Elements of finite model theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin ; Heidelberg ; New York ; Hong Kong ; London ; Milan ; Paris ; Tokyo
Springer
2004
|
| Series: | Texts in theoretical computer science
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 315 Seiten graph. Darst. |
| ISBN: | 3540212027 |
Staff View
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| 100 | 1 | |a Libkin, Leonid |d 1965- |0 (DE-588)1041244436 |4 aut | |
| 245 | 1 | 0 | |a Elements of finite model theory |c Leonid Libkin |
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Record in the Search Index
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| adam_text | Contents
1
Introduction
............................................... 1
1.1
A Database Example
.................................... 1
1.2
An Example from Complexity Theory
...................... 4
1.3
An Example from Formal Language Theory
................. 6
1.4
An Overview of the Book
................................. 8
1.5
Exercises
............................................... 10
2
Preliminaries
.............................................. 13
2.1
Background from Mathematical Logic
...................... 13
2.2
Background from Automata and Computability Theory
...... 17
2.3
Background from Complexity Theory
...................... 19
2.4
Bibliographic Notes
...................................... 21
3
Ehrenfeucht-Praïssé
Games
................................ 23
3.1
First Inexpressibility Proofs
............................... 23
3.2
Definition and Examples of
Ehrenfeucht-Fraïssé
Games
....... 26
3.3
Games and the Expressive Power of FO
.................... 32
3.4
Rank
-А;
Types
........................................... 33
3.5
Proof of the
Ehrenfeucht-Fraïssé
Theorem
.................. 35
3.6
More Inexpressibility Results
.............................. 37
3.7
Bibliographic Notes
...................................... 40
3.8
Exercises
............................................... 41
4
Locality and Winning Games
.............................. 45
4.1
Neighborhoods, Hanf-locality, and Gaifman-locality
.......... 45
4.2
Combinatorics of Neighborhoods
.......................... 49
4.3
Locality of FO
.......................................... 51
4.4
Structures of Small Degree
............................... 54
4.5
Locality of FO Revisited
................................. 57
4.6
Bibliographic Notes
...................................... 62
4.7
Exercises
............................................... 63
XII Contents
5
Ordered Structures
........................................ 67
5.1
Invariant Queries
........................................ 67
5.2
The Power of Order-invariant FO
.......................... 69
5.3
Locality of Order-invariant FO
............................ 73
5.4
Bibliographic Notes
...................................... 83
5.5
Exercises
............................................... 83
6
Complexity of First-Order Logic
........................... 87
6.1
Data, Expression, and Combined Complexity
............... 87
6.2
Circuits and FO Queries
................................. 89
6.3
Expressive Power with Arbitrary Predicates
................. 93
6.4
Uniformity and AC0
..................................... 95
6.5
Combined Complexity of FO
.............................. 99
6.6
Parametric Complexity and Locality
....................... 99
6.7
Conjunctive Queries
.....................................102
6.8
Bibliographic Notes
......................................108
6.9
Exercises
...............................................109
7
Monadic Second-Order Logic and Automata
...............113
7.1
Second-Order Logic and Its Fragments
.....................113
7.2
MSO Games and Types
..................................116
7.3
Existential and Universal MSO on Graphs
..................119
7.4
MSO on Strings and Regular Languages
....................124
7.5
FO on Strings and Star-Free Languages
....................127
7.6
Tree Automata
..........................................129
7.7
Complexity of MSO
.....................................133
7.8
Bibliographic Notes
......................................136
7.9
Exercises
...............................................137
8
Logics with Counting
......................................141
8.1
Counting and Unary Quantifiers
...........................141
8.2
An Infinitary Counting Logic
.............................145
8.3
Games for £^(Cnt)
....................................151
8.4
Counting and Locality
...................................153
8.5
Complexity of Counting Quantifiers
........................155
8.6
Aggregate Operators
.....................................158
8.7
Bibliographic Notes
......................................161
8.8
Exercises
...............................................161
9
Turing Machines and Finite Models
.......................165
9.1
Trakhtenbrot s Theorem and Failure of Completeness
........165
9.2
Fagin s Theorem and NP
.................................168
9.3
Bibliographic Notes
......................................174
9.4
Exercises
...............................................174
Contents
XIII
10
Fixed Point Logics and Complexity Classes
................177
10.1
Fixed Points of Operators on Sets
.........................178
10.2
Fixed Point Logics
.......................................180
10.3
Properties of LFP and IFP
...............................184
10.4
LFP, PFP, and Polynomial Time and Space
................192
10.5
Datalog
and LFP
......................................195
10.6
Transitive Closure Logic
...................................199
10.7
A Logic for Ptime?
