Descriptive complexity:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1999
|
| Schriftenreihe: | Graduate texts in computer science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XVI, 268 S. graph. Darst. |
| ISBN: | 0387986006 9780387986005 |
Internformat
MARC
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| 100 | 1 | |a Immerman, Neil |d 1953- |e Verfasser |0 (DE-588)12076718X |4 aut | |
| 245 | 1 | 0 | |a Descriptive complexity |c Neil Immerman |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1999 | |
| 300 | |a XVI, 268 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Graduate texts in computer science | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Komplexitätstheorie - Berechnungskomplexität - Modelltheorie - Prädikatenlogik | |
| 650 | 4 | |a Computational complexity | |
| 650 | 4 | |a Logic, Symbolic and mathematical | |
| 650 | 0 | 7 | |a Berechnungskomplexität |0 (DE-588)4134751-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Modelltheorie |0 (DE-588)4114617-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Prädikatenlogik |0 (DE-588)4046974-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Komplexitätstheorie |0 (DE-588)4120591-1 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-008427325 | ||
Datensatz im Suchindex
| _version_ | 1804127056729997312 |
|---|---|
| adam_text | Contents
Preface
vii
Introduction
1
1
Background in Logic
5
1.1
Introduction
and Preliminary Definitions............
5
1.2
Ordering and Arithmetic
..................... 12
1.2.1
FOCBIT)
=
FO(PLUS, TIMES)
............. 14
1.3
Isomorphism
........................... 16
1.4
First-Order Queries
....................... 17
2
Background in Complexity
23
2.1
Introduction
........................... 23
2.2
Preliminary Definitions
..................... 24
2.3
Reductions and Complete Problems
............... 27
2.4
Alternation
............................ 34
2.5
Simultaneous Resource Classes
................. 40
2.6
Summary
............................. 41
3
First-Order Reductions
45
3.1
FOCL
............................. 45
3.2
Dual of a First-Order Query
................... 46
3.3
Complete problems for
L
and NL
................ 50
3.4
Complete Problems for
P
.................... 53
xiv Contents
4
Inductive
Definitions
57
4.1
Least Fixed Point
........................ 57
4.2
The Depth of Inductive Definitions
............... 61
4.3
Iterating First-Order Formulas
.................. 63
5
Parallelism
67
5.1
Concurrent Random Access Machines
............. 68
5.2
Inductive Depth Equals Parallel Time
.............. 70
5.3
Number of Variables Versus Number of Processors
....... 74
5.4
Circuit Complexity
....................... 77
5.5
Alternating Complexity
..................... 85
5.5.1
Alternation as Parallelism
................ 87
6
Ehrenfeucht-Fraïssé
Games
91
6.1
Definition of the Games
..................... 91
6.2
Methodology for First-Order Expressibility
........... 99
6.3
First-Order Properties Are Local
................ 102
6.4
Bounded Variable Languages
.................. 104
6.5
Zero-One Laws
......................... 107
6.6
Ehrenfeucht-Fraïssé
Games with Ordering
........... 109
7
Second-Order Logic and Fagin s Theorem
113
7.1
Second-Order Logic
....................... 113
7.2
Proof of Fagin s Theorem
.................... 115
7.3
NP-Complete Problems
..................... 119
7.4
The Polynomial-Time Hierarchy
................ 121
8
Second-Order Lower Bounds
125
8.1
Second-Order Games
...................... 125
8.2
SO3(monadic) Lower Bound on Reachability
......... 129
8.3
Lower Bounds Including Ordering
............... 133
9
Complementation and Transitive Closure
139
9.1
Normal Form Theorem for FO(LFP)
.............. 139
9.2
Transitive Closure Operators
.................. 143
9.3
Normal Form for FOCTC)
.................... 144
9.4 Logspace
is Primitive Recursive
................. 148
9.5
NSPACEH«)]
-
co-NSPACEH«)]
............... 149
9.6
Restrictions of SO
........................ 151
10
Polynomial Space
157
10.1
Complete Problems for PSPACE
................ 157
10.2
Partial Fixed Points
....................... 160
10.3
DSPACEln*]
-
VAR[fc
+ 1]................... 162
10.4
Using Second-Order Logic to Capture PSPACE
........ 165
Contents xv
11
Uniformity and
Précompilation
169
11.1
An Unbounded Number of Variables
.............. 170
11.1.1
Tradeoffs Between Variables and Quantifier Depth
... 171
11.2
First-Order Projections
..................... 171
11.3
Help Bits
............................. 176
11.4
Generalized Quantifiers
..................... 177
12
The Role of Ordering
181
12.1
Using Logic to Characterize Graphs
............... 182
12.2
Characterizing Graphs Using Ck
................ 183
12.3
Adding Counting to First-Order Logic
............. 185
12.4
Pebble Games forC*
....................... 187
12.5
Vertex Refinement Corresponds to C2
.............. 189
12.6
Abiteboul-Vianu and Otto Theorems
.............. 193
12.7
Toward a Language for Order-Independent
Ρ
.......... 199
13
Lower Bounds
203
13.1
Hastad s Switching Lemma
................... 203
13.2
A Lower Bound for REACH«
.................. 208
13.3
Lower Bound for Fixed Point and Counting
.......... 213
14
Applications
221
14.1
Databases
............................ 221
14.1.1
SQL
........................... 222
14.1.2
Datalog
......................... 224
14.2
Dynamic Complexity
...................... 226
14.2.1
Dynamic Complexity Classes
.............. 227
14.3
Model Checking
......................... 234
14.3.1
Temporal Logic
..................... 235
14.4
Summary
............................. 239
15
Conclusions and Future Directions
241
15.1
Languages That Capture Complexity Classes
.......... 241
15.1.1
Complexity on the Face of a Query
........... 243
15.1.2
Stepwise Refinement
.................. 244
15.2
Why Is Finite Model Theory Appropriate?
