Introduction to the theory of computation:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston, Mass.
Cengage Learning
2013
|
| Edition: | 3. ed., internat. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 443 - 447 Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XXII, 458 S. graph. Darst. |
| ISBN: | 9781133187813 9781133187790 9780357670583 1133187811 113318779X |
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Record in the Search Index
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| adam_text | Titel: Introduction to the theory of computation
Autor: Sipser, Michael
Jahr: 2013
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
Preface to the Third Edition xxi
Introduction 1
0.1 Automata, Computability, and Complexity............. 1
Complexity theory......................... 2
Computability theory....................... 3
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
Summaryof mathematical terms................. 16
0.3 Definitions, Theorems, and Proofs................. 17
Finding proofs........................... 17
0.4 Typesof Proof............................ 21
Proof by construction....................... 21
Proof by contradictdon....................... 21
Proof byinduction......................... 22
Exercises, Problems, and Solutions................... 25
VI CONTENTS
Part One: Automata and Languages 29
1 Regulär 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 regulär Operations...................... 44
1.2 Nondeterminism........................... 47
Formal definition of a nondeterministic finite automaton . ... 53
Equivalence of NFAs and DFAs ................. 54
Closure under the regulär Operations............... 58
1.3 Regulär Expressions......................... 63
Formal definition of a regulär expression ............ 64
Equivalence with finite automata................. 66
1.4 Nonregular Languages........................ 77
The pumping lemma for regulär 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.........................111
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
2.4 Deterministic Context-Free Languages...............130
Properties ofDCFLs.......................133
Deterministic context-free grammars ..............135
RelationshipofDPDAsandDCFGs...............146
Parsing and LR(k) Grammars...................151
Exercises, Problems, and Solutions...................154
Part Two: Computability Theory 163
3 The Church-Turing Thesis 165
3.1 Turing Machines...........................165
Formal definition of a Turing machine..............167
CONTENTS VII
Examples of Turing machines...................170
3.2 Variantsof Turing Machines.....................176
Multitape Turing machines....................176
Nondeterministic Turing machines................178
Enumerators............................180
Equivalence with other modeis..................181
3.3 The Definition of Algorithm ....................182
Hilbert s problems.........................182
Terminology for describing Turing machines..........184
Exercises, Problems, and Solutions...................187
4 Decidability 193
4.1 Decidable Languages.........................194
Decidable problems concerning regulär languages.......194
Decidable problems concerning context-free languages.....198
4.2 Undecidability............................201
The diagonalization method...................202
An undecidable language.....................207
A Turing-unrecognizable language................209
Exercises, Problems, and Solutions...................210
5 Reducibility 215
5.1 Undecidable Problems from Language Theory..........216
Reductdons via computation histories...............220
5.2 A Simple Undecidable Problem...................227
5.3 Mapping Reducibility........................234
Computable functions.......................234
Formal definition of mapping reducibility............235
Exercises, Problems, and Solutions...................239
6 Advanced Topics in Computability Theory 245
6.1 The Recursion Theorem.......................245
Self-reference ...........................246
Terminology for the recursion theorem.............249
Applications............................250
6.2 Decidability of logical theories ...................252
A decidable theory.........................255
An undecidable theory.......................257
6.3 Turing Reducibility..........................260
6.4 A Definition of Information.....................261
Minimal length descriptions ...................262
Optimality of the definition....................266
Incompressible strings and randomness.............267
Exercises, Problems, and Solutions...................270
VIII CONTENTS
PartThree: Complexity Theory 273
7 Time Complexity 275
7.1 Measuring Complexity........................275
Big-0 and small-o notation....................276
Analyzing algorithms.......................279
Complexity relationships among modeis.............282
7.2 The Class P..............................284
Polynomial time..........................284
Examples of problems in P....................286
7.3 The Class NP.............................292
Examples of problems in NP...................295
The P versus NP question ....................297
7.4 NP-completeness...........................299
Polynomial time reducibility...................300
Definition of NP-completeness..................304
The Cook-Levin Theorem....................304
7.5 Additional NP-complete Problems.................311
The vertex cover problem.....................312
The Hamiltonian path problem .................314
The subset sum problem .....................319
Exercises, Problems, and Solutions...................322
8 Space Complexity 331
8.1 Savitch s Theorem..........................333
8.2 The Class PSPACE .........................336
8.3 PSPACE-completeness .......................337
The TQBF problem........................338
Winning strategies for games...................341
Generalized geography......................343
8.4 The Classes L and NL........................348
8.5 NL-completeness ..........................351
Searching in graphs........................353
8.6 NL equals coNL...........................354
Exercises, Problems, and Solutions...................356
9 Intractability 363
9.1 Hierarchy Theorems.........................364
Exponential space completeness.................371
9.2 Relativization.............................376
Limits of the diagonalization method ..............377
9.3 Circuit Complexity..........................379
Exercises, Problems, and Solutions...................388
10 Advanced Topics in Complexity Theory 393
10.1 Approximation Algorithms .....................393
CONTENTS IX
10.2 Probabilistic Algorithms.......................396
The class BPP...........................396
Primality..............................399
Read-once branching programs..................404
10.3 Alternation..............................408
Alternating time and space....................410
The Polynomial time hierarchy..................414
10.4 Interactive Proof Systems......................415
Graph nonisomorphism......................415
Definition of the model......................416
IP = PSPACE ...........................418
10.5 Parallel Computation ........................427
Uniform Boolean circuits.....................428
The class NC ...........................430
P-completeness ..........................432
10.6 Cryptography.............................433
Secretkeys.............................433
Public-key cryptosystems.....................435
One-way functions.........................435
Trapdoor functions ........................437
Exercises, Problems, and Solutions...................439
Selected Bibliography 443
Index 448
|
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| spelling | Sipser, Michael Verfasser (DE-588)131513176 aut Introduction to the theory of computation Michael Sipser 3. ed., internat. ed. Boston, Mass. Cengage Learning 2013 XXII, 458 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 443 - 447 Hier auch später erschienene, unveränderte Nachdrucke Formale Sprache (DE-588)4017848-1 gnd rswk-swf Berechnungskomplexität (DE-588)4134751-1 gnd rswk-swf Automatentheorie (DE-588)4003953-5 gnd rswk-swf Komplexitätstheorie (DE-588)4120591-1 gnd rswk-swf Theoretische Informatik (DE-588)4196735-5 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=025466598&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sipser, Michael Introduction to the theory of computation Formale Sprache (DE-588)4017848-1 gnd Berechnungskomplexität (DE-588)4134751-1 gnd Automatentheorie (DE-588)4003953-5 gnd Komplexitätstheorie (DE-588)4120591-1 gnd Theoretische Informatik (DE-588)4196735-5 gnd |
| subject_GND | (DE-588)4017848-1 (DE-588)4134751-1 (DE-588)4003953-5 (DE-588)4120591-1 (DE-588)4196735-5 |
| 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_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 | Formale Sprache (DE-588)4017848-1 gnd Berechnungskomplexität (DE-588)4134751-1 gnd Automatentheorie (DE-588)4003953-5 gnd Komplexitätstheorie (DE-588)4120591-1 gnd Theoretische Informatik (DE-588)4196735-5 gnd |
| topic_facet | Formale Sprache Berechnungskomplexität Automatentheorie Komplexitätstheorie Theoretische Informatik |
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