Elements of computation theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Springer
2009
|
| Schriftenreihe: | Texts in computer science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 422 S. graph. Darst. |
| ISBN: | 9781848824966 9781848824973 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804138854951682048 |
|---|---|
| adam_text | Contents
1
Mathematical Preliminaries
..................................... 1
1.1
Introduction
............................................... 1
1.2
Sets
...................................................... 1
1.3
Relations and Graphs
....................................... 3
1.4
Functions and Counting
..................................... 8
1.5
Proof Techniques
........................................... 16
1.6
Summary and Problems
..................................... 25
2
Regular Languages
............................................. 31
2.1
Introduction
............................................... 31
2.2
Language Basics
........................................... 32
2.3
Regular Expressions
........................................ 36
2.4
Regular Grammars
......................................... 40
2.5
Deterministic Finite Automata
................................ 45
2.6
Nondeterministic Finite Automata
............................ 55
2.7
Summary and Additional Problems
........................... 64
3
Equivalences
................................................... 69
3.1
Introduction
............................................... 69
3.2
NFA to
DEA
............................................... 69
3.3
Finite Automata and Regular Grammars
....................... 76
3.4
Regular Expression to NFA
.................................. 79
3.5
NFA to Regular Expression
.................................. 82
3.6
Summary and Additional Problems
........................... 90
4
Structure of Regular Languages
.................................. 93
4.1
Introduction
............................................... 93
4.2
Closure Properties
.......................................... 94
4.3
Nonregular Languages
...................................... 98
4.4
Myhill-Nerode Theorem
.................................... 105
4.5
State Minimization
......................................... 110
4.6
Summary and Additional Problems
........................... 119
xii Contents
Context-free Languages
......................................... 125
5.1
Introduction
............................................... 125
5.2
Context-free Grammars
..................................... 125
5.3
Parse Trees
................................................ 132
5.4
Ambiguity
................................................ 137
5.5
Eliminating Ugly Productions
................................ 141
5.6
Normal Forms
............................................. 147
5.7
Summary and Additional Problems
........................... 155
Structure of CFLs
.............................................. 159
6.1
Introduction
............................................... 159
6.2
Pushdown Automata
........................................ 159
6.3
CFG andPDA
............................................. 169
6.4
Pumping Lemma
........................................... 175
6.5
Closure Properties of CFLs
.................................. 182
6.6
Deterministic Pushdown Automata
............................ 186
6.7
Summary and Additional Problems
........................... 191
Computably Enumerable Languages
.............................. 201
7.1
Introduction
............................................... 201
7.2
Unrestricted Grammars
..................................... 201
7.3
Turing Machines
........................................... 205
7.4
Acceptance and Rejection
................................... 210
7.5
Using Old Machines
........................................ 217
7.6
Multitape TMs
............................................. 228
7.7
Nondeterministic TMs and Grammars
......................... 233
7.8
Summary and Additional Problems
........................... 240
A Noncomputably Enumerable Language
......................... 245
8.1
Introduction
............................................... 245
8.2
Turing Machines as Computers
............................... 246
8.3
TMs as Language Deciders
.................................. 251
8.4
How Many Machines?
...................................... 257
8.5
Acceptance Problem
........................................ 261
8.6
Chomsky Hierarchy
........................................ 267
8.7
Summary and Additional Problems
........................... 272
Algorithmic Solvability
.......................................... 281
9.1
Introduction
............................................... 281
9.2
Problem Reduction
......................................... 282
9.3
Rice s Theorem
............................................ 287
9.4
About Finite Automata
...................................... 293
9.5
AboutPDA
............................................... 295
9.6
Post s Correspondence Problem
............................... 301
9.7
About Logical Theories
..................................... 307
9.8
Other Interesting Problems
.................................. 314
9.9
Summary and Additional Problems
........................... 316
Contents xiii
10
Computational Complexity
...................................... 327
10.1
Introduction
............................................... 327
10.2
Rate of Growth of Functions
................................. 328
10.3
Complexity Classes
......................................... 333
10.4
Space Complexity
.......................................... 338
10.5
Time Complexity
.......................................... 342
10.6
The Class NP
.............................................. 348
10.7 MP-Completeness.......................................... 352
10.8
Some JVP-Complete Problems
................................ 358
10.9
Dealing with iVP-Complete Problems
.......................... 369
10.10
Summary and Additional Problems
........................... 372
Answers and Hints to Selected Problems
.............................. 385
References
......................................................... 407
Index
............................................................. 415
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| illustrated | Illustrated |
| indexdate | 2024-07-09T21:34:49Z |
| institution | BVB |
| isbn | 9781848824966 9781848824973 |
| language | English |
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| physical | XIII, 422 S. graph. Darst. |
| publishDate | 2009 |
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| series2 | Texts in computer science |
| spelling | Singh, Arindama Verfasser (DE-588)138264635 aut Elements of computation theory Arindama Singh London Springer 2009 XIII, 422 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in computer science Informatik Computer science Machine theory Berechnungstheorie (DE-588)4005581-4 gnd rswk-swf Formale Sprache (DE-588)4017848-1 gnd rswk-swf Berechnungstheorie (DE-588)4005581-4 s DE-604 Formale Sprache (DE-588)4017848-1 s Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017335538&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Singh, Arindama Elements of computation theory Informatik Computer science Machine theory Berechnungstheorie (DE-588)4005581-4 gnd Formale Sprache (DE-588)4017848-1 gnd |
| subject_GND | (DE-588)4005581-4 (DE-588)4017848-1 |
| title | Elements of computation theory |
| title_auth | Elements of computation theory |
| title_exact_search | Elements of computation theory |
| title_full | Elements of computation theory Arindama Singh |
| title_fullStr | Elements of computation theory Arindama Singh |
| title_full_unstemmed | Elements of computation theory Arindama Singh |
| title_short | Elements of computation theory |
| title_sort | elements of computation theory |
| topic | Informatik Computer science Machine theory Berechnungstheorie (DE-588)4005581-4 gnd Formale Sprache (DE-588)4017848-1 gnd |
| topic_facet | Informatik Computer science Machine theory Berechnungstheorie Formale Sprache |
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