Introduction to the theory of computation:
"Michael Sipser's philosophy in writing this book is simple: make the subject interesting and relevant, and the students will learn. His emphasis on unifying computer science theory - rather than offering a collection of low-level details - sets the book apart, as do his intuitive explanat...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston, Mass.
Course Technology
2006
|
| Ausgabe: | 2. ed., internat. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "Michael Sipser's philosophy in writing this book is simple: make the subject interesting and relevant, and the students will learn. His emphasis on unifying computer science theory - rather than offering a collection of low-level details - sets the book apart, as do his intuitive explanations. Throughout the book, Sipser - a noted authority on the theory of computation - builds students' knowledge of conceptual tools used in computer science, the aesthetic sense they need to create elegant systems, and the ability to think through problems on their own. INTRODUCTION TO THE THEORY OF COMPUTATION provides a mathematical treatment of computation theory grounded in theorems and proofs. Proofs are presented with a "proof idea" component to reveal the concepts underpinning the formalism. Algorithms are presented using prose instead of pseudocode to focus attention on the algorithms themselves, rather than on specific computational models. Topic coverage, terminology, and order of presentation are traditional for an upper-level course in computer science theory. Users of the Preliminary Edition (now out of print) will be interested to note several new chapters on complexity theory: Chapter 8 on space complexity; Chapter 9 on provable intractability, and Chapter 10 on advanced topics, including approximation algorithms, alternation, interactive proof systems, cryptography, and parallel computing." -- Publisher's description. |
| Beschreibung: | The content of this text differs from the U.S. version |
| Beschreibung: | XVII, 437 S. Ill., graph. Darst. |
| ISBN: | 9780619217648 0619217642 |
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Datensatz im Suchindex
| _version_ | 1804134547734921216 |
|---|---|
| adam_text | CONTENTS
Preface to the First Edition x
To the student x
To the educator xi
The first edition xii
Feedback to the author xii
Acknowledgments xiii
Preface to the Second Edition (International) xv
0 Introduction 1
0.1 Automata, Computability, and Complexity 1
Complexity theory 2
Computability theory 2
Automata theory 3
0.2 Mathematical Notions and Terminology 3
Sets 3
Sequences and tuples 6
Functions and relations 7
Graphs 10
Strings and languages 13
Boolean logic 14
Summary of mathematical terms 16
0.3 Definitions, Theorems, and Proofs 17
Finding proofs 17
v
VI CONTENTS
0.4 Types of Proof 21
Proof by construction 21
Proof by contradiction 21
Proof by induction 22
Exercises, Problems, and Solutions 25
Part One: Automata and Languages 29
1 Regular Languages 31
1.1 Finite Automata 31
Formal definition of a finite automaton 35
Examples of finite automata 37
Formal definition of computation 40
Designing finite automata 41
The regular operations 44
1.2 Nondeterminism 47
Formal definition of a nondeterministic finite automaton . ... 53
Equivalence of NFAs and DFAs 54
Closure under the regular operations 58
1.3 Regular Expressions 63
Formal definition of a regular expression 64
Equivalence with finite automata 66
1.4 Nonregular Languages 77
The pumping lemma for regular languages 77
Exercises, Problems, and Solutions 82
2 Context Free Languages 101
2.1 Context free Grammars 102
Formal definition of a context free grammar 104
Examples of context free grammars 105
Designing context free grammars 106
Ambiguity 107
Chomsky normal form 108
2.2 Pushdown Automata Ill
Formal definition of a pushdown automaton 113
Examples of pushdown automata 114
Equivalence with context free grammars 117
2.3 Non context free Languages 125
The pumping lemma for context free languages 125
Exercises, Problems, and Solutions 130
CONTENTS vii
Part Two: Computability Theory 137
3 The Church Turing Thesis 139
3.1 Turing Machines 139
Formal definition of a Turing machine 141
Examples of Turing machines 144
3.2 Variants of Turing Machines 150
Multitape Turing machines 150
Nondeterministic Turing machines 152
Enumerators 154
Equivalence with other models 155
3.3 The Definition of Algorithm 156
Hilbert s problems 156
Terminology for describing Turing machines 158
Exercises, Problems, and Solutions 161
4 Decidability 167
4.1 Decidable Languages 168