........... 244
15.3
Deep Mathematical Problems:
Ρ
versus NP
........... 245
15.4
Toward Proving Lower Bounds
................. 246
15.4.1
Role of Ordering
.................... 246
15.4.2
Approximation and Approximability
.......... 247
15.5
Applications of Descriptive Complexity
............ 248
15.5.1
Dynamic Complexity
.................. 248
15.5.2
Model Checking
..................... 248
15.5.3
Abstract State Machines
................ 248
15.6
Software Crisis and Opportunity
................ 249
xvi Contents
15.6.1
How can
Finite
Model
Theory Help?
.......... 250
References
251
Index
263
|
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| discipline | Informatik Mathematik |
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| spelling | Immerman, Neil 1953- Verfasser (DE-588)12076718X aut Descriptive complexity Neil Immerman New York [u.a.] Springer 1999 XVI, 268 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in computer science Hier auch später erschienene, unveränderte Nachdrucke Komplexitätstheorie - Berechnungskomplexität - Modelltheorie - Prädikatenlogik Computational complexity Logic, Symbolic and mathematical Berechnungskomplexität (DE-588)4134751-1 gnd rswk-swf Modelltheorie (DE-588)4114617-7 gnd rswk-swf Prädikatenlogik (DE-588)4046974-8 gnd rswk-swf Komplexitätstheorie (DE-588)4120591-1 gnd rswk-swf Komplexitätstheorie (DE-588)4120591-1 s DE-604 Berechnungskomplexität (DE-588)4134751-1 s Modelltheorie (DE-588)4114617-7 s Prädikatenlogik (DE-588)4046974-8 s Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008427325&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Immerman, Neil 1953- Descriptive complexity Komplexitätstheorie - Berechnungskomplexität - Modelltheorie - Prädikatenlogik Computational complexity Logic, Symbolic and mathematical Berechnungskomplexität (DE-588)4134751-1 gnd Modelltheorie (DE-588)4114617-7 gnd Prädikatenlogik (DE-588)4046974-8 gnd Komplexitätstheorie (DE-588)4120591-1 gnd |
| subject_GND | (DE-588)4134751-1 (DE-588)4114617-7 (DE-588)4046974-8 (DE-588)4120591-1 |
| title | Descriptive complexity |
| title_auth | Descriptive complexity |
| title_exact_search | Descriptive complexity |
| title_full | Descriptive complexity Neil Immerman |
| title_fullStr | Descriptive complexity Neil Immerman |
| title_full_unstemmed | Descriptive complexity Neil Immerman |
| title_short | Descriptive complexity |
| title_sort | descriptive complexity |
| topic | Komplexitätstheorie - Berechnungskomplexität - Modelltheorie - Prädikatenlogik Computational complexity Logic, Symbolic and mathematical Berechnungskomplexität (DE-588)4134751-1 gnd Modelltheorie (DE-588)4114617-7 gnd Prädikatenlogik (DE-588)4046974-8 gnd Komplexitätstheorie (DE-588)4120591-1 gnd |
| topic_facet | Komplexitätstheorie - Berechnungskomplexität - Modelltheorie - Prädikatenlogik Computational complexity Logic, Symbolic and mathematical Berechnungskomplexität Modelltheorie Prädikatenlogik Komplexitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008427325&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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