Introducing the theory of computation:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Sudbury, Mass.
Jones and Bartlett
2008
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 201-202) and index |
| Beschreibung: | xii, 228 p. ill. |
| ISBN: | 9780763741259 0763741256 |
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| 100 | 1 | |a Goddard, Wayne |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introducing the theory of computation |c Wayne Goddard |
| 264 | 1 | |a Sudbury, Mass. |b Jones and Bartlett |c 2008 | |
| 300 | |a xii, 228 p. |b ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references (p. 201-202) and index | ||
| 650 | 4 | |a Complexité de calcul (Informatique) | |
| 650 | 4 | |a Teoría de las máquinas | |
| 650 | 4 | |a Théorie des automates | |
| 650 | 4 | |a Machine theory | |
| 650 | 4 | |a Computational complexity | |
| 650 | 0 | 7 | |a Theoretische Informatik |0 (DE-588)4196735-5 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804137686510862336 |
|---|---|
| adam_text | ШШ
Preface
v
Part I Regular Languages
1
1
Finite Automata
3
1.1
A Finite
Automat
on Has States
................ 3
1.2
Building FAs
.......................... 5
1.3
Representing FAs
........................ 9
Exercises
............................ 10
2
Regular Expressions
13
2.1
Regular Expressions
...................... 13
2.2
Kleene
s
Theorem
........................ 16
2.3
Applications of
R
Es ......................
16
Exercises
............................ 17
3
Nondeterminism
20
3.1
Xondeterministic Finite Automata
.............. 20
3.2
What Is Nondeterminism?
................... 22
3.3 £-
Transitions
.......................... 23
3.4
Kleene
s
Theorem Revisited
.................. 24
3.5
Conversion from RE to XFA
.................. 24
3.6
Conversion from XFA to DFA
................. 26
3.7
Conversion from FA to RE
.................. 29
Exercises
............................ 31
4
Properties of Regular Languages
34
4.1
Closure Properties
....................... 34
Contents ix
4.2
Distinguishable Strings
..................... 36
4.3
The Pumping Lemma
..................... 38
Exercises
............................ 40
5
Applications of Finite Automata
44
5.1
String Processing
........................ 44
5.2
Finite-State Machines
..................... 45
5.3 Statecharts........................... 46
5.4
Lexical Analysis
........................ 46
Exercises
............................ 48
Summary
................................ 49
Interlude: JFLAP
........................... 50
Part II C ontext-Frec Languages
51
6
Context-Free Grammars
53
6.1
Productions
........................... 53
6.2
Further Examples
........................ 55
6.3
Derivation Trees and Ambiguity
............... 57
6.4
Regular Languages Revisited
................. 59
Exercises
............................ 60
7
Pushdown Automata
64
7.1
A PDA Has a Stack
...................... 64
7.2
rsondeterniinism and Further Examples
........... 67
7.3
Context-Free Languages
.................... (¡9
7.4
Applications of PDAs
..................... 69
Exercises
............................ 70
8
Grammars and Equivalences
73
8.1
Regular Grammars
....................... 73
8.2
The Chomsky Hierarchy
.................... 74
8.3
Usable and Nullable Variables
................. 75
8.4
Conversion from CFG to PDA
................ 76
8.5
An Alternative Representation
................ 77
8.6
Conversion from PDA to CFG
................ 78
Exercises
............................ 80
9
Properties of Context-Free Languages
83
9.1
Chomsky Normal Form
.................... 83
9.2
The Pumping Lemma: Proving Languages Not Context-Free
85
Exercises
............................ 88
Contents
10
Deterministic Parsing
91
10.1
Compilers
............................ 91
10.2
Bottom-Up Parsing
....................... 92
10.3
Table-Driven Parser for LR(1) Grammars
.......... 93
10.4
Construction of an SLR(l) Table
............... 96
10.5
Guaranteed Parsing
...................... 100
Exercises
............................ 102
Summary
................................ 106
Interlude: Grammars in Artificial Intelligence
......... 107
Part III Turing Machines
109
11
Turing Machines 111
11.1
A Turing Machine Has a Tape
................
