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Ackermann function


Ackermann function

Ackermann function

Book search results for Ackermann function

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     Ackermann Function
Publisher: Book on Demand Pod
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     Ackermann function
Publisher: VSD
Author(s): Ronald Cohn Jesse Russell

High Quality Content by WIKIPEDIA articles! In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered 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 print-on-demand technology.

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     An Early History of Recursive Functions and Computability from Godel to Turing
Publisher: Docent Press
Author(s): Rod Adams

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 mid-1930'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 The book includes previously unpublished letters between the author and many of the key historical figures.

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     Introduction to the Ackermann Function: Definition and Properties, Extension, Inverse Function, Use as Benchmark, and More
Publisher: Webster's Digital Services
Author(s): Gaby Alez



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     Experimental Algorithms: 11th International Symposium, SEA 2012, Bordeaux, France, June 7-9, 2012. Proceedings (Lecture Notes in Computer Science / Programming and Software Engineering)
Publisher: Springer
Author(s):

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.

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     Schaum's Outline of Discrete Mathematics, 3rd Ed. (Schaum's Outline Series)
Publisher: McGraw-Hill
Author(s): Seymour Lipschutz, Marc Lipson

Confusing Textbooks? Missed Lectures? Not Enough Time?

Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

This Schaum's Outline gives you

  • Practice problems with full explanations that reinforce knowledge
  • Coverage of the most up-to-date developments in your course field
  • In-depth 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 time-and get your best test scores!

Schaum's Outlines-Problem Solved.



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     Discrete Mathematics with Applications
Publisher: Brooks Cole
Author(s): Susanna S. Epp

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 upper-level mathematics courses.

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     Classic Shell Scripting
Publisher: O'Reilly Media
Author(s): Arnold Robbins, Nelson H.F. Beebe

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 administrators-a 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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     A New Kind of Science
Publisher: Wolfram Media
Author(s): Stephen Wolfram

This long-awaited 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 experiments---illustrated in the book by striking computer graphics---Wolfram 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 non-scientists alike to participate in what promises to be a major intellectual revolution.

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     Theory of Computation
Publisher: Wiley
Author(s): George Tourlakis

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: G�del'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.



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     Models of Computation: An Introduction to Computability Theory (Undergraduate Topics in Computer Science)
Publisher: Springer
Author(s): Maribel Fernandez

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 in-depth 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 Lambda-Calculus; - Logic-based computation models. and the second part covers object-oriented and interaction-based 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.

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     Rewriting, Computation and Proof: Essays Dedicated to Jean-Pierre Jouannaud on the Occasion of his 60th Birthday (Lecture Notes in Computer Science / Theoretical Computer Science and General Issues)
Publisher: Springer
Author(s):

Jean-Pierre Jouannaud has played a leading role in the field of rewriting and its technology. This Festschrift volume, published to honor him on his 60th Birthday, includes 13 refereed papers by leading researchers, current and former colleagues. The papers are grouped in thematic sections on Rewriting Foundations, Proof and Computation, and a final section entitled Towards Safety and Security.

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     Computability and Complexity: From a Programming Perspective (Foundations of Computing)
Publisher: The MIT Press
Author(s): Neil Deaton Jones

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 G�del number-oriented 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 programming-oriented 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



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     Automata and Computability (Undergraduate Texts in Computer Science)
Publisher: Springer
Author(s): Dexter C. Kozen

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 context-free languages. In the remaining chapters, Turing machines are introduced and the book culminates in analyses of effective computability, decidability, and G�del's incompleteness theorems. Students who already have some experience with elementary discrete mathematics will find this a well-paced first course, and a number of supplementary chapters introduce more advanced concepts.



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     Models and Computability (London Mathematical Society Lecture Note Series)
Publisher: Cambridge University Press
Author(s):

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, post-graduate researchers, and the informed and interested nonspecialist.

