Complexity Of Computer Computations

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Complexity of Computer Computations

Author : R. Miller
Publisher : Springer Science & Business Media
ISBN 13 : 1468420011
Total Pages : 228 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Complexity of Computer Computations by : R. Miller

Download or read book Complexity of Computer Computations written by R. Miller and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Symposium on the Complexity of Computer Compu tations was held at the IBM Thomas J. Watson Research Center in Yorktown Heights, New York, March 20-22, 1972. These Proceedings contain all papers presented at the Symposium together with a transcript of the concluding panel discussion and a comprehensive bibliography of the field. The Symposium dealt with complexity studies closely re lated to how computations are actually performed on computers. Although this area of study has not yet found an appropriate or generally accepted name, the area is recognizable by the signif icant commonality in problems, approaches, and motivations. The area can be described and delineated by examples such as the following. (1) Determining lower bounds on the number of operations or steps required for computational solutions of specific problems such as matrix and polynomial calculations, sorting and other combinatorial problems, iterative com putations, solving equations, and computer resource allocation. (2) Developing improved algorithms for the solution of such problems which provide good upper bounds on the number of required operations, along with experimental and v vi PREFACE theoretical evidence concerning the efficiency and numer ical accuracy of those algorithms. (3) Studying the effects on the efficiency of computation brought about by variations in sequencing and the intro duction of parallelism.

Complexity of Computer Computations

Author : R. Miller
Publisher : Springer
ISBN 13 : 9780306307072
Total Pages : 225 pages
Book Rating : 4.3/5 (7 download)

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Book Synopsis Complexity of Computer Computations by : R. Miller

Download or read book Complexity of Computer Computations written by R. Miller and published by Springer. This book was released on 1972-08-01 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Symposium on the Complexity of Computer Compu tations was held at the IBM Thomas J. Watson Research Center in Yorktown Heights, New York, March 20-22, 1972. These Proceedings contain all papers presented at the Symposium together with a transcript of the concluding panel discussion and a comprehensive bibliography of the field. The Symposium dealt with complexity studies closely re lated to how computations are actually performed on computers. Although this area of study has not yet found an appropriate or generally accepted name, the area is recognizable by the signif icant commonality in problems, approaches, and motivations. The area can be described and delineated by examples such as the following. (1) Determining lower bounds on the number of operations or steps required for computational solutions of specific problems such as matrix and polynomial calculations, sorting and other combinatorial problems, iterative com putations, solving equations, and computer resource allocation. (2) Developing improved algorithms for the solution of such problems which provide good upper bounds on the number of required operations, along with experimental and v vi PREFACE theoretical evidence concerning the efficiency and numer ical accuracy of those algorithms. (3) Studying the effects on the efficiency of computation brought about by variations in sequencing and the intro duction of parallelism.

Complexity and Real Computation

Author : Lenore Blum
Publisher : Springer Science & Business Media
ISBN 13 : 1461207010
Total Pages : 456 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Complexity and Real Computation by : Lenore Blum

Download or read book Complexity and Real Computation written by Lenore Blum and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Computational Complexity

Author : Sanjeev Arora
Publisher : Cambridge University Press
ISBN 13 : 0521424267
Total Pages : 609 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Computational Complexity by : Sanjeev Arora

Download or read book Computational Complexity written by Sanjeev Arora and published by Cambridge University Press. This book was released on 2009-04-20 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Computational Complexity and Feasibility of Data Processing and Interval Computations

Author : V. Kreinovich
Publisher : Springer Science & Business Media
ISBN 13 : 1475727933
Total Pages : 460 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Computational Complexity and Feasibility of Data Processing and Interval Computations by : V. Kreinovich

Download or read book Computational Complexity and Feasibility of Data Processing and Interval Computations written by V. Kreinovich and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Targeted audience • Specialists in numerical computations, especially in numerical optimiza tion, who are interested in designing algorithms with automatie result ver ification, and who would therefore be interested in knowing how general their algorithms caIi in principle be. • Mathematicians and computer scientists who are interested in the theory 0/ computing and computational complexity, especially computational com plexity of numerical computations. • Students in applied mathematics and computer science who are interested in computational complexity of different numerical methods and in learning general techniques for estimating this computational complexity. The book is written with all explanations and definitions added, so that it can be used as a graduate level textbook. What this book .is about Data processing. In many real-life situations, we are interested in the value of a physical quantity y that is diflicult (or even impossible) to measure directly. For example, it is impossible to directly measure the amount of oil in an oil field or a distance to a star. Since we cannot measure such quantities directly, we measure them indirectly, by measuring some other quantities Xi and using the known relation between y and Xi'S to reconstruct y. The algorithm that transforms the results Xi of measuring Xi into an estimate fj for y is called data processing.

