Mathematical Theory Of Computation
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Mathematical Theory Of Computation
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Author : Zohar Manna
language : en
Publisher: Courier Dover Publications
Release Date : 2003
Mathematical Theory Of Computation written by Zohar Manna and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Computers categories.
With the objective of making into a science the art of verifying computer programs (debugging), the author addresses both practical and theoretical aspects of the process. A classic of sequential program verification, this volume has been translated into almost a dozen other languages and is much in demand among graduate and advanced undergraduate computer science students. Subjects include computability (with discussions of finite automata and Turing machines); predicate calculus (basic notions, natural deduction, and the resolution method); verification of programs (both flowchart and algol-like programs); flowchart schemas (basic notions, decision problems, formalization in predicate calculus, and translation programs); and the fixpoint theory of programs (functions and functionals, recursive programs, and verification programs). The treamtent is self-contained, and each chapter concludes with bibliographic remarks, references, and problems.
Mathematics And Computation
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Author : Avi Wigderson
language : en
Publisher: Princeton University Press
Release Date : 2019-10-29
Mathematics And Computation written by Avi Wigderson and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-29 with Computers categories.
From the winner of the Turing Award and the Abel Prize, 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
Artificial And Mathematical Theory Of Computation
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Author : Vladimir Lifschitz
language : en
Publisher: Academic Press
Release Date : 2012-12-02
Artificial And Mathematical Theory Of Computation written by Vladimir Lifschitz and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Computers categories.
Artificial and Mathematical Theory of Computation is a collection of papers that discusses the technical, historical, and philosophical problems related to artificial intelligence and the mathematical theory of computation. Papers cover the logical approach to artificial intelligence; knowledge representation and common sense reasoning; automated deduction; logic programming; nonmonotonic reasoning and circumscription. One paper suggests that the design of parallel programming languages will invariably become more sophisticated as human skill in programming and software developments improves to attain faster running programs. An example of metaprogramming to systems concerns the design and control of operations of factory devices, such as robots and numerically controlled machine tools. Metaprogramming involves two design aspects: that of the activity of a single device and that of the interaction with other devices. One paper cites the application of artificial intelligence pertaining to the project "proof checker for first-order logic" at the Stanford Artificial Intelligence Laboratory. Another paper explains why the bisection algorithm widely used in computer science does not work. This book can prove valuable to engineers and researchers of electrical, computer, and mechanical engineering, as well as, for computer programmers and designers of industrial processes.
Theory Of Computation
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Author : George Tourlakis
language : en
Publisher: John Wiley & Sons
Release Date : 2014-08-21
Theory Of Computation written by George Tourlakis 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 2014-08-21 with Mathematics categories.
Learn the skills and acquire the intuition to assess the theoretical limitations of computer programming Offering an accessible approach to the topic, Theory of Computation focuses on the metatheory of computing and the theoretical boundaries between what various computational models can do and not do—from the most general model, the URM (Unbounded Register Machines), to the finite automaton. A wealth of programming-like examples and easy-to-follow explanations build the general theory gradually, which guides readers through the modeling and mathematical analysis of computational phenomena and provides insights on what makes things tick and also what restrains the ability of computational processes. Recognizing the importance of acquired practical experience, the book begins with the metatheory of general purpose computer programs, using URMs as a straightforward, technology-independent model of modern high-level programming languages while also exploring the restrictions of the URM language. Once readers gain an understanding of computability theory—including the primitive recursive functions—the author presents automata and languages, covering the regular and context-free languages as well as the machines that recognize these languages. Several advanced topics such as reducibilities, the recursion theorem, complexity theory, and Cook's theorem are also discussed. Features of the book include: A review of basic discrete mathematics, covering logic and induction while omitting specialized combinatorial topics A thorough development of the modeling and mathematical analysis of computational phenomena, providing a solid foundation of un-computability The connection between un-computability and un-provability: Gödel's first incompleteness theorem The book provides numerous examples of specific URMs as well as other programming languages including Loop Programs, FA (Deterministic Finite Automata), NFA (Nondeterministic Finite Automata), and PDA (Pushdown Automata). Exercises at the end of each chapter allow readers to test their comprehension of the presented material, and an extensive bibliography suggests resources for further study. Assuming only a basic understanding of general computer programming and discrete mathematics, Theory of Computation serves as a valuable book for courses on theory of computation at the upper-undergraduate level. The book also serves as an excellent resource for programmers and computing professionals wishing to understand the theoretical limitations of their craft.