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     Computability Theory (Chapman Hall/CRC Mathematics Series)
Publisher: Chapman and Hall/CRC
Author(s): S. Barry Cooper

Computability theory originated with the seminal work of G�del, Church, Turing, Kleene and Post in the 1930s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications. Recent work in computability theory has focused on Turing definability and promises to have far-reaching mathematical, scientific, and philosophical consequences.

Written by a leading researcher, Computability Theory provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level.

The book includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science.

Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable and lively way.

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     Data Structures and Algorithms in Java
Publisher: Cengage Learning Asia
Author(s): Adam Drozdek

Using the Java programming language, Drozdek highlights three important aspects of data structures and algorithms. First, the book places special emphasis on the connection between data structures and their algorithms, including an analysis of the algorithms complexity. Second, the book presents data structures in the context of object-oriented program design. Finally, the book closely examines data structure implementation.

Overall, this practical and theoretical book provides students with a solid foundation in data structures for future courses and work in design, implementation, testing, and maintenance of virtually any software system.

KEY FEATURES
(1) Updated! This new edition contains updated Java code to reflect the inclusion of generic classes in Java 5.
(2) Updated! Tables that list methods from java.util packages have been updated to reflect modifications and additions introduced in Java 5 and Java 6.
(3) New! Coverage of two new sorting methods.
(4) New! Coverage of a new hashing technique.
(5) Case Studies. Most chapters include a case study that illustrates a complete context in which algorithms and data structures can be used.
(6) Java code examples. Brief examples of Java code are included to illustrate the practical importance of data structures.
(7) Theoretical analysis. Presentation of algorithms are integrated with analyses of efficiency.
(8) Recursion topics. Clarifies recursion topics through their presentation in context of the run-time stack.

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     Data Structures and Algorithms
Publisher: Addison Wesley
Author(s): Alfred V. Aho, Jeffrey D. Ullman, John E. Hopcroft

The authors' treatment of data structures in Data Structures and Algorithms is unified by an informal notion of "abstract data types," allowing readers to compare different implementations of the same concept. Algorithm design techniques are also stressed and basic algorithm analysis is covered. Most of the programs are written in Pascal.

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     The Art of Computer Systems Performance Analysis: Techniques for Experimental Design, Measurement, Simulation, and Modeling
Publisher: Wiley
Author(s): R. K. Jain

The Art of Computer Systems Performance Analysis "At last, a welcome and needed text for computer professionals who require practical, ready-to-apply techniques for performance analysis. Highly recommended!" -Dr. Leonard Kleinrock University of California, Los Angeles "An entirely refreshing text which has just the right mixture of theory and real world practice. The book is ideal for both classroom instruction and self-study." -Dr. Raymond L. Pickholtz President, IEEE Communications Society "An extraordinarily comprehensive treatment of both theoretical and practical issues." -Dr. Jeffrey P. Buzen Internationally recognized performance analysis expert ". it is the most thorough book available to date" -Dr. Erol Gelenbe Universit? Ren? Descartes, Paris ". an extraordinary book.. A worthy addition to the bookshelf of any practicing computer or communications engineer" -Dr. Vinton G. Cer??? Chairman, ACM SIGCOMM "This is an unusual object, a textbook that one wants to sit down and peruse. The prose is clear and fluent, but more important, it is witty." -Allison Mankin The Mitre Washington Networking Center Newsletter

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     Algorithm Design: Foundations, Analysis, and Internet Examples
Publisher: Wiley
Author(s): Michael T. Goodrich, Roberto Tamassia

Michael Goodrich and Roberto Tamassia, authors of the successful, Data Structures and Algorithms in Java, 2/e, have written Algorithm Engineering, a text designed to provide a comprehensive introduction to the design, implementation and analysis of computer algorithms and data structures from a modern perspective. This book offers theoretical analysis techniques as well as algorithmic design patterns and experimental methods for the engineering of algorithms.
Market: Computer Scientists; Programmers.

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