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Author: Sanjeev Arora
Publisher: Cambridge University Press
ISBN: 0521424267
Category : Computers
Languages : en
Pages : 609
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Book Description
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Author: Sanjeev Arora
Publisher: Cambridge University Press
ISBN: 0521424267
Category : Computers
Languages : en
Pages : 609
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Book Description
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Author: Lane Hemaspaandra
Publisher: Springer Science & Business Media
ISBN: 9783540674191
Category : Computers
Languages : en
Pages : 396
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Book Description
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: Neil Johnson
Publisher: Simon and Schuster
ISBN: 1780740492
Category : Science
Languages : en
Pages : 256
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Book Description
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: Phil Hiver
Publisher: Multilingual Matters
ISBN: 1788925769
Category : Reference
Languages : en
Pages : 301
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Book Description
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: Steven Homer
Publisher: Springer Science & Business Media
ISBN: 1461406811
Category : Computers
Languages : en
Pages : 310
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Book Description
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
ISBN: 1134714742
Category : Social Science
Languages : en
Pages : 215
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Book Description
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: Peter Bürgisser
Publisher: Springer Science & Business Media
ISBN: 3662033380
Category : Mathematics
Languages : en
Pages : 630
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Book Description
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: Ingo Wegener
Publisher: Springer Science & Business Media
ISBN: 3540210458
Category : Computers
Languages : en
Pages : 307
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Book Description
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: Ding-Zhu Du
Publisher: John Wiley & Sons
ISBN: 1118031164
Category : Mathematics
Languages : en
Pages : 511
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Book Description
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: Lenore Blum
Publisher: Springer Science & Business Media
ISBN: 1461207010
Category : Computers
Languages : en
Pages : 456
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Book Description
The classical theory of computation has its origins in the work of Goedel, Turing, Church, and Kleene and has been an extraordinarily successful framework for theoretical computer science. The thesis of this book, however, is that it provides an inadequate foundation for modern scientific computation where most of the algorithms are real number algorithms. The goal of this book is to develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing. Along the way, the authors consider such fundamental problems as: * Is the Mandelbrot set decidable? * For simple quadratic maps, is the Julia set a halting set? * What is the real complexity of Newton's method? * Is there an algorithm for deciding the knapsack problem in a ploynomial number of steps? * Is the Hilbert Nullstellensatz intractable? * Is the problem of locating a real zero of a degree four polynomial intractable? * Is linear programming tractable over the reals? The book is divided into three parts: The first part provides an extensive introduction and then proves the fundamental NP-completeness theorems of Cook-Karp and their extensions to more general number fields as the real and complex numbers. The later parts of the book develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing.
