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Introduction To The Theory Of Computation,9780534950972
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Introduction To The Theory Of Computation

by
Edition:
2nd
ISBN13:

9780534950972

ISBN10:
0534950973
Format:
Hardcover
Pub. Date:
2/15/2005
Publisher(s):
Cengage Learning
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Summary

This highly anticipated revision builds upon the strengths of the previous edition. Sipser's candid, crystal-clear style allows students at every level to understand and enjoy this field. His innovative "proof idea" sections explain profound concepts in plain English. The new edition incorporates many improvements students and professors have suggested over the years, and offers updated, classroom-tested problem sets at the end of each chapter.

Author Biography

Michael Sipser is the head of the Mathematics Department. He enjoys teaching and pondering the many mysteries of complexity theory

Table of Contents

Preface to the First Edition xi
To the student xi
To the educator xii
The first edition xiii
Feedback to the author xiii
Acknowledgments xiv
Preface to the Second Edition xvii
Introduction
1(28)
Automata, Computability, and Complexity
1(2)
Complexity theory
2(1)
Computability theory
2(1)
Automata theory
3(1)
Mathematical Notions and Terminology
3(14)
Sets
3(3)
Sequences and tuples
6(1)
Functions and relations
7(3)
Graphs
10(3)
Strings and languages
13(1)
Boolean logic
14(2)
Summary of mathematical terms
16(1)
Definitions, Theorems, and Proofs
17(4)
Finding proofs
17(4)
Types of Proof
21(8)
Proof by construction
21(1)
Proof by contradiction
21(1)
Proof by induction
22(3)
Exercises, Problems, and Solutions
25(4)
Part One: Automata and Languages
29(106)
Regular Languages
31(68)
Finite Automata
31(16)
Formal definition of a finite automaton
35(2)
Examples of finite automata
37(3)
Formal definition of computation
40(1)
Designing finite automata
41(3)
The regular operations
44(3)
Nondeterminism
47(16)
Formal definition of a nondeterministic finite automaton
53(1)
Equivalence of NFAs and DFAs
54(4)
Closure under the regular operations
58(5)
Regular Expressions
63(14)
Formal definition of a regular expression
64(2)
Equivalence with finite automata
66(11)
Nonregular Languages
77(22)
The pumping lemma for regular languages
77(5)
Exercises, Problems, and Solutions
82(17)
Context-Free Languages
99(36)
Context-free Grammars
100(9)
Formal definition of a context-free grammar
102(1)
Examples of context-free grammars
103(1)
Designing context-free grammars
104(1)
Ambiguity
105(1)
Chomsky normal form
106(3)
Pushdown Automata
109(14)
Formal definition of a pushdown automaton
111(1)
Examples of pushdown automata
112(3)
Equivalence with context-free grammars
115(8)
Non-context-free Languages
123(12)
The pumping lemma for context-free languages
123(5)
Exercises, Problems, and Solutions
128(7)
Part Two: Computability Theory
135(110)
The Church-Turing Thesis
137(28)
Turing Machines
137(11)
Formal definition of a Turing machine
139(3)
Examples of Turing machines
142(6)
Variants of Turing Machines
148(6)
Multitape Turing machines
148(2)
Nondeterministic Turing machines
150(2)
Enumerators
152(1)
Equivalence with other models
153(1)
The Definition of Algorithm
154(11)
Hilbert's problems
154(2)
Terminology for describing Turing machines
156(3)
Exercises, Problems, and Solutions
159(6)
Decidability
165(22)
Decidable Languages
166(7)
Decidable problems concerning regular languages
166(4)
Decidable problems concerning context-free languages
170(3)
The Halting Problem
173(14)
The diagonalization method
174(5)
The halting problem is undecidable
179(2)
A Turing-unrecognizable language
181(1)
Exercises, Problems, and Solutions
182(5)
Reducibility
187(30)
Undecidable Problems from Language Theory
188(11)
Reductions via computation histories
192(7)
A Simple Undecidable Problem
199(7)
Mapping Reducibility
206(11)
Computable functions
206(1)
Formal definition of mapping reducibility
207(4)
Exercises, Problems, and Solutions
211(6)
Advanced Topics in Computability Theory
217(28)
The Recursion Theorem
217(7)
Self-reference
218(3)
Terminology for the recursion theorem
221(1)
Applications
222(2)
Decidability of logical theories
224(8)
A decidable theory
227(2)
An undecidable theory
229(3)
Turing Reducibility
232(1)
A Definition of Information
233(12)
Minimal length descriptions
234(4)
Optimality of the definition
238(1)
Incompressible strings and randomness
239(3)
Exercises, Problems, and Solutions
242(3)
Part Three: Complexity Theory
245(170)
Time Complexity
247(56)
Measuring Complexity
247(9)
Big-O and small-o notation
248(3)
Analyzing algorithms
251(3)
Complexity relationships among models
254(2)
The Class P
256(8)
Polynomial time
256(2)
Examples of problems in P
258(6)
The Class NP
264(7)
Examples of problems in NP
267(2)
The P versus NP question
269(2)
NP-completeness
271(12)
Polynomial time reducibility
272(4)
Definition of NP-completeness
276(1)
The Cook-Levin Theorem
276(7)
Additional NP-complete Problems
283(20)
The vertex cover problem
284(2)
The Hamiltonian path problem
286(5)
The subset sum problem
291(3)
Exercises, Problems, and Solutions
294(9)
Space Complexity
303(32)
Savitch's Theorem
305(3)
The Class PSPACE
308(1)
PSPACE-completeness
309(11)
The TQBF problem
310(3)
Winning strategies for games
313(2)
Generalized geography
315(5)
The Classes L and NL
320(3)
NL-completeness
323(3)
Searching in graphs
325(1)
NL equals coNL
326(9)
Exercises, Problems, and Solutions
328(7)
Intractability
335(30)
Hierarchy Theorems
336(12)
Exponential space completeness
343(5)
Relativization
348(3)
Limits of the diagonalization method
349(2)
Circuit Complexity
351(14)
Exercises, Problems, and Solutions
360(5)
Advanced topics in complexity theory
365(50)
Approximation Algorithms
365(3)
Probabilistic Algorithms
368(12)
The class BPP
368(3)
Primality
371(5)
Read-once branching programs
376(4)
Alternation
380(7)
Alternative time and space
381(5)
The Polynomial time hierarchy
386(1)
Interactive Proof Systems
387(12)
Graph nonisomorphism
387(1)
Definition of the model
388(2)
IP = PSPACE
390(9)
Parallel Computation
399(6)
Uniform Boolean circuits
400(2)
The class NC
402(2)
P-completeness
404(1)
Cryptography
405(10)
Secret keys
405(2)
Public-key cryptosystems
407(1)
One-way functions
407(2)
Trapdoor functions
409(2)
Exercises, Problems, and Solutions
411(4)
Selected Bibliography 415(6)
Index 421


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