Computational Complexity of Counting and Sampling

Author : Istvan Miklos
Publisher : CRC Press
ISBN 13 : 1351971603
Total Pages : 292 pages
Book Rating : 4.3/5 (519 download)

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Book Synopsis Computational Complexity of Counting and Sampling by : Istvan Miklos

Download or read book Computational Complexity of Counting and Sampling written by Istvan Miklos and published by CRC Press. This book was released on 2019-02-21 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Complexity of Counting and Sampling provides readers with comprehensive and detailed coverage of the subject of computational complexity. It is primarily geared toward researchers in enumerative combinatorics, discrete mathematics, and theoretical computer science. The book covers the following topics: Counting and sampling problems that are solvable in polynomial running time, including holographic algorithms; #P-complete counting problems; and approximation algorithms for counting and sampling. First, it opens with the basics, such as the theoretical computer science background and dynamic programming algorithms. Later, the book expands its scope to focus on advanced topics, like stochastic approximations of counting discrete mathematical objects and holographic algorithms. After finishing the book, readers will agree that the subject is well covered, as the book starts with the basics and gradually explores the more complex aspects of the topic. Features: Each chapter includes exercises and solutions Ideally written for researchers and scientists Covers all aspects of the topic, beginning with a solid introduction, before shifting to computational complexity’s more advanced features, with a focus on counting and sampling

Complexity of Computer Computations

Author :
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (141 download)

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Download or read book Complexity of Computer Computations written by and published by . This book was released on 1972 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computability and Complexity

Author : Neil D. Jones
Publisher : MIT Press
ISBN 13 : 9780262100649
Total Pages : 494 pages
Book Rating : 4.1/5 (6 download)

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Book Synopsis Computability and Complexity by : Neil D. Jones

Download or read book Computability and Complexity written by Neil D. Jones and published by MIT Press. This book was released on 1997 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computability and complexity theory should be of central concern to practitioners as well as theorists. Unfortunately, however, the field is known for its impenetrability. Neil Jones's goal as an educator and author is to build a bridge between computability and complexity theory and other areas of computer science, especially programming. In a shift away from the Turing machine- and G�del number-oriented classical approaches, Jones uses concepts familiar from programming languages to make computability and complexity more accessible to computer scientists and more applicable to practical programming problems. According to Jones, the fields of computability and complexity theory, as well as programming languages and semantics, have a great deal to offer each other. Computability and complexity theory have a breadth, depth, and generality not often seen in programming languages. The programming language community, meanwhile, has a firm grasp of algorithm design, presentation, and implementation. In addition, programming languages sometimes provide computational models that are more realistic in certain crucial aspects than traditional models. New results in the book include a proof that constant time factors do matter for its programming-oriented model of computation. (In contrast, Turing machines have a counterintuitive "constant speedup" property: that almost any program can be made to run faster, by any amount. Its proof involves techniques irrelevant to practice.) Further results include simple characterizations in programming terms of the central complexity classes PTIME and LOGSPACE, and a new approach to complete problems for NLOGSPACE, PTIME, NPTIME, and PSPACE, uniformly based on Boolean programs. Foundations of Computing series

Mathematics and Computation

Author : Avi Wigderson
Publisher : Princeton University Press
ISBN 13 : 0691189137
Total Pages : 434 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Mathematics and Computation by : Avi Wigderson

Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Theory of Computational Complexity

Author : Ding-Zhu Du
Publisher : John Wiley & Sons
ISBN 13 : 1118031164
Total Pages : 511 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Theory of Computational Complexity by : Ding-Zhu Du

Download or read book Theory of Computational Complexity written by Ding-Zhu Du and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Complexity of Computer Computations

Author : R.E. Miller
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (841 download)

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Book Synopsis Complexity of Computer Computations by : R.E. Miller

Download or read book Complexity of Computer Computations written by R.E. Miller and published by . This book was released on 1972 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computational Error and Complexity in Science and Engineering

Author : Vangipuram Lakshmikantham
Publisher : Elsevier
ISBN 13 : 008045951X
Total Pages : 260 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Computational Error and Complexity in Science and Engineering by : Vangipuram Lakshmikantham

Download or read book Computational Error and Complexity in Science and Engineering written by Vangipuram Lakshmikantham and published by Elsevier. This book was released on 2005-03-04 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book “Computational Error and Complexity in Science and Engineering pervades all the science and engineering disciplines where computation occurs. Scientific and engineering computation happens to be the interface between the mathematical model/problem and the real world application. One needs to obtain good quality numerical values for any real-world implementation. Just mathematical quantities symbols are of no use to engineers/technologists. Computational complexity of the numerical method to solve the mathematical model, also computed along with the solution, on the other hand, will tell us how much computation/computational effort has been spent to achieve that quality of result. Anyone who wants the specified physical problem to be solved has every right to know the quality of the solution as well as the resources spent for the solution. The computed error as well as the complexity provide the scientific convincing answer to these questions. Specifically some of the disciplines in which the book will be readily useful are (i) Computational Mathematics, (ii) Applied Mathematics/Computational Engineering, Numerical and Computational Physics, Simulation and Modelling. Operations Research (both deterministic and stochastic), Computing Methodologies, Computer Applications, and Numerical Methods in Engineering. Key Features: - Describes precisely ready-to-use computational error and complexity - Includes simple easy-to-grasp examples wherever necessary. - Presents error and complexity in error-free, parallel, and probabilistic methods. - Discusses deterministic and probabilistic methods with error and complexity. - Points out the scope and limitation of mathematical error-bounds. - Provides a comprehensive up-to-date bibliography after each chapter. · Describes precisely ready-to-use computational error and complexity · Includes simple easy-to-grasp examples wherever necessary. · Presents error and complexity in error-free, parallel, and probabilistic methods. · Discusses deterministic and probabilistic methods with error and complexity. · Points out the scope and limitation of mathematical error-bounds. · Provides a comprehensive up-to-date bibliography after each chapter.

