Models of Computation

An Introduction to Computability Theory

By: Maribel FernÃ¡ndez

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Paperback | 21 April 2009

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200 Pages

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17.78 x 24.13 x 1.27

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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.

Industry Reviews

From the reviews: "The focus of this relatively short book is on newer object-oriented and interaction-oriented models, including recent work in quantum computing and systems biology. ! the book is designed for advanced undergraduate and graduate students. ! Each chapter starts by clearly indicating what will be covered and ends with a series of exercises. ! the book as a whole is extremely well written. Definitions are clearly stated ! . Each model of computation is precisely defined, and the examples are clear and to the point." (K. Harrow, ACM Computing Reviews, September, 2009) "It is a pleasure to see a book which takes a different approach to computer theory. ! This short book can be used for a one-term course ! . A valuable primer for students of programming languages. Summing Up: Highly recommended. Upper-division undergraduates and graduate students." (P. Cull, Choice, Vol. 47 (3), November, 2009)

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You Can Find This Book In

Non-Fiction Mathematics Mathematical Foundation Mathematical Logic Computing & I.T.Computer Programming & Software Development Software Engineering Programming & Scripting Languages Algorithms & Data Structures Computer Science Human-Computer Interaction User Interface Design & Usability

Mathematical Theory of Computation Compilers & Interpreters

Introduction	p. 1
Models of computation	p. 3
Some non-computable functions	p. 4
Further reading	p. 7
Exercises	p. 7
Traditional Models of Computation
Automata and Turing Machines	p. 11
Formal languages and automata	p. 12
Finite automata	p. 13
Deterministic and non-deterministic automata	p. 16
The power of finite automata	p. 18
Push-down automata	p. 20
Turing machines	p. 23
Variants of Turing machines	p. 28
The universal Turing machine	p. 29
Imperative programming	p. 29
Further reading	p. 30
Exercises	p. 31
The Lambda Calculus	p. 33
Lambda-calculus: Syntax	p. 34
Computation	p. 38
Substitution	p. 40
Normal forms	p. 42
Properties of reductions	p. 43
Reduction strategies	p. 44
Arithmetic functions	p. 45
Booleans	p. 46
Recursion	p. 48
Functional programming	p. 49
Further reading	p. 50
Exercises	p. 50
Recursive Functions	p. 55
Primitive recursive functions	p. 56
Partial recursive functions	p. 61
Programming with functions	p. 63
Further reading	p. 67
Exercises	p. 67
Logic-Based Models of Computation	p. 69
The Herbrand universe	p. 69
Logic programs	p. 70
Answers	p. 73
Computing with logic programs	p. 76
Unification	p. 76
The Principle of Resolution	p. 79
Prolog and the logic programming paradigm	p. 84
Further reading	p. 86
Exercises	p. 86
Modern Models of Computation
Computing with Objects	p. 93
Object calculus: Syntax	p. 94
Reduction rules	p. 96
Computation power	p. 98
Object-oriented programming	p. 99
Combining objects and functions	p. 101
Further reading	p. 104
Exercises	p. 104
Interaction-Based Models of Computation	p. 107
The paradigm of interaction	p. 107
Numbers and arithmetic operations	p. 111
Turing completeness	p. 114
More examples: Lists	p. 115
Combinators for interaction nets	p. 117
Textual languages and strategies for interaction nets	p. 118
A textual interaction calculus	p. 120
Properties of the calculus	p. 125
Normal forms and strategies	p. 126
Extensions to model non-determinism	p. 127
Further reading	p. 129
Exercises	p. 130
Concurrency	p. 131
Specifying concurrent systems	p. 134
Simulation and bisimulation	p. 137
A language to write processes	p. 139
A language for communicating processes	p. 142
Another view of concurrency: The chemical metaphor	p. 147
Further reading	p. 147
Exercises	p. 148
Emergent Models of Computation	p. 151
Bio-computing	p. 152
Membrane calculi	p. 152
Protein interaction calculi	p. 153
Quantum computing	p. 154
Further reading	p. 157
Answers to Selected Exercises	p. 159
Bibliography	p. 179
Index	p. 183
Table of Contents provided by Ingram. All Rights Reserved.

Models of Computation

An Introduction to Computability Theory

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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