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This book provides algorithms and ideas for computationalists. Subjects treated include low-level algorithms, bit wizardry, combinatorial generation, fast transforms like the Fourier transform, and fast arithmetic for both real numbers and finite fields. Various optimization techniques are described and the actual performance of many given implementations is examined. The focus is on material that does not usually appear in textbooks on algorithms. The implementations are done in C++ and the GP language, written for POSIX-compliant platforms such as the Linux and BSD operating systems.
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Title: New Software Engineering Paradigm Based on Complexity Science: An Introduction to NSE Author: Jay Xiong Software has become the driving force for the development of all kinds of businesses, engineering, sciences and the global economy. But software itself is not well engineered, resulting in a total economic cost that is disturbingly high. Jay Xiong, a leading entrepreneur in the field of software engineering, realized many of the problems in software engineering stem from an incorrect paradigm. Software is a nonlinear complex system, but the existing software engineering paradigm is based on linear thinking, reductionism, and a superposition principle that the whole of a system is the sum of its parts. Xiong believes that the solution to software problems lies with complexity science, which is the science of studying complex systems with many interactive components. In New Software Engineering Paradigm Based on Complexity Science: An Introduction to NSE, Xiong details how complexity science can be a powerful means to solve all critical issues existing in today's software engineering through a two-step process. Step one discusses shifting the engineering paradigm to one based on nonlinear process and complexity science. For that, he posits the Nonlinear Software Engineering (NSE) paradigm. And step two applies complexity science to efficiently handle the problems of an individual complex system. This text introduces many new concepts, ideas, algorithms, models, methods, techniques and tools. It is aimed at anyone who has any relation to computer science and software engineering. The tools NSE_CLICK- an automatic acceptance testing platform for outsourcing (or internally developed) C/C++ products, and NSE_CLICK_J - an automatic acceptance testing platform for outsourcing (or internally developed) Java products are particularly designed for non-technical readers to view/review how the acceptance testing of a software product developed with NSE can be performed automatically, and how the product developed with NSE is truly maintainable at the customer site.
Complex analysis --- Computer science --- complexe analyse (wiskunde) --- informatica
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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 KarpâLipton. 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
Complex analysis --- Computer science --- toegepaste informatica --- complexe analyse (wiskunde)
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New discoveries about algorithms are leading scientists beyond the Church-Turing Thesis, which governs the "algorithmic universe" and asserts the conventionality of recursive algorithms. A new paradigm for computation, the super-recursive algorithm, offers promising prospects for algorithms of much greater computing power and efficiency. Super-Recursive Algorithms provides an accessible, focused examination of the theory of super-recursive algorithms and its ramifications for the computer industry, networks, artificial intelligence, embedded systems, and the Internet. The book demonstrates how these algorithms are more appropriate as mathematical models for modern computers, and how these algorithms present a better framework for computing methods in such areas as numerical analysis, array searching, and controlling and monitoring systems. In addition, a new practically-oriented perspective on the theory of algorithms, computation, and automata, as a whole, is developed. Problems of efficiency, software development, parallel and distributed processing, pervasive and emerging computation, computer architecture, machine learning, brain modeling, knowledge discovery, and intelligent systems are addressed. Topics and Features: * Encompasses and systematizes all main classes of super-recursive algorithms and the theory behind them * Describes the strengthening link between the theory of super-recursive algorithms and actual algorithms close to practical realization * Examines the theory's basis as a foundation for advancements in computing, information science, and related technologies * Encompasses and systematizes all main types of mathematical models of algorithms * Highlights how super-recursive algorithms pave the way for more advanced design, utilization, and maintenance of computers * Examines and restructures the existing variety of mathematical models of complexity of algorithms and computation, introducing new models * Possesses a comprehensive bibliography and index This clear exposition, motivated by numerous examples and illustrations, serves to develop a new paradigm for complex, high-performance computing based on both partial recursive functions and more inclusive recursive algorithms. Researchers and advanced students interested in theory of computation and algorithms will find the book an essential resource for an important new class of algorithms.
Complex analysis --- Computer science --- toegepaste informatica --- complexe analyse (wiskunde)
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When precise algorithmic solutions are difficult to compute, the use of approximation algorithms can help. Design and Analysis of Approximation Algorithms is a textbook for a graduate course in theoretical computer science taught globally in universities. It can also be used as a reference work for researchers in the area of design and analysis algorithms. There are few texts available for this standard course, and those that do exist mainly follow a problem-oriented format. This text follows a structured, technique-oriented presentation. Approximation algorithms are organized into chapters based on the design techniques for the algorithms, enabling the reader to study algorithms of the same nature with ease, and providing an improved understanding of the design and analysis techniques for approximation algorithms. Instructors benefit from this approach allowing for an easy way to present the ideas and techniques of algorithms with a unified approach.
Complex analysis --- Computer. Automation --- complexe analyse (wiskunde) --- automatisering
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Complex analysis --- Computer science --- toegepaste informatica --- complexe analyse (wiskunde)
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Complex analysis --- Computer science --- complexe analyse (wiskunde) --- informatica
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