Decidable problems concerning regular languages 168
Decidable problems concerning context free languages 172
4.2 The Halting Problem 175
The diagonalization method 176
The halting problem is undecidable 181
A Turing unrecognizable language 183
Exercises, Problems, and Solutions 184
5 Reducibility 191
5.1 Undecidable Problems from Language Theory 192
Reductions via computation histories 196
5.2 A Simple Undecidable Problem 203
5.3 Mapping Reducibility 210
Computable functions 210
Formal definition of mapping reducibility 211
Exercises, Problems, and Solutions 215
6 Advanced Topics in Computability Theory 221
6.1 The Recursion Theorem 221
Self reference 222
Terminology for the recursion theorem 225
Applications 226
Vlii CONTENTS
6.2 Decidability of logical theories 228
A decidable theory 231
An undecidable theory 233
6.3 Turing Reducibility 236
6.4 A Definition of Information 237
Minimal length descriptions 238
Optimality of the definition 242
Incompressible strings and randomness 243
Exercises, Problems, and Solutions 246
Part Three: Complexity Theory 249
7 Time Complexity 251
7.1 Measuring Complexity 251
Big O and small o notation 252
Analyzing algorithms 255
Complexity relationships among models 258
7.2 The Class P 260
Polynomial time 260
Examples of problems in P 262
7.3 The Class NP 268
Examples of problems in NP 271
The P versus NP question 273
7.4 NP completeness 275
Polynomial time reducibility 276
Definition of NP completeness 280
The Cook Levin Theorem 280
7.5 Additional NP complete Problems 287
The vertex cover problem 288
The Hamiltonian path problem 290
The subset sum problem 295
Exercises, Problems, and Solutions 298
8 Space Complexity 307
8.1 Savitch s Theorem 309
8.2 The Class PSPACE 312
8.3 PSPACE completeness 313
The TQBF problem 314
Winning strategies for games 317
Generalized geography 319
CONTENTS ix
8.4 The Classes L and NL 324
8.5 NL completeness 327
Searching in graphs 329
8.6 NL equals coNL 330
Exercises, Problems, and Solutions 332
9 Intractability 339
9.1 Hierarchy Theorems 340
Exponential space completeness 347
9.2 Relativization 352
Limits of the diagonalization method 353
9.3 Circuit Complexity 355
Exercises, Problems, and Solutions 364
10 Advanced topics in complexity theory 371
10.1 Approximation Algorithms 371
10.2 Probabilistic Algorithms 374
The class BPP 374
Primality 377
Read once branching programs 382
10.3 Alternation 386
Alternating time and space 387
The Polynomial time hierarchy 392
10.4 Interactive Proof Systems 393
Graph nonisomorphism 393
Definition of the model 394
IP = PSPACE 396
10.5 Parallel Computation 405
Uniform Boolean circuits 406
The class NC 408
P completeness 410
10.6 Cryptography 411
Secret keys 411
Public key cryptosystems 413
One way functions 413
Trapdoor functions 415
Exercises, Problems, and Solutions 417
Selected Bibliography 421
Index 427
|
| adam_txt |
CONTENTS
Preface to the First Edition x
To the student x
To the educator xi
The first edition xii
Feedback to the author xii
Acknowledgments xiii
Preface to the Second Edition (International) xv
0 Introduction 1
0.1 Automata, Computability, and Complexity 1
Complexity theory 2
Computability theory 2
Automata theory 3
0.2 Mathematical Notions and Terminology 3
Sets 3
Sequences and tuples 6
Functions and relations 7
Graphs 10
Strings and languages 13
Boolean logic 14
Summary of mathematical terms 16
0.3 Definitions, Theorems, and Proofs 17
Finding proofs 17
v
VI CONTENTS
0.4 Types of Proof 21
Proof by construction 21
Proof by contradiction 21
Proof by induction 22
Exercises, Problems, and Solutions 25
Part One: Automata and Languages 29
1 Regular Languages 31
1.1 Finite Automata 31
Formal definition of a finite automaton 35
Examples of finite automata 37
Formal definition of computation 40
Designing finite automata 41
The regular operations 44
1.2 Nondeterminism 47
Formal definition of a nondeterministic finite automaton . . 53
Equivalence of NFAs and DFAs 54
Closure under the regular operations 58
1.3 Regular Expressions 63
Formal definition of a regular expression 64
Equivalence with finite automata 66
1.4 Nonregular Languages 77
The pumping lemma for regular languages 77
Exercises, Problems, and Solutions 82
2 Context Free Languages 101
2.1 Context free Grammars 102
Formal definition of a context free grammar 104
Examples of context free grammars 105
Designing context free grammars 106
Ambiguity 107
Chomsky normal form 108
2.2 Pushdown Automata Ill
Formal definition of a pushdown automaton 113
Examples of pushdown automata 114
Equivalence with context free grammars 117
2.3 Non context free Languages 125
The pumping lemma for context free languages 125
