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Foundations Of Computation Theory
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Book Synopsis Foundations of Computation by : Carol Critchlow
Download or read book Foundations of Computation written by Carol Critchlow and published by . This book was released on 2011 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Computation is a free textbook for a one-semester course in theoretical computer science. It has been used for several years in a course at Hobart and William Smith Colleges. The course has no prerequisites other than introductory computer programming. The first half of the course covers material on logic, sets, and functions that would often be taught in a course in discrete mathematics. The second part covers material on automata, formal languages and grammar that would ordinarily be encountered in an upper level course in theoretical computer science.
Book Synopsis Foundations of Computation Theory by : M. Karpinski
Download or read book Foundations of Computation Theory written by M. Karpinski and published by Lecture Notes in Computer Science. This book was released on 1983-08 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theory of Computation by : Dexter C. Kozen
Download or read book Theory of Computation written by Dexter C. Kozen and published by Springer Science & Business Media. This book was released on 2006-09-19 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Foundations of Computability Theory by : Borut Robič
Download or read book The Foundations of Computability Theory written by Borut Robič and published by Springer. This book was released on 2015-09-14 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational crisis of mathematics in the early twentieth century, and formalism; in Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability; in Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy. This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science.
Book Synopsis Computability, Complexity, and Languages by : Martin Davis
Download or read book Computability, Complexity, and Languages written by Martin Davis and published by Academic Press. This book was released on 1994-02-03 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory text covers the key areas of computer science, including recursive function theory, formal languages, and automata. Additions to the second edition include: extended exercise sets, which vary in difficulty; expanded section on recursion theory; new chapters on program verification and logic programming; updated references and examples throughout.
Book Synopsis Elements of Computation Theory by : Arindama Singh
Download or read book Elements of Computation Theory written by Arindama Singh and published by Springer Science & Business Media. This book was released on 2009-04-30 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to the Theory of Computation by : Michael Sipser
Download or read book Introduction to the Theory of Computation written by Michael Sipser and published by Thomson/Course Technology. This book was released on 2006 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Book Synopsis Introduction to the Theory of Computation by : Michael Sipser
Download or read book Introduction to the Theory of Computation written by Michael Sipser and published by Cengage Learning. This book was released on 2012-06-27 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now you can clearly present even the most complex computational theory topics to your students with Sipser’s distinct, market-leading INTRODUCTION TO THE THEORY OF COMPUTATION, 3E. The number one choice for today’s computational theory course, this highly anticipated revision retains the unmatched clarity and thorough coverage that make it a leading text for upper-level undergraduate and introductory graduate students. This edition continues author Michael Sipser’s well-known, approachable style with timely revisions, additional exercises, and more memorable examples in key areas. A new first-of-its-kind theoretical treatment of deterministic context-free languages is ideal for a better understanding of parsing and LR(k) grammars. This edition’s refined presentation ensures a trusted accuracy and clarity that make the challenging study of computational theory accessible and intuitive to students while maintaining the subject’s rigor and formalism. Readers gain a solid understanding of the fundamental mathematical properties of computer hardware, software, and applications with a blend of practical and philosophical coverage and mathematical treatments, including advanced theorems and proofs. INTRODUCTION TO THE THEORY OF COMPUTATION, 3E’s comprehensive coverage makes this an ideal ongoing reference tool for those studying theoretical computing. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Book Synopsis Foundations of Computation Theory by : M. Karpinski
Download or read book Foundations of Computation Theory written by M. Karpinski and published by . This book was released on 2014-01-15 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theory of Computation by : George Tourlakis
Download or read book Theory of Computation written by George Tourlakis and published by John Wiley & Sons. This book was released on 2014-08-21 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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
Book Synopsis Foundations of Computer Science by : Alfred V. Aho
Download or read book Foundations of Computer Science written by Alfred V. Aho and published by W. H. Freeman. This book was released on 1994-10-15 with total page 786 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algorithmic Number Theory: Efficient algorithms by : Eric Bach
Download or read book Algorithmic Number Theory: Efficient algorithms written by Eric Bach and published by MIT Press. This book was released on 1996 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 1.
Book Synopsis On the Theoretical Foundations of Computer Science. An Introductory Essay by : Gabriel Kabanda
Download or read book On the Theoretical Foundations of Computer Science. An Introductory Essay written by Gabriel Kabanda and published by GRIN Verlag. This book was released on 2019-07-12 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Essay from the year 2019 in the subject Computer Science - Theory, grade: 4.00, Atlantic International University, language: English, abstract: The paper presents an analytical exposition, critical context and integrative conclusion on the discussion on the meaning, significance and potential applications of theoretical foundations of computer science with respect to Algorithms Design and Analysis, Complexity Theory, Turing Machines, Finite Automata, Cryptography and Machine Learning. An algorithm is any well-defined computational procedure that takes some value or sets of values as input and produces some values or sets of values as output. A Turing machine consists of a finite program, called the finite control, capable of manipulating a linear list of cells, called the tape, using one access pointer, called the head. Cellular automata is an array of finite state machines (inter-related). A universal Turing machine U is a Turing machine that can imitate the behavior of any other Turing machine T. Automata are a particularly simple, but useful, model of computation which were were initially proposed as a simple model for the behavior of neurons. A model of computation is a mathematical abstraction of computers which is used by computer scientists to perform a rigorous study of computation. An automaton with a finite number of states is called a Finite Automaton (FA) or Finite State Machine (FSM). The Church-Turing Thesis states that the Turing machine is equivalent in computational ability to any general mathematical device for computation, including digital computers. The important themes in Theoretical Computer Science (TCS) are efficiency, impossibility results, approximation, central role of randomness, and reductions (NP-completeness and other intractability results).
Book Synopsis The Foundations of Computability Theory by : Borut Robič
Download or read book The Foundations of Computability Theory written by Borut Robič and published by Springer Nature. This book was released on 2020-11-13 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational crisis of mathematics in the early twentieth century, and formalism. In Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability. In Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy. Finally, in the new Part IV the author revisits the computability (Church-Turing) thesis in greater detail. He offers a systematic and detailed account of its origins, evolution, and meaning, he describes more powerful, modern versions of the thesis, and he discusses recent speculative proposals for new computing paradigms such as hypercomputing. This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science. This new edition is completely revised, with almost one hundred pages of new material. In particular the author applied more up-to-date, more consistent terminology, and he addressed some notational redundancies and minor errors. He developed a glossary relating to computability theory, expanded the bibliographic references with new entries, and added the new part described above and other new sections.
Book Synopsis Foundations of Computation Theory by : Akeo Adachi
Download or read book Foundations of Computation Theory written by Akeo Adachi and published by IOS Press. This book was released on 1990 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
