Numbers Information And Complexity
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An Introduction To Kolmogorov Complexity And Its Applications
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Author : Ming Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
An Introduction To Kolmogorov Complexity And Its Applications written by Ming Li and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Briefly, we review the basic elements of computability theory and prob ability theory that are required. Finally, in order to place the subject in the appropriate historical and conceptual context we trace the main roots of Kolmogorov complexity. This way the stage is set for Chapters 2 and 3, where we introduce the notion of optimal effective descriptions of objects. The length of such a description (or the number of bits of information in it) is its Kolmogorov complexity. We treat all aspects of the elementary mathematical theory of Kolmogorov complexity. This body of knowledge may be called algo rithmic complexity theory. The theory of Martin-Lof tests for random ness of finite objects and infinite sequences is inextricably intertwined with the theory of Kolmogorov complexity and is completely treated. We also investigate the statistical properties of finite strings with high Kolmogorov complexity. Both of these topics are eminently useful in the applications part of the book. We also investigate the recursion theoretic properties of Kolmogorov complexity (relations with Godel's incompleteness result), and the Kolmogorov complexity version of infor mation theory, which we may call "algorithmic information theory" or "absolute information theory. " The treatment of algorithmic probability theory in Chapter 4 presup poses Sections 1. 6, 1. 11. 2, and Chapter 3 (at least Sections 3. 1 through 3. 4).
Computational Complexity
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Author : Sanjeev Arora
language : en
Publisher: Cambridge University Press
Release Date : 2009-04-20
Computational Complexity written by Sanjeev Arora and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-20 with Computers categories.
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Numbers Information And Complexity
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Author : Ingo Althöfer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Numbers Information And Complexity written by Ingo Althöfer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Technology & Engineering categories.
Numbers, Information and Complexity is a collection of about 50 articles in honour of Rudolf Ahlswede. His main areas of research are represented in the three sections, `Numbers and Combinations', `Information Theory (Channels and Networks, Combinatorial and Algebraic Coding, Cryptology, with the related fields Data Compression, Entropy Theory, Symbolic Dynamics, Probability and Statistics)', and `Complexity'. Special attention was paid to the interplay between the fields. Surveys on topics of current interest are included as well as new research results. The book features surveys on Combinatorics about topics such as intersection theorems, which are not yet covered in textbooks, several contributions by leading experts in data compression, and relations to Natural Sciences are discussed.
Algorithms And Complexity In Mathematics Epistemology And Science
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Author : Nicolas Fillion
language : en
Publisher: Springer
Release Date : 2019-02-07
Algorithms And Complexity In Mathematics Epistemology And Science written by Nicolas Fillion and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-07 with Mathematics categories.
ACMES (Algorithms and Complexity in Mathematics, Epistemology, and Science) is a multidisciplinary conference series that focuses on epistemological and mathematical issues relating to computation in modern science. This volume includes a selection of papers presented at the 2015 and 2016 conferences held at Western University that provide an interdisciplinary outlook on modern applied mathematics that draws from theory and practice, and situates it in proper context. These papers come from leading mathematicians, computational scientists, and philosophers of science, and cover a broad collection of mathematical and philosophical topics, including numerical analysis and its underlying philosophy, computer algebra, reliability and uncertainty quantification, computation and complexity theory, combinatorics, error analysis, perturbation theory, experimental mathematics, scientific epistemology, and foundations of mathematics. By bringing together contributions from researchers who approach the mathematical sciences from different perspectives, the volume will further readers' understanding of the multifaceted role of mathematics in modern science, informed by the state of the art in mathematics, scientific computing, and current modeling techniques.
Lower Bounds In Communication Complexity
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Author : Troy Lee
language : en
Publisher: Now Publishers Inc
Release Date : 2009
Lower Bounds In Communication Complexity written by Troy Lee and has been published by Now Publishers Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Computers categories.
The communication complexity of a function f(x, y) measures the number of bits that two players, one who knows x and the other who knows y, must exchange to determine the value f(x, y). Communication complexity is a fundamental measure of complexity of functions. Lower bounds on this measure lead to lower bounds on many other measures of computational complexity. This monograph surveys lower bounds in the field of communication complexity. Our focus is on lower bounds that work by first representing the communication complexity measure in Euclidean space. That is to say, the first step in these lower bound techniques is to find a geometric complexity measure, such as rank or trace norm, that serves as a lower bound to the underlying communication complexity measure. Lower bounds on this geometric complexity measure are then found using algebraic and geometric tools.
