Theory of computation:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Springer
2006
|
| Schriftenreihe: | Texts in computer science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XIII, 418 S. graph. Darst. |
| ISBN: | 1846282977 9781846282973 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804135420918759424 |
|---|---|
| adam_text | Contents
Preface
vii
Lectures
1
1
The Complexity of Computations
.........................3
2
Time and Space Complexity Classes and Savitch s Theorem
. 11
3
Separation Results
.....................................17
4
The
Immerman-Szelepcsényi
Theorem
....................22
5
Logspaee Computability
................................25
6
The Circuit Value Problem
..............................30
A The Knaster-Tarski Theorem
...........................35
7
Alternation
...........................................44
8
Problems Complete for PSPACE
........................51
9
The Polynomial-Time Hierarchy
.........................57
10
More on the Polynomial-Time Hierarchy
..................62
11
Parallel Complexity
....................................66
12
Relation of NC to Time-Space Classes
....................70
13
Probabilistic Complexity
................................74
14
BPP CE2pnnJ
......................................82
В
Chinese Remaindering
..................................86
С
Complexity of Primality Testing
.........................90
D
Berlekamp s Algorithm
.................................95
15
Interactive Proofs
......................................99
16
PSPACE
С
IP
.......................................103
17
IP
Ç
PSPACE
.......................................109
18
Probabilistically Checkable Proofs
......................113
19
NP
С
PCPin K
1)....................................119
Contents
20
More on PCP
........................................124
E A
Crash Course in
Logic
...............................128
21
Complexity of Decidable Theories
.......................135
22
Complexity of the Theory of Real Addition
..............140
23
Lower Bound for the Theory of Real Addition
............146
24
Lower Bound for Integer Addition
.......................151
25
Automata on Infinite Strings and SIS
...................154
26
Determinization of
ω-
Automata
.........................161
27
Safra s Construction
...................................167
28
Relativized Complexity
................................171
29
Nonexistence of Sparse Complete Sets
...................175
F
Unique Satisfiability
...................................180
G
Toda s
Theorem
......................................185
30
Circuit Lower Bounds and Relativized PSPACE
=
PH
___192
31
Lower Bounds for Constant Depth Circuits
...............198
H
The Switching Lemma
.................................204
I Tail Bounds
..........................................211
32
The Gap Theorem and Other Pathology
.................215
33
Partial Recursive Functions and
Godei
Numberings
.......220
34
Applications of the Recursion Theorem
..................226
J
Abstract Complexity
..................................231
35
The Arithmetic Hierarchy
..............................236
36
Complete Problems in the Arithmetic Hierarchy
..........242
37
Post s Problem
.......................................247
38
The Friedberg-Muchnik Theorem
.......................253
39
The Analytic Hierarchy
................................257
40
Kleene s Theorem
.....................................263
41
Fair Termination and Harel s Theorem
..................267
Exercises
273
Homework
1 ..............................................275
Homework
2 ..............................................276
Homework
3 ..............................................277
Homework
4 ..............................................279
Homework
5 ..............................................280
Homework
6 ..............................................281
Homework
7 ..............................................282
Homework
8 ..............................................283
Homework
9 ..............................................284
Homework
10 .............................................285
Homework
11 .............................................286
Homework
12 .............................................287
Miscellaneous Exercises
....................................289
Contents
Hints and Solutions
317
Homework
1
Solutions
......................................319
Homework
2
Solutions
......................................323
Homework
3
Solutions
......................................326
Homework
4
Solutions
......................................329
Homework
5
Solutions
......................................332
Homework
6
Solutions
......................................334
Homework
7
Solutions
......................................337
Homework
8
Solutions
......................................343
Homework
9
Solutions
......................................347
Homework
10
Solutions