Exercises, Problems, and Solutions 130
CONTENTS vii
Part Two: Computability Theory 137
3 The Church Turing Thesis 139
3.1 Turing Machines 139
Formal definition of a Turing machine 141
Examples of Turing machines 144
3.2 Variants of Turing Machines 150
Multitape Turing machines 150
Nondeterministic Turing machines 152
Enumerators 154
Equivalence with other models 155
3.3 The Definition of Algorithm 156
Hilbert's problems 156
Terminology for describing Turing machines 158
Exercises, Problems, and Solutions 161
4 Decidability 167
4.1 Decidable Languages 168
Decidable problems concerning regular languages 168
Decidable problems concerning context free languages 172
4.2 The Halting Problem 175
The diagonalization method 176
The halting problem is undecidable 181
A Turing unrecognizable language 183
Exercises, Problems, and Solutions 184
5 Reducibility 191
5.1 Undecidable Problems from Language Theory 192
Reductions via computation histories 196
5.2 A Simple Undecidable Problem 203
5.3 Mapping Reducibility 210
Computable functions 210
Formal definition of mapping reducibility 211
Exercises, Problems, and Solutions 215
6 Advanced Topics in Computability Theory 221
6.1 The Recursion Theorem 221
Self reference 222
Terminology for the recursion theorem 225
Applications 226
Vlii CONTENTS
6.2 Decidability of logical theories 228
A decidable theory 231
An undecidable theory 233
6.3 Turing Reducibility 236
6.4 A Definition of Information 237
Minimal length descriptions 238
Optimality of the definition 242
Incompressible strings and randomness 243
Exercises, Problems, and Solutions 246
Part Three: Complexity Theory 249
7 Time Complexity 251
7.1 Measuring Complexity 251
Big O and small o notation 252
Analyzing algorithms 255
Complexity relationships among models 258
7.2 The Class P 260
Polynomial time 260
Examples of problems in P 262
7.3 The Class NP 268
Examples of problems in NP 271
The P versus NP question 273
7.4 NP completeness 275
Polynomial time reducibility 276
Definition of NP completeness 280
The Cook Levin Theorem 280
7.5 Additional NP complete Problems 287
The vertex cover problem 288
The Hamiltonian path problem 290
The subset sum problem 295
Exercises, Problems, and Solutions 298
8 Space Complexity 307
8.1 Savitch's Theorem 309
8.2 The Class PSPACE 312
8.3 PSPACE completeness 313
The TQBF problem 314
Winning strategies for games 317
Generalized geography 319
CONTENTS ix
8.4 The Classes L and NL 324
8.5 NL completeness 327
Searching in graphs 329
8.6 NL equals coNL 330
Exercises, Problems, and Solutions 332
9 Intractability 339
9.1 Hierarchy Theorems 340
Exponential space completeness 347
9.2 Relativization 352
Limits of the diagonalization method 353
9.3 Circuit Complexity 355
Exercises, Problems, and Solutions 364
10 Advanced topics in complexity theory 371
10.1 Approximation Algorithms 371
10.2 Probabilistic Algorithms 374
The class BPP 374
Primality 377
Read once branching programs 382
10.3 Alternation 386
Alternating time and space 387
The Polynomial time hierarchy 392
10.4 Interactive Proof Systems 393
Graph nonisomorphism 393
Definition of the model 394
IP = PSPACE 396
10.5 Parallel Computation 405
Uniform Boolean circuits 406
The class NC 408
P completeness 410
10.6 Cryptography 411
Secret keys 411
Public key cryptosystems 413
One way functions 413
Trapdoor functions 415
Exercises, Problems, and Solutions 417
Selected Bibliography 421
Index 427 |
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| edition | 2. ed., internat. ed. |
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Throughout the book, Sipser - a noted authority on the theory of computation - builds students' knowledge of conceptual tools used in computer science, the aesthetic sense they need to create elegant systems, and the ability to think through problems on their own. INTRODUCTION TO THE THEORY OF COMPUTATION provides a mathematical treatment of computation theory grounded in theorems and proofs. Proofs are presented with a "proof idea" component to reveal the concepts underpinning the formalism. Algorithms are presented using prose instead of pseudocode to focus attention on the algorithms themselves, rather than on specific computational models. Topic coverage, terminology, and order of presentation are traditional for an upper-level course in computer science theory. 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| id | DE-604.BV020840422 |
| illustrated | Illustrated |
| index_date | 2024-07-02T13:16:19Z |
| indexdate | 2024-07-09T20:26:21Z |
| institution | BVB |
| isbn | 9780619217648 0619217642 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014162314 |
