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Author : Sanjeev Arora,Boaz Barak
Publisher : Cambridge University Press
Page : 609 pages
File Size : 48,8 Mb
Release : 2009-04-20
Category : Computers
ISBN : 9780521424264
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Author : Peter Bürgisser,Michael Clausen,Amin Shokrollahi
Publisher : Springer Science & Business Media
Page : 658 pages
File Size : 52,5 Mb
Release : 1996-12-16
Category : Mathematics
ISBN : 3540605827
The algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search for a precise and sufficiently general formalization of the notions of computability and algorithm. In the 1930s, a number of quite different concepts for this purpose were pro posed, such as Turing machines, WHILE-programs, recursive functions, Markov algorithms, and Thue systems. All these concepts turned out to be equivalent, a fact summarized in Church's thesis, which says that the resulting definitions form an adequate formalization of the intuitive notion of computability. This had and continues to have an enormous effect. First of all, with these notions it has been possible to prove that various problems are algorithmically unsolvable. Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem. Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under standing of the intrinsic computational difficulty of problems.
Author : Lane Hemaspaandra,Mitsunori Ogihara
Publisher : Springer Science & Business Media
Page : 396 pages
File Size : 49,8 Mb
Release : 2001-12-01
Category : Computers
ISBN : 3540674195
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.
Author : Göktuğ Morçöl
Publisher : Routledge
Page : 314 pages
File Size : 52,8 Mb
Release : 2013-05-02
Category : Political Science
ISBN : 9781136283468
Complexity theory has become popular in the natural and social sciences over the last few decades as a result of the advancements in our understanding of the complexities in natural and social phenomena. Concepts and methods of complexity theory have been applied by scholars of public affairs in North America and Europe, but a comprehensive framework for these applications is lacking. A Complexity Theory for Public Policy proposes a conceptual synthesis and sets a foundation for future developments and applications. In this book, Göktuğ Morçöl convincingly makes the case that complexity theory can help us understand better the self-organizational, emergent, and co-evolutionary characteristics of complex policy systems. In doing so, he discuss the epistemological implications of complexity theory and the methods complexity researchers use, and those methods they could use. As the complexity studies spread more around the world in the coming decades, the contents of this book will become appealing to larger audiences, particularly to scholars and graduate students in public affairs. The unique combination of synthesis and explanation of concepts and methods found in this book will serve as reference frames for future works.
Author : Neil Johnson
Publisher : Simon and Schuster
Page : 256 pages
File Size : 43,8 Mb
Release : 2009-10-01
Category : Science
ISBN : 9781780740492
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.
Author : Keith Morrison
Publisher : Routledge
Page : 230 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Education
ISBN : 9781135140533
Interest in complexity theory, a relation of chaos theory, has become well established in the business community in recent years. Complexity theory argues that systems are complex interactions of many parts which cannot be predicted by accepted linear equations. In this book, Keith Morrison introduces complexity theory to the world of education, drawing out its implications for school leadership. He suggests that schools are complex, nonlinear and unpredictable systems, and that this impacts significantly within them. As schools race to keep up with change and innovation, he suggests that it is possible to find order without control and to lead without coercion. Key areas: * schools and self-organisation * leadership for self-organisation * supporting emergence through the learning organisation * schools and their environments * communication * fitness landscapes This book will be of interest to headteachers and middle managers, and those on higher level courses in educational leadership and management.
Author : Steven Homer,Alan L. Selman
Publisher : Springer Science & Business Media
Page : 310 pages
File Size : 51,9 Mb
Release : 2011-12-09
Category : Computers
ISBN : 9781461406815
This revised and extensively expanded edition of Computability and Complexity Theory comprises essential materials that are core knowledge in the theory of computation. The book is self-contained, with a preliminary chapter describing key mathematical concepts and notations. Subsequent chapters move from the qualitative aspects of classical computability theory to the quantitative aspects of complexity theory. Dedicated chapters on undecidability, NP-completeness, and relative computability focus on the limitations of computability and the distinctions between feasible and intractable. Substantial new content in this edition includes: a chapter on nonuniformity studying Boolean circuits, advice classes and the important result of Karp─Lipton. a chapter studying properties of the fundamental probabilistic complexity classes a study of the alternating Turing machine and uniform circuit classes. an introduction of counting classes, proving the famous results of Valiant and Vazirani and of Toda a thorough treatment of the proof that IP is identical to PSPACE With its accessibility and well-devised organization, this text/reference is an excellent resource and guide for those looking to develop a solid grounding in the theory of computing. Beginning graduates, advanced undergraduates, and professionals involved in theoretical computer science, complexity theory, and computability will find the book an essential and practical learning tool. Topics and features: Concise, focused materials cover the most fundamental concepts and results in the field of modern complexity theory, including the theory of NP-completeness, NP-hardness, the polynomial hierarchy, and complete problems for other complexity classes Contains information that otherwise exists only in research literature and presents it in a unified, simplified manner Provides key mathematical background information, including sections on logic and number theory and algebra Supported by numerous exercises and supplementary problems for reinforcement and self-study purposes
Author : David Byrne
Publisher : Routledge
Page : 215 pages
File Size : 45,6 Mb
Release : 2002-01-04
Category : Social Science
ISBN : 9781134714742
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.
