Ackermann function
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Product Group: Book
Manufacturer: VSD
High Quality Content by WIKIPEDIA articles! In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliestdiscovered examples of a total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive. This book was created using printondemand technology.
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Product Group: Book
Manufacturer: Docent Press
An Early History of Recursive Functions and Computability traces the development of recursive functions from their origins in the late nineteenth century, when recursion was first used as a method of defining simple arithmetic functions, up to the mid1930's, when the class of general recursive functions was introduced by Godel, formalized by Kleene and used by Church in his thesis. The book explains how the proposal given in Church's 1936 paper, now known as Church's thesis, first arose and concludes with the consideration of another class of functions, the Turing computable functions, that were specially created to be equivalent to the class of effectively calculable functions. The book includes previously unpublished letters between the author and many of the key historical figures.
[More details on An Early History of Recursive Functions and Computability from Godel to Turing ]

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Product Group: Book
Manufacturer: Springer
This textbook provides undergraduate students with an introduction to the basic theoretical models of computability, and develops some of the model's rich and varied structure. The first part of the book is devoted to finite automata and their properties. Pushdown automata provide a broader class of models and enable the analysis of contextfree languages. In the remaining chapters, Turing machines are introduced and the book culminates in analyses of effective computability, decidability, and Gödel's incompleteness theorems. Students who already have some experience with elementary discrete mathematics will find this a wellpaced first course, and a number of supplementary chapters introduce more advanced concepts.
[More details on Automata and Computability (Undergraduate Texts in Computer Science) ]

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Product Group: Book
Manufacturer: Springer
This book constitutes the refereed proceedings of the 11th International Symposium on Experimental Algorithms, SEA 2012, held Bordeaux, France, in June 2012. The 31 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 64 submissions and present current research in the area of design, analysis, and experimental evaluation and engineering of algorithms, as well as in various aspects of computational optimization and its applications.
[More details on Experimental Algorithms: 11th International Symposium, SEA 2012, Bordeaux, France, June 79, 2012. Proceedings (Lecture Notes in Computer Science / Programming and Software Engineering) ]

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Product Group: Book
Manufacturer: McGrawHill
Confusing Textbooks? Missed Lectures? Not Enough Time?
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This Schaum's Outline gives you
 Practice problems with full explanations that reinforce knowledge
 Coverage of the most uptodate developments in your course field
 Indepth review of practices and applications
Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study timeand get your best test scores!
Schaum's OutlinesProblem Solved.
[More details on Schaum's Outline of Discrete Mathematics, 3rd Ed. (Schaum's Outline Series) ]

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Product Group: Book
Manufacturer: Brooks Cole
Susanna Epp's DISCRETE MATHEMATICS WITH APPLICATIONS, FOURTH EDITION provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography, and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. Overall, Epp's emphasis on reasoning provides students with a strong foundation for computer science and upperlevel mathematics courses.
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Product Group: Book
Manufacturer: O'Reilly Media
Shell scripting skills never go out of style. It's the shell that unlocks the real potential of Unix. Shell scripting is essential for Unix users and system administratorsa way to quickly harness and customize the full power of any Unix system. With shell scripts, you can combine the fundamental Unix text and file processing commands to crunch data and automate repetitive tasks. But beneath this simple promise lies a treacherous ocean of variations in Unix commands and standards. Classic Shell Scripting is written to help you reliably navigate these tricky waters.
Writing shell scripts requires more than just a knowledge of the shell language, it also requires familiarity with the individual Unix programs: why each one is there, how to use them by themselves, and in combination with the other programs. The authors are intimately familiar with the tips and tricks that can be used to create excellent scripts, as well as the traps that can make your best effort a bad shell script. With Classic Shell Scripting you'll avoid hours of wasted effort. You'll learn not only write useful shell scripts, but how to do it properly and portably.
The ability to program and customize the shell quickly, reliably, and portably to get the best out of any individual system is an important skill for anyone operating and maintaining Unix or Linux systems. Classic Shell Scripting gives you everything you need to master these essential skills.
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Product Group: Book
Manufacturer: Wolfram Media
This longawaited work from one of the world's most respected scientists presents a series of dramatic discoveries never before made public. Starting from a collection of simple computer experimentsillustrated in the book by striking computer graphicsWolfram shows how their unexpected results force a whole new way of looking at the operation of our universe.
Wolfram uses his approach to tackle a remarkable array of fundamental problems in science: from the origin of the Second Law of thermodynamics, to the development of complexity in biology, the computational limitations of mathematics, the possibility of a truly fundamental theory of physics, and the interplay between free will and determinism.
Written with exceptional clarity, and illustrated by more than a thousand original pictures, this seminal book allows scientists and nonscientists alike to participate in what promises to be a major intellectual revolution.
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Product Group: Book
Manufacturer: Wiley
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 programminglike examples and easytofollow 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, technologyindependent model of modern highlevel 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 contextfree 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 uncomputability

