Author : Lane Hemaspaandra
Publisher : Springer Science & Business Media
Page : 396 pages
File Size : 42,26 MB
Release : 2001-12-01
Category : Computers
ISBN : 9783540674191
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 : Jon Norberg
Publisher : Columbia University Press
Page : 340 pages
File Size : 39,68 MB
Release : 2008-07-11
Category : Science
ISBN : 9780231508865
Complexity theory illuminates the many interactions between natural and social systems, providing a better understanding of the general principles that can help solve some of today's most pressing environmental issues. Complexity theory was developed from key ideas in economics, physics, biology, and the social sciences and contributes to important new concepts for approaching issues of environmental sustainability such as resilience, scaling, and networks. Complexity Theory for a Sustainable Future is a hands-on treatment of this exciting new body of work and its applications, bridging the gap between theoretical and applied perspectives in the management of complex adaptive systems. Focusing primarily on natural resource management and community-based conservation, the book features contributions by leading scholars in the field, many of whom are among the leaders of the Resilience Alliance. Theoreticians will find a valuable synthesis of new ideas on resilience, sustainability, asymmetries, information processing, scaling, and networks. Managers and policymakers will benefit from the application of these ideas to practical approaches and empirical studies linked to social-ecological systems. Chapters present new twists on such existing approaches as scenario planning, scaling analyses, and adaptive management, and the book concludes with recommendations on how to manage natural resources, how to involve stakeholders in the dynamics of a system, and how to explain the difficult topic of scale. A vital reference for an emerging discipline, this volume provides a clearer understanding of the conditions required for systems self-organization, since the capacity of any system to self-organize is crucial for its sustainability over time.
Author : Sanjeev Arora
Publisher : Cambridge University Press
Page : 609 pages
File Size : 20,17 MB
Release : 2009-04-20
Category : Computers
ISBN : 0521424267
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Author : Peter Bürgisser
Publisher : Springer Science & Business Media
Page : 630 pages
File Size : 34,27 MB
Release : 2013-03-14
Category : Mathematics
ISBN : 3662033380
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 : David Byrne
Publisher : Routledge
Page : 215 pages
File Size : 12,77 MB
Release : 2002-01-04
Category : Social Science
ISBN : 1134714742
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
Publisher : John Wiley & Sons
Page : 511 pages
File Size : 36,88 MB
Release : 2011-10-24
Category : Mathematics
ISBN : 1118031164
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 : Neil Johnson
Publisher : Simon and Schuster
Page : 256 pages
File Size : 13,68 MB
Release : 2009-10-01
Category : Science
ISBN : 1780740492
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 : K. Ko
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 21,81 MB
Release : 2012-12-06
Category : Computers
ISBN : 1468468022
Starting with Cook's pioneering work on NP-completeness in 1970, polynomial complexity theory, the study of polynomial-time com putability, has quickly emerged as the new foundation of algorithms. On the one hand, it bridges the gap between the abstract approach of recursive function theory and the concrete approach of analysis of algorithms. It extends the notions and tools of the theory of computability to provide a solid theoretical foundation for the study of computational complexity of practical problems. In addition, the theoretical studies of the notion of polynomial-time tractability some times also yield interesting new practical algorithms. A typical exam ple is the application of the ellipsoid algorithm to combinatorial op timization problems (see, for example, Lovasz [1986]). On the other hand, it has a strong influence on many different branches of mathe matics, including combinatorial optimization, graph theory, number theory and cryptography. As a consequence, many researchers have begun to re-examine various branches of classical mathematics from the complexity point of view. For a given nonconstructive existence theorem in classical mathematics, one would like to find a construc tive proof which admits a polynomial-time algorithm for the solution. One of the examples is the recent work on algorithmic theory of per mutation groups. In the area of numerical computation, there are also two tradi tionally independent approaches: recursive analysis and numerical analysis.
Author : J. Flum
Publisher : Springer Science & Business Media
Page : 494 pages
File Size : 45,5 MB
Release : 2006-05-01
Category : Computers
ISBN : 354029953X
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.
Author : Steven Homer
Publisher : Springer Science & Business Media
Page : 310 pages
File Size : 38,63 MB
Release : 2011-12-09
Category : Computers
ISBN : 1461406811
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