Author : Ding-Zhu Du,Ker-I Ko
Publisher : John Wiley & Sons
Page : 511 pages
File Size : 47,7 Mb
Release : 2011-10-24
Category : Mathematics
ISBN : 9781118031162
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.
Author : Phil Hiver,Ali H. Al-Hoorie
Publisher : Multilingual Matters
Page : 301 pages
File Size : 42,8 Mb
Release : 2019-12-06
Category : Reference
ISBN : 9781788925761
This book provides practical guidance on research methods and designs that can be applied to Complex Dynamic Systems Theory (CDST) research. It discusses the contribution of CDST to the field of applied linguistics, examines what this perspective entails for research and introduces practical methods and templates, both qualitative and quantitative, for how applied linguistics researchers can design and conduct research using the CDST framework. Introduced in the book are methods ranging from those in widespread use in social complexity, to more familiar methods in use throughout applied linguistics. All are inherently suited to studying both dynamic change in context and interconnectedness. This accessible introduction to CDST research will equip readers with the knowledge to ensure compatibility between empirical research designs and the theoretical tenets of complexity. It will be of value to researchers working in the areas of applied linguistics, language pedagogy and educational linguistics and to scholars and professionals with an interest in second/foreign language acquisition and complexity theory.
Author : Jamie Murray,Thomas Webb,Steven Wheatley
Publisher : Routledge
Page : 292 pages
File Size : 52,6 Mb
Release : 2018-07-17
Category : Law
ISBN : 9781351658171
This collection of essays explores the different ways the insights from complexity theory can be applied to law. Complexity theory – a variant of systems theory – views law as an emergent, complex, self-organising system comprised of an interactive network of actors and systems that operate with no overall guiding hand, giving rise to complex, collective behaviour in law communications and actions. Addressing such issues as the unpredictability of legal systems, the ability of legal systems to adapt to changes in society, the importance of context, and the nature of law, the essays look to the implications of a complexity theory analysis for the study of public policy and administrative law, international law and human rights, regulatory practices in business and finance, and the practice of law and legal ethics. These are areas where law, which craves certainty, encounters unending, irresolvable complexity. This collection shows the many ways complexity theory thinking can reshape and clarify our understanding of the various problems relating to the theory and practice of law.
Author : Ingo Wegener
Publisher : Springer Science & Business Media
Page : 307 pages
File Size : 53,6 Mb
Release : 2005-04-11
Category : Computers
ISBN : 9783540210450
Reflects recent developments in its emphasis on randomized and approximation algorithms and communication models All topics are considered from an algorithmic point of view stressing the implications for algorithm design
Author : Dexter C. Kozen
Publisher : Springer Science & Business Media
Page : 423 pages
File Size : 48,9 Mb
Release : 2006-09-19
Category : Computers
ISBN : 9781846284779
This textbook is uniquely written with dual purpose. It cover cores material in the foundations of computing for graduate students in computer science and also provides an introduction to some more advanced topics for those intending further study in the area. This innovative text focuses primarily on computational complexity theory: the classification of computational problems in terms of their inherent complexity. The book contains an invaluable collection of lectures for first-year graduates on the theory of computation. Topics and features include more than 40 lectures for first year graduate students, and a dozen homework sets and exercises.
Author : Nam P. Suh
Publisher : Oxford University Press
Page : 128 pages
File Size : 46,6 Mb
Release : 2005-02-24
Category : Technology & Engineering
ISBN : 9780199799077
Nam P. Suh focussed his axiomatic design theories on methods to understand and deal with complexity. Suh is a well-respected designer and researcher in the fields of manufacturing and composite materials. He is best known for his systems that aim to speed up and simplify the process of design for manufacturing. The 'axioms' in axiomatic design refer to a process to help engineers reduce design specifications down to their simplest components, so that the engineers can produce the simplest possible solution to a problem. Complexity, besides being a key area of burgeoning research in disciplines interested in complex systems and chaos theory (like computer science and physics), is a complicating factor in engineering design that many engineers find difficult to overcome. Suh's multidisciplinary exploration of complex systems is meant to eliminate much of the confusion and allow engineers to accommodate complexity within simple, elegant design solutions.
Author : J. Flum,M. Grohe
Publisher : Springer Science & Business Media
Page : 494 pages
File Size : 48,9 Mb
Release : 2006-05-01
Category : Computers
ISBN : 9783540299530
This book is a state-of-the-art introduction into both algorithmic techniques for fixed-parameter tractability and the structural theory of parameterized complexity classes. It presents detailed proofs of recent advanced results that have not appeared in book form before and replaces the earlier publication "Parameterized Complexity" by Downey and Fellows as the definitive book on this subject. The book will interest computer scientists, mathematicians and graduate students engaged with algorithms and problem complexity.