Tourlakis Theory of Computation

1. Auflage 2012
ISBN: 978-1-118-31533-0
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 416 Seiten, E-Book

Learn the skills and acquire the intuition to assess thetheoretical limitations of computer programming
Offering an accessible approach to the topic, Theory ofComputation focuses on the metatheory of computing and thetheoretical boundaries between what various computational modelscan do and not do--from the most general model, the URM(Unbounded Register Machines), to the finite automaton. A wealth ofprogramming-like examples and easy-to-follow explanations build thegeneral theory gradually, which guides readers through the modelingand mathematical analysis of computational phenomena and providesinsights on what makes things tick and also what restrains theability of computational processes.
Recognizing the importance of acquired practical experience, thebook begins with the metatheory of general purpose computerprograms, using URMs as a straightforward, technology-independentmodel of modern high-level programming languages while alsoexploring the restrictions of the URM language. Once readers gainan understanding of computability theory--including theprimitive recursive functions--the author presents automataand languages, covering the regular and context-free languages aswell as the machines that recognize these languages. Severaladvanced topics such as reducibilities, the recursion theorem,complexity theory, and Cook's theorem are also discussed. Featuresof the book include:
* A review of basic discrete mathematics, covering logic andinduction while omitting specialized combinatorial topics
* A thorough development of the modeling and mathematical analysisof computational phenomena, providing a solid foundation ofun-computability
* The connection between un-computability and un-provability:Gödel's first incompleteness theorem
The book provides numerous examples of specific URMs as well asother programming languages including Loop Programs, FA(Deterministic Finite Automata), NFA (Nondeterministic FiniteAutomata), and PDA (Pushdown Automata). Exercises at the end ofeach chapter allow readers to test their comprehension of thepresented material, and an extensive bibliography suggestsresources for further study.
Assuming only a basic understanding of general computerprogramming and discrete mathematics, Theory of Computationserves as a valuable book for courses on theory of computation atthe upper-undergraduate level. The book also serves as an excellentresource for programmers and computing professionals wishing tounderstand the theoretical limitations of their craft.

Autoren/Hrsg.

Tourlakis, George

Inhaltsverzeichnis

Preface xi
1. Mathematical Foundations 1
1.1 Sets and Logic; Naïvely 1
1.2 Relations and Functions 40
1.3 Big and Small Infinite Sets; Diagonalization 52
1.4 Induction from a User's Perspective 61
1.5 Why Induction Ticks 68
1.6 Inductively Defined Sets
1.7 Recursive Definitions of Functions
1.8 Additional Exercises 85
2. Algorithms, Computable Functions and Computations91
2.1 A Theory of Computability 91
2.2 A programming Formalism for the Primitive RecursiveFunctions Function Class 147
2.3 URM Computations and their Arithmetization 141
2.4 A double-recursion that leads outside the PrimitiveRecursive Function Class
2.5 Semi-computable Relations: Unsolvability
2.6 The Iteration Theorem of Kleene 172
2.7 Diagonalization Revisited; Unsolvability via Reductions175
2.8 Productive and Creative Sets 209
2.9 The Recursion Theorem 214
2. 10 Completeness 217
2.11 Unprovability from Unsolvability 221
2.12 Additional Exercises 234
3. A Subset of the URM Language; FA and NFA 241
3.1 Deterministic Finite Automata and their Languages 243
3.2 Nondeterministic Finite Automata
3.3 Regular Expressions 266
3.4 Regular Grammars and Languages 277
3.5 Additional Exercises 287
4. Adding a stack of a NFA: Pushdown Automata
4.1 The PDA 294
4.2 PDA Computations 294
4.3 The PDA-acceptable Languages are the Context Free Languages305
4.4 Non-Context Free Languages; Another Pumping Lemma 312
4.5 Additional Exercise 322
5. Computational Complexity 325
5.1 Adding a second stack; Turning Machines 325
5.2 Axt, loop program, and Grzegorczyk hierarchies
5.3 Additional Exercised

Über Autor(innen)

George Tourlakis, PHD, is University Professor of ComputerScience and Engineering at York University in Toronto, Canada. Hehas published extensively in his areas of research interest, whichinclude calculational logic, modal logic, computability, andcomplexity theory. Dr. Tourlakis is the author of MathematicalLogic, also published by Wiley.