.....................................351
Homework
11
Solutions
.....................................354
Homework
12
Solutions
.....................................357
Hints for Selected Miscellaneous Exercises
....................361
Solutions to Selected Miscellaneous Exercises
.................367
References
391
Notation and Abbreviations
399
Index
409
|
| adam_txt |
Contents
Preface
vii
Lectures
1
1
The Complexity of Computations
.3
2
Time and Space Complexity Classes and Savitch's Theorem
. 11
3
Separation Results
.17
4
The
Immerman-Szelepcsényi
Theorem
.22
5
Logspaee Computability
.25
6
The Circuit Value Problem
.30
A The Knaster-Tarski Theorem
.35
7
Alternation
.44
8
Problems Complete for PSPACE
.51
9
The Polynomial-Time Hierarchy
.57
10
More on the Polynomial-Time Hierarchy
.62
11
Parallel Complexity
.66
12
Relation of NC to Time-Space Classes
.70
13
Probabilistic Complexity
.74
14
BPP CE2pnnJ
.82
В
Chinese Remaindering
.86
С
Complexity of Primality Testing
.90
D
Berlekamp's Algorithm
.95
15
Interactive Proofs
.99
16
PSPACE
С
IP
.103
17
IP
Ç
PSPACE
.109
18
Probabilistically Checkable Proofs
.113
19
NP
С
PCPin'K
1).119
Contents
20
More on PCP
.124
E A
Crash Course in
Logic
.128
21
Complexity of Decidable Theories
.135
22
Complexity of the Theory of Real Addition
.140
23
Lower Bound for the Theory of Real Addition
.146
24
Lower Bound for Integer Addition
.151
25
Automata on Infinite Strings and SIS
.154
26
Determinization of
ω-
Automata
.161
27
Safra's Construction
.167
28
Relativized Complexity
.171
29
Nonexistence of Sparse Complete Sets
.175
F
Unique Satisfiability
.180
G
Toda's
Theorem
.185
30
Circuit Lower Bounds and Relativized PSPACE
=
PH
_192
31
Lower Bounds for Constant Depth Circuits
.198
H
The Switching Lemma
.204
I Tail Bounds
.211
32
The Gap Theorem and Other Pathology
.215
33
Partial Recursive Functions and
Godei
Numberings
.220
34
Applications of the Recursion Theorem
.226
J
Abstract Complexity
.231
35
The Arithmetic Hierarchy
.236
36
Complete Problems in the Arithmetic Hierarchy
.242
37
Post's Problem
.247
38
The Friedberg-Muchnik Theorem
.253
39
The Analytic Hierarchy
.257
40
Kleene's Theorem
.263
41
Fair Termination and Harel's Theorem
.267
Exercises
273
Homework
1 .275
Homework
2 .276
Homework
3 .277
Homework
4 .279
Homework
5 .280
Homework
6 .281
Homework
7 .282
Homework
8 .283
Homework
9 .284
Homework
10 .285
Homework
11 .286
Homework
12 .287
Miscellaneous Exercises
.289
Contents
Hints and Solutions
317
Homework
1
Solutions
.319
Homework
2
Solutions
.323
Homework
3
Solutions
.326
Homework
4
Solutions
.329
Homework
5
Solutions
.332
Homework
6
Solutions
.334
Homework
7
Solutions
.337
Homework
8
Solutions
.343
Homework
9
Solutions
.347
Homework
10
Solutions
.351
Homework
11
Solutions
.354
Homework
12
Solutions
.357
Hints for Selected Miscellaneous Exercises
.361
Solutions to Selected Miscellaneous Exercises
.367
References
391
Notation and Abbreviations
399
Index
409 |
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| spelling | Kozen, Dexter 1951- Verfasser (DE-588)135740436 aut Theory of computation Dexter C. Kozen London Springer 2006 XIII, 418 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in computer science Mathematische programmering gtt Informatik Mathematik Computational complexity Computer science Mathematics Recursion theory Theoretische Informatik (DE-588)4196735-5 gnd rswk-swf Komplexitätstheorie (DE-588)4120591-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Komplexitätstheorie (DE-588)4120591-1 s DE-604 Theoretische Informatik (DE-588)4196735-5 s 1\p DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2705393&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014841069&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kozen, Dexter 1951- Theory of computation Mathematische programmering gtt Informatik Mathematik Computational complexity Computer science Mathematics Recursion theory Theoretische Informatik (DE-588)4196735-5 gnd Komplexitätstheorie (DE-588)4120591-1 gnd |
| subject_GND | (DE-588)4196735-5 (DE-588)4120591-1 (DE-588)4123623-3 |
| title | Theory of computation |
| title_auth | Theory of computation |
| title_exact_search | Theory of computation |
| title_exact_search_txtP | Theory of computation |
| title_full | Theory of computation Dexter C. Kozen |
| title_fullStr | Theory of computation Dexter C. Kozen |
| title_full_unstemmed | Theory of computation Dexter C. Kozen |
| title_short | Theory of computation |
| title_sort | theory of computation |
| topic | Mathematische programmering gtt Informatik Mathematik Computational complexity Computer science Mathematics Recursion theory Theoretische Informatik (DE-588)4196735-5 gnd Komplexitätstheorie (DE-588)4120591-1 gnd |
| topic_facet | Mathematische programmering Informatik Mathematik Computational complexity Computer science Mathematics Recursion theory Theoretische Informatik Komplexitätstheorie Lehrbuch |
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