| oclc_num | 64006340 |
| open_access_boolean | |
| owner | DE-573 DE-824 DE-Aug4 DE-1050 DE-92 DE-945 DE-703 DE-859 DE-11 DE-522 DE-91G DE-BY-TUM DE-B768 DE-83 |
| owner_facet | DE-573 DE-824 DE-Aug4 DE-1050 DE-92 DE-945 DE-703 DE-859 DE-11 DE-522 DE-91G DE-BY-TUM DE-B768 DE-83 |
| physical | XVII, 437 S. Ill., graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Course Technology |
| record_format | marc |
| spelling | Sipser, Michael Verfasser aut Introduction to the theory of computation Michael Sipser 2. ed., internat. ed. Boston, Mass. Course Technology 2006 XVII, 437 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier The content of this text differs from the U.S. version "Michael Sipser's philosophy in writing this book is simple: make the subject interesting and relevant, and the students will learn. His emphasis on unifying computer science theory - rather than offering a collection of low-level details - sets the book apart, as do his intuitive explanations. Throughout the book, Sipser - a noted authority on the theory of computation - builds students' knowledge of conceptual tools used in computer science, the aesthetic sense they need to create elegant systems, and the ability to think through problems on their own. INTRODUCTION TO THE THEORY OF COMPUTATION provides a mathematical treatment of computation theory grounded in theorems and proofs. Proofs are presented with a "proof idea" component to reveal the concepts underpinning the formalism. Algorithms are presented using prose instead of pseudocode to focus attention on the algorithms themselves, rather than on specific computational models. Topic coverage, terminology, and order of presentation are traditional for an upper-level course in computer science theory. Users of the Preliminary Edition (now out of print) will be interested to note several new chapters on complexity theory: Chapter 8 on space complexity; Chapter 9 on provable intractability, and Chapter 10 on advanced topics, including approximation algorithms, alternation, interactive proof systems, cryptography, and parallel computing." -- Publisher's description. Hesaplama güçlüğü Makine teorisi Teoria da computação larpcal Computational complexity Machine theory Theoretische Informatik (DE-588)4196735-5 gnd rswk-swf Komplexitätstheorie (DE-588)4120591-1 gnd rswk-swf Formale Sprache (DE-588)4017848-1 gnd rswk-swf Automatentheorie (DE-588)4003953-5 gnd rswk-swf Berechnungskomplexität (DE-588)4134751-1 gnd rswk-swf Theoretische Informatik (DE-588)4196735-5 s DE-604 Komplexitätstheorie (DE-588)4120591-1 s Berechnungskomplexität (DE-588)4134751-1 s Automatentheorie (DE-588)4003953-5 s Formale Sprache (DE-588)4017848-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014162314&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sipser, Michael Introduction to the theory of computation Hesaplama güçlüğü Makine teorisi Teoria da computação larpcal Computational complexity Machine theory Theoretische Informatik (DE-588)4196735-5 gnd Komplexitätstheorie (DE-588)4120591-1 gnd Formale Sprache (DE-588)4017848-1 gnd Automatentheorie (DE-588)4003953-5 gnd Berechnungskomplexität (DE-588)4134751-1 gnd |
| subject_GND | (DE-588)4196735-5 (DE-588)4120591-1 (DE-588)4017848-1 (DE-588)4003953-5 (DE-588)4134751-1 |
| title | Introduction to the theory of computation |
| title_auth | Introduction to the theory of computation |
| title_exact_search | Introduction to the theory of computation |
| title_exact_search_txtP | Introduction to the theory of computation |
| title_full | Introduction to the theory of computation Michael Sipser |
| title_fullStr | Introduction to the theory of computation Michael Sipser |
| title_full_unstemmed | Introduction to the theory of computation Michael Sipser |
| title_short | Introduction to the theory of computation |
| title_sort | introduction to the theory of computation |
| topic | Hesaplama güçlüğü Makine teorisi Teoria da computação larpcal Computational complexity Machine theory Theoretische Informatik (DE-588)4196735-5 gnd Komplexitätstheorie (DE-588)4120591-1 gnd Formale Sprache (DE-588)4017848-1 gnd Automatentheorie (DE-588)4003953-5 gnd Berechnungskomplexität (DE-588)4134751-1 gnd |
| topic_facet | Hesaplama güçlüğü Makine teorisi Teoria da computação Computational complexity Machine theory Theoretische Informatik Komplexitätstheorie Formale Sprache Automatentheorie Berechnungskomplexität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014162314&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT sipsermichael introductiontothetheoryofcomputation |