The Mathematical Theory Of Communication
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Author : Claude E Shannon
language : en
Publisher: University of Illinois Press
Release Date : 1998-09-01
The Mathematical Theory Of Communication written by Claude E Shannon and has been published by University of Illinois Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-01 with Language Arts & Disciplines categories.
Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.
Theory Of Computation
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Author : Dexter C. Kozen
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-08
Theory Of Computation written by Dexter C. Kozen 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 2006-05-08 with Computers categories.
This textbook is uniquely written with dual purpose. It cover cores material in the foundations of computing for graduate students in computer science and also provides an introduction to some more advanced topics for those intending further study in the area. This innovative text focuses primarily on computational complexity theory: the classification of computational problems in terms of their inherent complexity. The book contains an invaluable collection of lectures for first-year graduates on the theory of computation. Topics and features include more than 40 lectures for first year graduate students, and a dozen homework sets and exercises.
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.
Elements Of Computation Theory
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Author : Arindama Singh
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-30
Elements Of Computation Theory written by Arindama Singh 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 2009-04-30 with Computers categories.
The foundation of computer science is built upon the following questions: What is an algorithm? What can be computed and what cannot be computed? What does it mean for a function to be computable? How does computational power depend upon programming constructs? Which algorithms can be considered feasible? For more than 70 years, computer scientists are searching for answers to such qu- tions. Their ingenious techniques used in answering these questions form the theory of computation. Theory of computation deals with the most fundamental ideas of computer s- ence in an abstract but easily understood form. The notions and techniques employed are widely spread across various topics and are found in almost every branch of c- puter science. It has thus become more than a necessity to revisit the foundation, learn the techniques, and apply them with con?dence. Overview and Goals This book is about this solid, beautiful, and pervasive foundation of computer s- ence. It introduces the fundamental notions, models, techniques, and results that form the basic paradigms of computing. It gives an introduction to the concepts and mathematics that computer scientists of our day use to model, to argue about, and to predict the behavior of algorithms and computation. The topics chosen here have shown remarkable persistence over the years and are very much in current use.
Introduction To The Theory Of Computation
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Author : Michael Sipser
language : en
Publisher: Thomson/Course Technology
Release Date : 2006
Introduction To The Theory Of Computation written by Michael Sipser and has been published by Thomson/Course Technology this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Computational complexity categories.
"Intended as an upper-level undergraduate or introductory graduate text in computer science theory," this book lucidly covers the key concepts and theorems of the theory of computation. The presentation is remarkably clear; for example, the "proof idea," which offers the reader an intuitive feel for how the proof was constructed, accompanies many of the theorems and a proof. Introduction to the Theory of Computation covers the usual topics for this type of text plus it features a solid section on complexity theory--including an entire chapter on space complexity. The final chapter introduces more advanced topics, such as the discussion of complexity classes associated with probabilistic algorithms.
Mathematical Theory Of Optimization
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Author : Ding-Zhu Du
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-10-31
Mathematical Theory Of Optimization written by Ding-Zhu Du 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 2001-10-31 with Computers categories.
This book provides an introduction to the mathematical theory of optimization. It emphasizes the convergence theory of nonlinear optimization algorithms and applications of nonlinear optimization to combinatorial optimization. Mathematical Theory of Optimization includes recent developments in global convergence, the Powell conjecture, semidefinite programming, and relaxation techniques for designs of approximation solutions of combinatorial optimization problems.