Computational Complexity

Author : Christos H. Papadimitriou
Publisher : Pearson
ISBN 13 :
Total Pages : 552 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Computational Complexity by : Christos H. Papadimitriou

Download or read book Computational Complexity written by Christos H. Papadimitriou and published by Pearson. This book was released on 1994 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first unified introduction and reference for the field of computational complexity. Virtually non-existent only 25 years ago, computational complexity has expanded tremendously and now comprises a major part of the researh activity in theoretical science.

Kolmogorov Complexity and Computational Complexity

Author : Osamu Watanabe
Publisher : Springer Science & Business Media
ISBN 13 : 364277735X
Total Pages : 111 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Kolmogorov Complexity and Computational Complexity by : Osamu Watanabe

Download or read book Kolmogorov Complexity and Computational Complexity written by Osamu Watanabe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical theory of computation has given rise to two important ap proaches to the informal notion of "complexity": Kolmogorov complexity, usu ally a complexity measure for a single object such as a string, a sequence etc., measures the amount of information necessary to describe the object. Compu tational complexity, usually a complexity measure for a set of objects, measures the compuational resources necessary to recognize or produce elements of the set. The relation between these two complexity measures has been considered for more than two decades, and may interesting and deep observations have been obtained. In March 1990, the Symposium on Theory and Application of Minimal Length Encoding was held at Stanford University as a part of the AAAI 1990 Spring Symposium Series. Some sessions of the symposium were dedicated to Kolmogorov complexity and its relations to the computational complexity the ory, and excellent expository talks were given there. Feeling that, due to the importance of the material, some way should be found to share these talks with researchers in the computer science community, I asked the speakers of those sessions to write survey papers based on their talks in the symposium. In response, five speakers from the sessions contributed the papers which appear in this book.

Complexity and Information

Author : J. F. Traub
Publisher : Cambridge University Press
ISBN 13 : 9780521485067
Total Pages : 152 pages
Book Rating : 4.4/5 (85 download)

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Book Synopsis Complexity and Information by : J. F. Traub

Download or read book Complexity and Information written by J. F. Traub and published by Cambridge University Press. This book was released on 1998-12-10 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The twin themes of computational complexity and information pervade this 1998 book. It starts with an introduction to the computational complexity of continuous mathematical models, that is, information-based complexity. This is then used to illustrate a variety of topics, including breaking the curse of dimensionality, complexity of path integration, solvability of ill-posed problems, the value of information in computation, assigning values to mathematical hypotheses, and new, improved methods for mathematical finance. The style is informal, and the goals are exposition, insight and motivation. A comprehensive bibliography is provided, to which readers are referred for precise statements of results and their proofs. As the first introductory book on the subject it will be invaluable as a guide to the area for the many students and researchers whose disciplines, ranging from physics to finance, are influenced by the computational complexity of continuous problems.

Algorithms and Complexity

Author : Gerard Meurant
Publisher : Elsevier
ISBN 13 : 0080933912
Total Pages : 1003 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Algorithms and Complexity by : Gerard Meurant

Download or read book Algorithms and Complexity written by Gerard Meurant and published by Elsevier. This book was released on 2014-06-28 with total page 1003 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first part presents chapters on models of computation, complexity theory, data structures, and efficient computation in many recognized sub-disciplines of Theoretical Computer Science.

Arithmetic Complexity of Computations

Author : Shmuel Winograd
Publisher : SIAM
ISBN 13 : 9781611970364
Total Pages : 96 pages
Book Rating : 4.9/5 (73 download)

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Book Synopsis Arithmetic Complexity of Computations by : Shmuel Winograd

Download or read book Arithmetic Complexity of Computations written by Shmuel Winograd and published by SIAM. This book was released on 1980-01-01 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on finding the minimum number of arithmetic operations needed to perform the computation and on finding a better algorithm when improvement is possible. The author concentrates on that class of problems concerned with computing a system of bilinear forms. Results that lead to applications in the area of signal processing are emphasized, since (1) even a modest reduction in the execution time of signal processing problems could have practical significance; (2) results in this area are relatively new and are scattered in journal articles; and (3) this emphasis indicates the flavor of complexity of computation.