The connection between uncomputability and unprovability: 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 upperundergraduate level. The book also serves as an excellent resource for programmers and computing professionals wishing to understand the theoretical limitations of their craft.
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Product Group: Book
Manufacturer: Springer
A Concise Introduction to Computation Models and Computability Theory provides an introduction to the essential concepts in computability, using several models of computation, from the standard Turing Machines and Recursive Functions, to the modern computation models inspired by quantum physics. An indepth analysis of the basic concepts underlying each model of computation is provided. Divided into two parts, the first highlights the traditional computation models used in the first studies on computability:  Automata and Turing Machines;  Recursive functions and the LambdaCalculus;  Logicbased computation models. and the second part covers objectoriented and interactionbased models. There is also a chapter on concurrency, and a final chapter on emergent computation models inspired by quantum mechanics. At the end of each chapter there is a discussion on the use of computation models in the design of programming languages.
[More details on Models of Computation: An Introduction to Computability Theory (Undergraduate Topics in Computer Science) ]

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Product Group: Book
Manufacturer: The MIT Press
Computability and complexity theory should be of central concern to practitioners as well as theorists. Unfortunately, however, the field is known for its impenetrability. Neil Jones's goal as an educator and author is to build a bridge between computability and complexity theory and other areas of computer science, especially programming. In a shift away from the Turing machine and Gödel numberoriented classical approaches, Jones uses concepts familiar from programming languages to make computability and complexity more accessible to computer scientists and more applicable to practical programming problems.According to Jones, the fields of computability and complexity theory, as well as programming languages and semantics, have a great deal to offer each other. Computability and complexity theory have a breadth, depth, and generality not often seen in programming languages. The programming language community, meanwhile, has a firm grasp of algorithm design, presentation, and implementation. In addition, programming languages sometimes provide computational models that are more realistic in certain crucial aspects than traditional models.New results in the book include a proof that constant time factors do matter for its programmingoriented model of computation. (In contrast, Turing machines have a counterintuitive "constant speedup" property: that almost any program can be made to run faster, by any amount. Its proof involves techniques irrelevant to practice.) Further results include simple characterizations in programming terms of the central complexity classes PTIME and LOGSPACE, and a new approach to complete problems for NLOGSPACE, PTIME, NPTIME, and PSPACE, uniformly based on Boolean programs.Foundations of Computing series
[More details on Computability and Complexity: From a Programming Perspective (Foundations of Computing) ]

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Product Group: Book
Manufacturer: Cambridge University Press
Together, Models and Computability and its sister volume Sets and Proofs provide readers with a comprehensive guide to the current state of mathematical logic. All the authors are leaders in their fields and are drawn from the invited speakers at "Logic Colloquium '97" (the major international meeting of the Association of Symbolic Logic). It is expected that the breadth and timeliness of these two volumes will prove an invaluable and unique resource for specialists, postgraduate researchers, and the informed and interested nonspecialist.
[More details on Models and Computability (London Mathematical Society Lecture Note Series) ]

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