Rent 9781133187790 | Introduction to the Theory of Computation

Summary Table of Contents Author Biography

Gain a clear understanding of even the most complex, highly theoretical computational theory topics in the approachable presentation found only in the market-leading INTRODUCTION TO THE THEORY OF COMPUTATION, 3E. The number one choice for today's computational theory course, this revision continues the book's well-know, approachable style with timely revisions, additional practice, and more memorable examples in key areas. A new first-of-its-kind theoretical treatment of deterministic context-free languages is ideal for a better understanding of parsing and LR(k) grammars. You gain a solid understanding of the fundamental mathematical properties of computer hardware, software, and applications with a blend of practical and philosophical coverage and mathematical treatments, including advanced theorems and proofs. INTRODUCTION TO THE THEORY OF COMPUTATION, 3E's comprehensive coverage makes this a valuable reference for your continued studies in theoretical computing.

... MORE

Preface to the First Edition	p. xi
To the student	p. xi
To the educator	p. xii
The first edition	p. xiii
Feedback to the author	p. xiii
Acknowledgments	p. xiv
Preface to the Second Edition	p. xvii
Preface to the Third Edition	p. xxi
Introduction	p. 1
Automata, Computability, and Complexity	p. 1
Complexity theory	p. 2
Computability theory	p. 3
Automata theory	p. 3
Mathematical Notions and Terminology	p. 3
Sets	p. 3
Sequences and tuples	p. 6
Functions and relations	p. 7
Graphs	p. 10
Strings and languages	p. 13
Boolean logic	p. 14
Summary of mathematical terms	p. 16
Definitions, Theorems, and Proofs	p. 17
Finding proofs	p. 17
Types of Proof	p. 21
Proof by construction	p. 21
Proof by contradiction	p. 21
Proof by induction	p. 22
Exercises, Problems, and Solutions	p. 25
Automata and Languages	p. 29
Regular Languages	p. 31
Finite Automata	p. 31
Formal definition of a finite automaton	p. 35
Examples of finite automata	p. 37
Formal definition of computation	p. 40
Designing finite automata	p. 41
The regular operations	p. 44
Nondeterminism	p. 47
Formal definition of a nondeterministic finite automaton	p. 53
Equivalence of NFAs and DFAs	p. 54
Closure under the regular operations	p. 58
Regular Expressions	p. 63
Formal definition of a regular expression	p. 64
Equivalence with finite automata	p. 66
Nonregular Languages	p. 77
The pumping lemma for regular languages	p. 77
Exercises, Problems, and Solutions	p. 82
Context-Free Languages	p. 101
Context-Free Grammars	p. 102
Formal definition of a context-free grammar	p. 104
Examples of context-free grammars	p. 105
Designing context-free grammars	p. 106
Ambiguity	p. 107
Chomsky normal form	p. 108
Pushdown Automata	p. 111
Formal definition of a pushdown automaton	p. 113
Examples of pushdown automata	p. 114
Equivalence with context-free grammars	p. 117
Non-Context-Free Languages	p. 125
The pumping lemma for context-free languages	p. 125
Deterministic Context-Free Languages	p. 130
Properties of DCFLs	p. 133
Deterministic context-free grammars	p. 135
Relationship of DPDAs and DCFGs	p. 146
Parsing and LR(k) Grammars	p. 151
Exercises, Problems, and Solutions	p. 154
Computability Theory	p. 163
The Church-Turing Thesis	p. 165
Turing Machines	p. 165
Formal definition of a Turing machine	p. 167
Examples of Turing machines	p. 170
Variants of Turing Machines	p. 176
Multitape Turing machines	p. 176
Nondeterministic Turing machines	p. 178
Enumerators	p. 180
Equivalence with other models	p. 181
The Definition of Algorithm	p. 182
Hilbert's problems	p. 182
Terminology for describing Turing machines	p. 184
