Elements of the Theory of Computation

by ;
Edition: 2nd
Format: Paperback
Pub. Date: 1997-08-07
Publisher(s): Pearson
List Price: $186.65

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Summary

Lewis and Papadimitriou present this long awaited Second Edition of their best-selling theory of computation. The authors are well-known for their clear presentation that makes the material accessible to a a broad audience and requires no special previous mathematical experience.In this new edition, the authors incorporate a somewhat more informal, friendly writing style to present both classical and contemporary theories of computation. Algorithms, complexity analysis, and algorithmic ideas are introduced informally in Chapter 1, and are pursued throughout the book. Each section is followed by problems.

Table of Contents

Preface to the First Edition vii(2)
Preface to the Second Edition ix
Introduction 1(4)
1 Sets, Relations, and Languages
5(50)
1.1 Sets
5(4)
1.2 Relations and functions
9(4)
1.3 Special types of binary relations
13(7)
1.4 Finite and infinite sets
20(3)
1.5 Three fundamental proof techniques
23(7)
1.6 Closures and algorithms
30(12)
1.7 Alphabets and languages
42(5)
1.8 Finite representations of languages
47(5)
References
52(3)
2 Finite Automata
55(58)
2.1 Deterministic finite automata
55(8)
2.2 Nondeterministic finite automata
63(12)
2.3 Finite automata and regular expressions
75(11)
2.4 Languages that are and are not regular
86(6)
2.5 State minimization
92(10)
2.6 Algorithmic aspects of finite automata
102(8)
References
110(3)
3 Context-free Languages
113(66)
3.1 Context-free grammars
113(9)
3.2 Parse trees
122(8)
3.3 Pushdown automata
130(6)
3.4 Pushdown automata and context-free grammars
136(7)
3.5 Languages that are and are not context-free
143(7)
3.6 Algorithms for context-free grammars
150(8)
3.7 Determinism and parsing
158(17)
References
175(4)
4 Turing machines
179(66)
4.1 The definition of a Turing machine
179(15)
4.2 Computing with Turing machines
194(6)
4.3 Extensions of Turing machines
200(10)
4.4 Random access Turing machines
210(11)
4.5 Nondeterministic Turing machines
221(6)
4.6 Grammars
227(6)
4.7 Numerical functions
233(10)
References
243(2)
5 Undecidability
245(30)
5.1 The Church-Turing thesis
245(2)
5.2 Universal Turing machines
247(4)
5.3 The halting problem
251(3)
5.4 Unsolvable problems about Turing machines
254(4)
5.5 Unsolvable problems about grammars
258(4)
5.6 An unsolvable tiling problem
262(5)
5.7 Properties of recursive languages
267(5)
References
272(3)
6 Computational Complexity
275(26)
6.1 The class P
275(3)
6.2 Problems, problems
278(10)
6.3 Boolean satisfiability
288(4)
6.4 The class (NP)
292(7)
References
299(2)
7 NP-completeness
301(52)
7.1 Polynomial-time reductions
301(8)
7.2 Cook's Theorem
309(8)
7.3 More (NP)-complete problems
317(16)
7.4 Coping with (NP)-completeness
333(17)
References
350(3)
Index 353

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