Ill
11.2
More Examples
......................... 115
11.3
TM Subroutines
........................ 117
11.4
TMs That Do Not Halt
.................... 118
Exercises
............................ 118
12
Variations of Turing Machines
122
12.1
TMs as Transducers
...................... 122
12.2
Variations on the Model
.................... 123
12.3
Multiple Tapes
......................... 124
12.4
Nondeterminism and Halting
................. 125
12.5
Church s Thesis
......................... 126
12.6
Universal TMs
......................... 126
Exercises
............................ 127
13
Decidable Problems and Recursive Languages
131
13.1
Recursive and Recursively Enumerable Languages
..... 131
13.2
Decidable Questions
...................... 133
13.3
Decidable Questions about Simple Models
.......... 133
13.4
Reasoning about Computation
................ 135
13.5
Other Models
.......................... 136
Exercises
............................ 136
Summary
................................ 139
Interlude: Alternative Computers
................. 140
Part IV Undecidability
141
14
Diagonalization and the Halting Problem
143
14.1
Self-Denial
............................143
14.2
Countable Sets
.........................144
Contents xi
14.3 Diagonalization......................... 145
14.4
The Halting
Problem...................... 148
Exercises
............................ 150
15
More Undecidable
Problems 151
15.1
Reductions
........................... 151
15.2
Questions about TMs
..................... 152
15.3
Other Machines
......................... 154
15.4
Post s Correspondence Problem
................ 156
Exercises
............................ 157
16
Recursive Functions
159
16.1
Primitive Recursive Functions
................. 159
16.2
Examples: Functions and Predicates
............. 161
16.3
Functions That Are Not Primitive Recursive
........ 163
16.4
Bounded and Unbounded Minimization
........... 164
Exercises
............................ 165
Summary
................................ 167
Interlude: People
........................... 168
Part V Complexity Theory
169
17
Time Complexity
171
17.1
Time
............................... 171
17.2
Polynomial Time
........................ 172
17.3
Examples
............................ 173
17.4
Nondeterministic Time
..................... 175
17.5
Certificates and Examples
................... 176
17.6 ?
versus
KP........................... 178
Exercises
............................ 179
18
Space Complexity
181
18.1
Deterministic Space
...................... 181
18.2
Nondeterministic Space
.................... 183
18.3
Polynomial Space
........................ 183
18.4
Logarithmic Space
....................... 185
Exercises
............................ 186
19
^^-Completeness
187
19.1
NiP-Complete Problems
.................... 187
19.2
Examples
............................ 188
xii Contents
19.3
Proving NT-Completeness by Reduction
........... 190
Exercises
............................ 194
Summary
................................ 198
Interlude: Dealing with Hard Problems
............. 199
References and Further Reading
201
Selected Solutions to Exercises
203
Glossary
217
Index
225
|
| adam_txt |
ШШ
Preface
v
Part I Regular Languages
1
1
Finite Automata
3
1.1
A Finite
Automat
on Has States
. 3
1.2
Building FAs
. 5
1.3
Representing FAs
. 9
Exercises
. 10
2
Regular Expressions
13
2.1
Regular Expressions
. 13
2.2
Kleene
s
Theorem
. 16
2.3
Applications of
R
Es .
16
Exercises
. 17
3
Nondeterminism
20
3.1
Xondeterministic Finite Automata
. 20
3.2
What Is Nondeterminism?
. 22
3.3 £-
Transitions
. 23
3.4
Kleene
s
Theorem Revisited
. 24
3.5
Conversion from RE to XFA
. 24
3.6
Conversion from XFA to DFA
. 26
3.7
Conversion from FA to RE
. 29
Exercises
. 31
4
Properties of Regular Languages
34
4.1
Closure Properties
. 34
Contents ix
4.2
Distinguishable Strings
. 36
4.3
The Pumping Lemma
. 38
Exercises
. 40
5
Applications of Finite Automata
44
5.1
String Processing
. 44
5.2
Finite-State Machines
. 45
5.3 Statecharts. 46
5.4
Lexical Analysis
. 46
Exercises
. 48
Summary
. 49
Interlude: JFLAP
. 50
Part II C'ontext-Frec Languages
51
6
Context-Free Grammars
53
6.1
Productions
. 53
6.2
Further Examples
. 55
6.3
Derivation Trees and Ambiguity
. 57
6.4
Regular Languages Revisited
. 59
Exercises
. 60
7
Pushdown Automata
64
7.1
A PDA Has a Stack
. 64
7.2
rsondeterniinism and Further Examples
. 67
7.3
Context-Free Languages
. (¡9
7.4
Applications of PDAs
. 69
Exercises
. 70
8
Grammars and Equivalences
73
8.1
Regular Grammars
. 73
8.2
The Chomsky Hierarchy
. 74
8.3
Usable and Nullable Variables
. 75
8.4
Conversion from CFG to PDA
. 76
8.5
An Alternative Representation
. 77
8.6
Conversion from PDA to CFG
. 78
Exercises
. 80
9
Properties of Context-Free Languages
83
9.1
Chomsky Normal Form
. 83
9.2
The Pumping Lemma: Proving Languages Not Context-Free
85
Exercises
. 88
Contents
10
Deterministic Parsing
91
10.1
Compilers
. 91
10.2
Bottom-Up Parsing
. 92
10.3
Table-Driven Parser for LR(1) Grammars
. 93
10.4
Construction of an SLR(l) Table
. 96
10.5
Guaranteed Parsing
. 100
Exercises
. 102
Summary
. 106
Interlude: Grammars in Artificial Intelligence
. 107
Part III Turing Machines
109
11
Turing Machines 111
11.1
A Turing Machine Has a Tape
.
