Complexity Theory Of Real Functions PDF Download
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| Author | : K. Ko |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 318 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 1468468022 |
Download Complexity Theory of Real Functions Book in PDF, ePub and Kindle
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 | : K. Ko |
| Publisher | : |
| Total Pages | : 324 |
| Release | : 1991-10-01 |
| Genre | : |
| ISBN | : 9781468468038 |
Download Complexity Theory of Real Functions Book in PDF, ePub and Kindle
| Author | : Lenore Blum |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 456 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 1461207010 |
Download Complexity and Real Computation Book in PDF, ePub and Kindle
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.
| Author | : Sanjeev Arora |
| Publisher | : Cambridge University Press |
| Total Pages | : 609 |
| Release | : 2009-04-20 |
| Genre | : Computers |
| ISBN | : 0521424267 |
Download Computational Complexity Book in PDF, ePub and Kindle
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
| Author | : Ding-Zhu Du |
| Publisher | : John Wiley & Sons |
| Total Pages | : 517 |
| Release | : 2014-06-30 |
| Genre | : Mathematics |
| ISBN | : 1118306082 |
Download Theory of Computational Complexity Book in PDF, ePub and Kindle
Praise for the First Edition "... complete, up-to-date coverage of computational complexity theory...the book promises to become the standard reference on computational complexity." —Zentralblatt MATH A thorough revision based on advances in the field of computational complexity and readers’ feedback, the Second Edition of Theory of Computational Complexity presents updates to the principles and applications essential to understanding modern computational complexity theory. The new edition continues to serve as a comprehensive resource on the use of software and computational approaches for solving algorithmic problems and the related difficulties that can be encountered. Maintaining extensive and detailed coverage, Theory of Computational Complexity, Second Edition, examines the theory and methods behind complexity theory, such as computational models, decision tree complexity, circuit complexity, and probabilistic complexity. The Second Edition also features recent developments on areas such as NP-completeness theory, as well as: A new combinatorial proof of the PCP theorem based on the notion of expander graphs, a research area in the field of computer science Additional exercises at varying levels of difficulty to further test comprehension of the presented material End-of-chapter literature reviews that summarize each topic and offer additional sources for further study Theory of Computational Complexity, Second Edition, is an excellent textbook for courses on computational theory and complexity at the graduate level. The book is also a useful reference for practitioners in the fields of computer science, engineering, and mathematics who utilize state-of-the-art software and computational methods to conduct research.
| Author | : Stasys Jukna |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 618 |
| Release | : 2012-01-06 |
| Genre | : Mathematics |
| ISBN | : 3642245080 |
Download Boolean Function Complexity Book in PDF, ePub and Kindle
Boolean circuit complexity is the combinatorics of computer science and involves many intriguing problems that are easy to state and explain, even for the layman. This book is a comprehensive description of basic lower bound arguments, covering many of the gems of this “complexity Waterloo” that have been discovered over the past several decades, right up to results from the last year or two. Many open problems, marked as Research Problems, are mentioned along the way. The problems are mainly of combinatorial flavor but their solutions could have great consequences in circuit complexity and computer science. The book will be of interest to graduate students and researchers in the fields of computer science and discrete mathematics.
| Author | : Lane Hemaspaandra |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 396 |
| Release | : 2001-12-01 |
| Genre | : Computers |
| ISBN | : 9783540674191 |
Download The Complexity Theory Companion Book in PDF, ePub and Kindle
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 | : Stanislaw Lojasiewicz |
| Publisher | : |
| Total Pages | : 248 |
| Release | : 1988-08-18 |
| Genre | : Mathematics |
| ISBN | : |
Download An Introduction to the Theory of Real Functions Book in PDF, ePub and Kindle
A concise, classical approach to the theory of real functions, set in the topological context of metric spaces. Newly translated by G. H. Lawden of the Univ. of Sussex and expanded from the earlier Polish editions to include remarks on the extension of finitely many additive functions to a measure, construction of a continuous, non-differential function of a general type, the Banach-Vitali theorem, and Stepanov's theorem. Prerequisites are set theory, topology, and calculus.
| Author | : A. C. M. van Rooij |
| Publisher | : Cambridge University Press |
| Total Pages | : 222 |
| Release | : 1982-03-25 |
| Genre | : Mathematics |
| ISBN | : 9780521239448 |
Download A Second Course on Real Functions Book in PDF, ePub and Kindle
When considering a mathematical theorem one ought not only to know how to prove it but also why and whether any given conditions are necessary. All too often little attention is paid to to this side of the theory and in writing this account of the theory of real functions the authors hope to rectify matters. They have put the classical theory of real functions in a modern setting and in so doing have made the mathematical reasoning rigorous and explored the theory in much greater depth than is customary. The subject matter is essentially the same as that of ordinary calculus course and the techniques used are elementary (no topology, measure theory or functional analysis). Thus anyone who is acquainted with elementary calculus and wishes to deepen their knowledge should read this.
| Author | : Jin-yi Cai |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 234 |
| Release | : 1993-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780821885758 |
Download Advances in Computational Complexity Theory Book in PDF, ePub and Kindle
* Recent papers on computational complexity theory * Contributions by some of the leading experts in the field This book will prove to be of lasting value in this fast-moving field as it provides expositions not found elsewhere. The book touches on some of the major topics in complexity theory and thus sheds light on this burgeoning area of research.