Software Measurement And Estimation
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Author : Linda M. Laird
language : en
Publisher: John Wiley & Sons
Release Date : 2006-06-05
Software Measurement And Estimation written by Linda M. Laird and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-05 with Computers categories.
An effective, quantitative approach for estimating and managing software projects How many people do I need? When will the quality be good enough for commercial sale? Can this really be done in two weeks? Rather than relying on instinct, the authors of Software Measurement and Estimation offer a new, tested approach that includes the quantitative tools, data, and knowledge needed to make sound estimations. The text begins with the foundations of measurement, identifies the appropriate metrics, and then focuses on techniques and tools for estimating the effort needed to reach a given level of quality and performance for a software project. All the factors that impact estimations are thoroughly examined, giving you the tools needed to regularly adjust and improve your estimations to complete a project on time, within budget, and at an expected level of quality. This text includes several features that have proven to be successful in making the material accessible and easy to master: * Simple, straightforward style and logical presentation and organization enables you to build a solid foundation of theory and techniques to tackle complex estimations * Examples, provided throughout the text, illustrate how to use theory to solve real-world problems * Projects, included in each chapter, enable you to apply your newfound knowledge and skills * Techniques for effective communication of quantitative data help you convey your findings and recommendations to peers and management Software Measurement and Estimation: A Practical Approach allows practicing software engineers and managers to better estimate, manage, and effectively communicate the plans and progress of their software projects. With its classroom-tested features, this is an excellent textbook for advanced undergraduate-level and graduate students in computer science and software engineering. An Instructor Support FTP site is available from the Wiley editorial department.
Counting Sampling And Integrating Algorithms And Complexity
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Author : Mark Jerrum
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Counting Sampling And Integrating Algorithms And Complexity written by Mark Jerrum and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The subject of these notes is counting and related topics, viewed from a computational perspective. A major theme of the book is the idea of accumulating information about a set of combinatorial structures by performing a random walk on those structures. These notes will be of value not only to teachers of postgraduate courses on these topics, but also to established researchers. For the first time this body of knowledge has been brought together in a single volume.
Human Factors Guidelines For Road Systems
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Author : John L. Campbell
language : en
Publisher: Transportation Research Board
Release Date : 2010
Human Factors Guidelines For Road Systems written by John L. Campbell and has been published by Transportation Research Board this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Technology & Engineering categories.
NCHRP report 600 explores human factors principles and findings for consideration by highway designers and traffic engineers. The report is designed to help the nonexpert in human factors to consider more effectively the roadway user's capabilities and limitations in the design and operation of highway facilities.
Algebraic Complexity Theory
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Author : Peter Bürgisser
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Algebraic Complexity Theory written by Peter Bürgisser and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
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.
Theory And Practice Of Contrast
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Author : Mariusz Stanowski
language : en
Publisher: CRC Press
Release Date : 2021-06-09
Theory And Practice Of Contrast written by Mariusz Stanowski and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-09 with Science categories.
The book Theory and Practice of Contrast completes, corrects and integrates the foundations of science and humanities, which include: theory of art, philosophy (aesthetics, epistemology, ontology, axiology), cognitive science, theory of information, theory of complexity and physics. Through the integration of these distant disciplines, many unresolved issues in contemporary science have been clarified or better understood, among others: defining impact (contrast) and using this definition in different fields of knowledge; understanding what beauty/art is and what our aesthetic preferences depend on; deeper understanding of what complexity and information are in essence, and providing their general definitions. Complexity means integration, value and goodness - concepts that seem to be neglected today. The book also has a high degree of integration/complexity, although each chapter introduces a new issue. The last chapter: "Binary Model of the Universe" draws attention to the need for including in physics the analysis of our mind and the resulting new possibilities, which include the mentioned (digital) model of the universe. Despite the difficult issues raised here, this study is written in accessible language and may be interesting not only for scientists and academics.