200 problems, and 400 figures.

Dealing with Complexity

Dealing with Complexity
Author: Robert L. Flood
Publisher: Springer Science & Business Media
Total Pages: 291
Release: 2013-03-09
Genre: Business & Economics
ISBN: 1475722354

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Contents 11. 2. 2. Four Main Areas of Dispute 247 11. 2. 3. Summary . . . 248 11. 3. Making Sense of the Issues . . 248 11. 3. 1. Introduction . . . . 248 11. 3. 2. The Scientific Approach 248 11. 3. 3. Science and Matters of Society . 249 11. 3. 4. Summary . 251 11. 4. Tying It All Together . . . . 251 11. 4. 1. Introduction . . . . 251 11. 4. 2. A Unifying Framework 251 11. 4. 3. Critical Systems Thinking 253 11. 4. 4. Summary 254 11. 5. Conclusion 254 Questions . . . 255 REFERENCES . . . . . . . . . . . . . . . . . . . 257 INDEX . . . . . . . . . . . . . . . . . . . . . . 267 Chapter One SYSTEMS Origin and Evolution, Terms and Concepts 1. 1. INTRODUCTION We start this book with Theme A (see Figure P. I in the Preface), which aims to develop an essential and fundamental understanding of systems science. So, what is systems science? When asked to explain what systems science is all about, many systems scientists are confronted with a rather daunting task. The discipline tends to be presented and understood in a fragmented way and very few people hold an overview understanding of the subject matter, while also having sufficient in-depth competence in many and broad-ranging subject areas where the ideas are used. Indeed, it was precisely this difficulty that identified the need for a comprehensive well-documented account such as is presented here in Dealing with Complexity.

Introduction to the Theory of Complex Systems

Introduction to the Theory of Complex Systems
Author: Stefan Thurner
Publisher:
Total Pages: 431
Release: 2018
Genre: Social sciences
ISBN: 9780191861062

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Complex systems are everywhere. Ecosystems, financial markets, traffic, the economy, the internet and social media are complex systems. This textbook summarizes our understanding of complex systems and the methodological progress made over the past 20 years in a clear, structured, and comprehensive way.

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.

An Introduction to Kolmogorov Complexity and Its Applications

An Introduction to Kolmogorov Complexity and Its Applications
Author: Ming Li
Publisher: Springer Science & Business Media
Total Pages: 655
Release: 2013-03-09
Genre: Mathematics
ISBN: 1475726066

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Briefly, we review the basic elements of computability theory and prob ability theory that are required. Finally, in order to place the subject in the appropriate historical and conceptual context we trace the main roots of Kolmogorov complexity. This way the stage is set for Chapters 2 and 3, where we introduce the notion of optimal effective descriptions of objects. The length of such a description (or the number of bits of information in it) is its Kolmogorov complexity. We treat all aspects of the elementary mathematical theory of Kolmogorov complexity. This body of knowledge may be called algo rithmic complexity theory. The theory of Martin-Lof tests for random ness of finite objects and infinite sequences is inextricably intertwined with the theory of Kolmogorov complexity and is completely treated. We also investigate the statistical properties of finite strings with high Kolmogorov complexity. Both of these topics are eminently useful in the applications part of the book. We also investigate the recursion theoretic properties of Kolmogorov complexity (relations with Godel's incompleteness result), and the Kolmogorov complexity version of infor mation theory, which we may call "algorithmic information theory" or "absolute information theory. " The treatment of algorithmic probability theory in Chapter 4 presup poses Sections 1. 6, 1. 11. 2, and Chapter 3 (at least Sections 3. 1 through 3. 4).

Complexity

Complexity
Author: John Henry Holland
Publisher: Oxford University Press, USA
Total Pages: 121
Release: 2014
Genre: History
ISBN: 0199662541

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In this very short introduction, John Holland presents an introduction to the science of complexity. Using examples from biology and economics, he shows how complexity science models the behaviour of complex systems.