Ill
11.2
More Examples
. 115
11.3
TM Subroutines
. 117
11.4
TMs That Do Not Halt
. 118
Exercises
. 118
12
Variations of Turing Machines
122
12.1
TMs as Transducers
. 122
12.2
Variations on the Model
. 123
12.3
Multiple Tapes
. 124
12.4
Nondeterminism and Halting
. 125
12.5
Church's Thesis
. 126
12.6
Universal TMs
. 126
Exercises
. 127
13
Decidable Problems and Recursive Languages
131
13.1
Recursive and Recursively Enumerable Languages
. 131
13.2
Decidable Questions
. 133
13.3
Decidable Questions about Simple Models
. 133
13.4
Reasoning about Computation
. 135
13.5
Other Models
. 136
Exercises
. 136
Summary
. 139
Interlude: Alternative Computers
. 140
Part IV Undecidability
141
14
Diagonalization and the Halting Problem
143
14.1
Self-Denial
.143
14.2
Countable Sets
.144
Contents xi
14.3 Diagonalization. 145
14.4
The Halting
Problem. 148
Exercises
. 150
15
More Undecidable
Problems 151
15.1
Reductions
. 151
15.2
Questions about TMs
. 152
15.3
Other Machines
. 154
15.4
Post's Correspondence Problem
. 156
Exercises
. 157
16
Recursive Functions
159
16.1
Primitive Recursive Functions
. 159
16.2
Examples: Functions and Predicates
. 161
16.3
Functions That Are Not Primitive Recursive
. 163
16.4
Bounded and Unbounded Minimization
. 164
Exercises
. 165
Summary
. 167
Interlude: People
. 168
Part V Complexity Theory
169
17
Time Complexity
171
17.1
Time
. 171
17.2
Polynomial Time
. 172
17.3
Examples
. 173
17.4
Nondeterministic Time
. 175
17.5
Certificates and Examples
. 176
17.6 ?
versus
KP. 178
Exercises
. 179
18
Space Complexity
181
18.1
Deterministic Space
. 181
18.2
Nondeterministic Space
. 183
18.3
Polynomial Space
. 183
18.4
Logarithmic Space
. 185
Exercises
. 186
19
^^-Completeness
187
19.1
NiP-Complete Problems
. 187
19.2
Examples
. 188
xii Contents
19.3
Proving NT-Completeness by Reduction
. 190
Exercises
. 194
Summary
. 198
Interlude: Dealing with Hard Problems
. 199
References and Further Reading
201
Selected Solutions to Exercises
203
Glossary
217
Index
225 |
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| index_date | 2024-07-02T20:59:41Z |
| indexdate | 2024-07-09T21:16:14Z |
| institution | BVB |
| isbn | 9780763741259 0763741256 |
| language | English |
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| spelling | Goddard, Wayne Verfasser aut Introducing the theory of computation Wayne Goddard Sudbury, Mass. Jones and Bartlett 2008 xii, 228 p. ill. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. 201-202) and index Complexité de calcul (Informatique) Teoría de las máquinas Théorie des automates Machine theory Computational complexity Theoretische Informatik (DE-588)4196735-5 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Theoretische Informatik (DE-588)4196735-5 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016519866&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Goddard, Wayne Introducing the theory of computation Complexité de calcul (Informatique) Teoría de las máquinas Théorie des automates Machine theory Computational complexity Theoretische Informatik (DE-588)4196735-5 gnd |
| subject_GND | (DE-588)4196735-5 (DE-588)4151278-9 |
| title | Introducing the theory of computation |
| title_auth | Introducing the theory of computation |
| title_exact_search | Introducing the theory of computation |
| title_exact_search_txtP | Introducing the theory of computation |
| title_full | Introducing the theory of computation Wayne Goddard |
| title_fullStr | Introducing the theory of computation Wayne Goddard |
| title_full_unstemmed | Introducing the theory of computation Wayne Goddard |
| title_short | Introducing the theory of computation |
| title_sort | introducing the theory of computation |
| topic | Complexité de calcul (Informatique) Teoría de las máquinas Théorie des automates Machine theory Computational complexity Theoretische Informatik (DE-588)4196735-5 gnd |
| topic_facet | Complexité de calcul (Informatique) Teoría de las máquinas Théorie des automates Machine theory Computational complexity Theoretische Informatik Einführung |
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