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Author : Dana S. Scott
Publisher : Unknown
Page : 24 pages
File Size : 51,6 Mb
Release : 1970
Category : Lattice theory
ISBN : 0902928015
Author : Arindama Singh
Publisher : Springer Science & Business Media
Page : 422 pages
File Size : 41,9 Mb
Release : 2009-04-30
Category : Computers
ISBN : 9781848824973
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.
Author : George Tourlakis
Publisher : John Wiley & Sons
Page : 410 pages
File Size : 51,5 Mb
Release : 2014-08-21
Category : Mathematics
ISBN : 9781118315354
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.
Author : Klaus Ambos-Spies,Benedikt Löwe,Wolfgang Merkle
Publisher : Springer Science & Business Media
Page : 524 pages
File Size : 54,7 Mb
Release : 2009-07-15
Category : Computers
ISBN : 9783642030734
This book constitutes the proceedings of the 5th Conference on Computability in Europe, CiE 2009, held in Heidelberg, Germany, during July 19-24, 2009. The 34 papers presented together with 17 invited lectures were carefully reviewed and selected from 100 submissions. The aims of the conference is to advance our theoretical understanding of what can and cannot be computed, by any means of computation. It is the largest international meeting focused on computability theoretic issues.
Author : 伊藤貴康
Publisher : 株式会社 三恵社
Page : 320 pages
File Size : 47,5 Mb
Release : 2010-10
Category : Electronic
ISBN : 4883617831
Author : Avi Wigderson
Publisher : Princeton University Press
Page : 434 pages
File Size : 48,8 Mb
Release : 2019-10-29
Category : Computers
ISBN : 9780691189130
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
Author : Michael Sipser
Publisher : Thomson/Course Technology
Page : 437 pages
File Size : 53,6 Mb
Release : 2006
Category : Computational complexity
ISBN : 0619217642
"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.
Author : Antoni Mazurkiewicz,A. Mazurkiewicz
Publisher : Springer Science & Business Media
Page : 630 pages
File Size : 46,7 Mb
Release : 1976-07
Category : Computers
ISBN : 3540078541
Author : Richard E. Ewing,Kenneth I. Gross,Clyde F. Martin
Publisher : Springer Science & Business Media
Page : 223 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461249849
This volume is the Proceedings of the symposium held at the University of Wyoming in August, 1985, to honor Gail Young on his seventieth birthday (which actually took place on October 3, 1985) and on the occasion of his retirement. Nothing can seem more natural to a mathematician in this country than to honor Gail Young. Gail embodies all the qualities that a mathematician should possess. He is an active and effective research mathematician, having written over sixty pa pers in topology, n-dimensional analysis, complex variables, and "miscellanea." He is an outstanding expositor, as his fine book Topology, written with J. G. Hocking (Addison Wesley, 1961), amply demonstrates. He has a superlative record in public office of outstanding, unstinting service to the mathematical community and to the cause of education. But what makes Gail unique and special is that throughout all aspects of his distinguished career, he has emphasized human values in everything he has done. In touching the lives of so many of us, he has advanced the entire profession. Deservedly, he has innumerable friends in the mathematical community, the academic community, and beyond.
Author : Jozef Gruska,Branislav Rovan,Juraj Wiedermann
Publisher : Springer Science & Business Media
Page : 810 pages
File Size : 54,9 Mb
Release : 1986-08-01
Category : Computers
ISBN : 3540167838
Author : A.B. Cremers,H.-P. Kriegel
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 48,9 Mb
Release : 1982-12
Category : Computers
ISBN : 3540119736
Author : J. Gruska
Publisher : Springer Science & Business Media
Page : 624 pages
File Size : 44,6 Mb
Release : 1977-08
Category : Computers
ISBN : 3540083537
Author : Javier Echeverria,Andoni Ibarra,Thomas Mormann
Publisher : Walter de Gruyter
Page : 440 pages
File Size : 44,7 Mb
Release : 2012-10-25
Category : Mathematics
ISBN : 9783110870299
Author : Olaf Owe,Martin Steffen,Jan Arne Telle
Publisher : Springer
Page : 373 pages
File Size : 42,9 Mb
Release : 2011-08-09
Category : Computers
ISBN : 9783642229534
This book constitutes the refereed proceedings of the 18th International Symposium Fundamentals of Computation Theory, FCT 2011, held in Oslo, Norway, in August 2011. The 28 revised full papers presented were carefully reviewed and selected from 78 submissions. FCT 2011 focused on algorithms, formal methods, and emerging fields, such as ad hoc, dynamic and evolving systems; algorithmic game theory; computational biology; foundations of cloud computing and ubiquitous systems; and quantum computation.
Author : Eric Lehman,F. Thomson Leighton,Albert R. Meyer
Publisher : Unknown
Page : 988 pages
File Size : 40,9 Mb
Release : 2017-03-08
Category : Business & Economics
ISBN : 9888407066
This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.