Simply Complexity

Simply Complexity
Author: Neil Johnson
Publisher: Simon and Schuster
Total Pages: 256
Release: 2009-10-01
Genre: Science
ISBN: 1780740492

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The new branch of science which will reveal how to avoid the rush hour, overcome cancer, and find the perfect date What do traffic jams, stock market crashes, and wars have in common? They are all explained using complexity, an unsolved puzzle that many researchers believe is the key to predicting - and ultimately solving - everything from terrorist attacks and pandemic viruses right down to rush hour traffic congestion. Complexity is considered by many to be the single most important scientific development since general relativity and promises to make sense of no less than the very heart of the Universe. Using it, scientists can find order emerging from seemingly random interactions of all kinds, from something as simple as flipping coins through to more challenging problems such as predicting shopping habits, the patterns in modern jazz, and the growth of cancer tumours.

Theory of Computational Complexity

Theory of Computational Complexity
Author: Ding-Zhu Du
Publisher: John Wiley & Sons
Total Pages: 511
Release: 2011-10-24
Genre: Mathematics
ISBN: 1118031164

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A complete treatment of fundamentals and recent advances in complexity theory Complexity theory studies the inherent difficulties of solving algorithmic problems by digital computers. This comprehensive work discusses the major topics in complexity theory, including fundamental topics as well as recent breakthroughs not previously available in book form. Theory of Computational Complexity offers a thorough presentation of the fundamentals of complexity theory, including NP-completeness theory, the polynomial-time hierarchy, relativization, and the application to cryptography. It also examines the theory of nonuniform computational complexity, including the computational models of decision trees and Boolean circuits, and the notion of polynomial-time isomorphism. The theory of probabilistic complexity, which studies complexity issues related to randomized computation as well as interactive proof systems and probabilistically checkable proofs, is also covered. Extraordinary in both its breadth and depth, this volume: * Provides complete proofs of recent breakthroughs in complexity theory * Presents results in well-defined form with complete proofs and numerous exercises * Includes scores of graphs and figures to clarify difficult material An invaluable resource for researchers as well as an important guide for graduate and advanced undergraduate students, Theory of Computational Complexity is destined to become the standard reference in the field.

An Introduction to Complex Systems

An Introduction to Complex Systems
Author: Joe Tranquillo
Publisher: Springer
Total Pages: 405
Release: 2019-02-13
Genre: Technology & Engineering
ISBN: 3030025896

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This book explores the interdisciplinary field of complex systems theory. By the end of the book, readers will be able to understand terminology that is used in complex systems and how they are related to one another; see the patterns of complex systems in practical examples; map current topics, in a variety of fields, to complexity theory; and be able to read more advanced literature in the field. The book begins with basic systems concepts and moves on to how these simple rules can lead to complex behavior. The author then introduces non-linear systems, followed by pattern formation, and networks and information flow in systems. Later chapters cover the thermodynamics of complex systems, dynamical patterns that arise in networks, and how game theory can serve as a framework for decision making. The text is interspersed with both philosophical and quantitative arguments, and each chapter ends with questions and prompts that help readers make more connections. “The text provides a useful overview of complex systems, with enough detail to allow a reader unfamiliar with the topic to understand the basics. The book stands out for its comprehensiveness and approachability. It will be particularly useful as a text for introductory physics courses. Tranquillo’s strength is in delivering a vast amount of information in a succinct manner.... A reader can find information quickly and efficiently—that is, in my opinion, the book’s greatest value.” (Stefani Crabtree, Physics Today)

Complexity Theory and the Social Sciences

Complexity Theory and the Social Sciences
Author: David Byrne
Publisher: Routledge
Total Pages: 215
Release: 2002-01-04
Genre: Social Science
ISBN: 1134714742

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Chaos and complexity are the new buzz words in both science and contemporary society. The ideas they represent have enormous implications for the way we understand and engage with the world. Complexity Theory and the Social Sciences introduces students to the central ideas which surround the chaos/complexity theories. It discusses key concepts before using them as a way of investigating the nature of social research. By applying them to such familiar topics as urban studies, education and health, David Byrne allows readers new to the subject to appreciate the contribution which complexity theory can make to social research and to illuminating the crucial social issues of our day.