Exercises, Problems, and Solutions	p. 187
Decidability	p. 193
Decidable Languages	p. 194
Decidable problems concerning regular languages	p. 194
Decidable problems concerning context-free languages	p. 198
Undecidability	p. 201
The diagonalization method	p. 202
An undecidable language	p. 207
A Turing-unrecognizable language	p. 209
Exercises, Problems, and Solutions	p. 210
Reducibility	p. 215
Undecidable Problems from Language Theory	p. 216
Reductions via computation histories	p. 220
A Simple Undecidable Problem	p. 227
Mapping Reducibility	p. 234
Computable functions	p. 234
Formal definition of mapping reducibility	p. 235
Exercises, Problems, and Solutions	p. 239
Advanced Topics in Computability Theory	p. 245
The Recursion Theorem	p. 245
Self-reference	p. 246
Terminology for the recursion theorem	p. 249
Applications	p. 250
Decidability of logical theories	p. 252
A decidable theory	p. 255
An undecidable theory	p. 257
Turing Reducibility	p. 260
A Definition of Information	p. 261
Minimal length descriptions	p. 262
Optimality of the definition	p. 266
Incompressible strings and randomness	p. 267
Exercises, Problems, and Solutions	p. 270
Complexity Theory	p. 273
Time Complexity	p. 275
Measuring Complexity	p. 275
Big-O and small-o notation	p. 276
Analyzing algorithms	p. 279
Complexity relationships among models	p. 282
The Class P	p. 284
Polynomial time	p. 284
Examples of problems in P	p. 286
The Class NP	p. 292
Examples of problems in NP	p. 295
The P versus NP question	p. 297
NP-completeness	p. 299
Polynomial time reducibility	p. 300
Definition of NP-completeness	p. 304
The Cook-Levin Theorem	p. 304
Additional NP-complete Problems	p. 311
The vertex cover problem	p. 312
The Hamiltonian path problem	p. 314
The subset sum problem	p. 319
Exercises, Problems, arid Solutions	p. 322
Space Complexity	p. 331
Savitch�s Theorem	p. 333
The Class PSPACE	p. 336
PSPACE-completeness	p. 337
The TQBF problem	p. 338
Winning strategies for games	p. 341
Generalized geography	p. 343
The Classes L and NL	p. 348
NL-completeness	p. 351
Searching in graphs	p. 353
NL equals coNL	p. 354
Exercises, Problems, and Solutions	p. 356
Intractability	p. 363
Hierarchy Theorems	p. 364
Exponential space completeness	p. 371
Relativization	p. 376
Limits of the diagonalization method	p. 377
Circuit Complexity	p. 379
Exercises, Problems, and Solutions	p. 388
Advanced Topics in Complexity Theory	p. 393
Approximation Algorithms	p. 393
Probabilistic Algorithms	p. 395
The class BPP	p. 395
Primality	p. 399
Read-once branching programs	p. 404
Alternation	p. 408
Alternating time and space	p. 410
The Polynomial time hierarchy	p. 414
Interactive Proof Systems	p. 415
Graph nonisomorphism	p. 415
Definition of the model	p. 415
IP = PSPACE	p. 418
Parallel Computation	p. 427
Uniform Boolean circuits	p. 428
The class NC	p. 430
P-completeness	p. 432
Cryptography	p. 433
Secret keys	p. 433
Public-key cryptosystems	p. 435
One-way functions	p. 435
Trapdoor functions	p. 437
Exercises, Problems, and Solutions	p. 439
Selected Bibliography	p. 443
Index	p. 448
Table of Contents provided by Ingram. All Rights Reserved.

Michael Sipser has taught theoretical computer science and other mathematical subjects at the Massachusetts Institute of Technology for the past 32 years. He is the Head of the Mathematics Department and a member of the Computer Science and Artificial Intelligence Laboratory (CSAIL). He enjoys teaching and pondering the many mysteries of complexity theory.

RENT TEXTBOOKS

Introduction to the Theory of Computation

Why Rent from Knetbooks?

Top 5 reasons to order all your textbooks from Knetbooks:

Related Products