......................................204
10.8
Bibliographic Notes
......................................206
10.9
Exercises
...............................................207
11
Finite Variable Logics
.....................................211
11.1
Logics with Finitely Many Variables
.......................211
11.2
Pebble Games
...........................................215
11.3
Definability of Types
.....................................220
11.4
Ordering of Types
.......................................225
11.5
Canonical Structures and the Abiteboul-Vianu Theorem
......229
11.6
Bibliographic Notes
......................................232
11.7
Exercises
...............................................233
12
Zero-One Laws
............................................235
12.1
Asymptotic Probabilities and Zero-One Laws
...............235
12.2
Extension Axioms
.......................................238
12.3
The Random Graph
.....................................241
12.4
Zero-One Law and Second-Order Logic
.....................243
12.5
Almost Everywhere Equivalence of Logics
..................245
12.6
Bibliographic Notes
......................................246
12.7
Exercises
...............................................247
13
Embedded Finite Models
..................................249
13.1
Embedded Finite Models: the Setting
......................249
13.2
Analyzing Embedded Finite Models
........................252
13.3
Active-Generic Collapse
..................................256
13.4
Restricted Quantifier Collapse
.............................260
13.5
The Random Graph and Collapse to MSO
..................265
13.6
An Application: Constraint Databases
.....................267
13.7
Bibliographic Notes
......................................270
13.8
Exercises
...............................................271
14
Other Applications of Finite Model Theory
................275
14.1
Finite Model Property and Decision Problems
...............275
14.2
Temporal and Modal Logics
..............................278
14.3
Constraint Satisfaction and Homomorphisms of Finite Models
. 285
14.4
Bibliographic Notes
......................................288
XIV Contents
References
.....................................................291
List of Notation
...............................................305
Index
..........................................................307
Name Index
...................................................313
|
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| indexdate | 2024-07-09T19:59:01Z |
| institution | BVB |
| isbn | 3540212027 |
| language | German |
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| spelling | Libkin, Leonid 1965- (DE-588)1041244436 aut Elements of finite model theory Leonid Libkin Berlin ; Heidelberg ; New York ; Hong Kong ; London ; Milan ; Paris ; Tokyo Springer 2004 XIV, 315 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in theoretical computer science Endliche Modelltheorie - Lehrbuch Model theory Endliche Modelltheorie (DE-588)4615978-2 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Endlicher Graph (DE-588)4283258-5 gnd rswk-swf Komplexität (DE-588)4135369-9 gnd rswk-swf Endliche Modelltheorie (DE-588)4615978-2 s DE-604 Komplexität (DE-588)4135369-9 s Algorithmus (DE-588)4001183-5 s Finite-Elemente-Methode (DE-588)4017233-8 s Endlicher Graph (DE-588)4283258-5 s Erscheint auch als Online-Ausgabe 978-3-662-07003-1 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012846339&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Libkin, Leonid 1965- Elements of finite model theory Endliche Modelltheorie - Lehrbuch Model theory Endliche Modelltheorie (DE-588)4615978-2 gnd Algorithmus (DE-588)4001183-5 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Endlicher Graph (DE-588)4283258-5 gnd Komplexität (DE-588)4135369-9 gnd |
| subject_GND | (DE-588)4615978-2 (DE-588)4001183-5 (DE-588)4017233-8 (DE-588)4283258-5 (DE-588)4135369-9 |
| title | Elements of finite model theory |
| title_auth | Elements of finite model theory |
| title_exact_search | Elements of finite model theory |
| title_full | Elements of finite model theory Leonid Libkin |
| title_fullStr | Elements of finite model theory Leonid Libkin |
| title_full_unstemmed | Elements of finite model theory Leonid Libkin |
| title_short | Elements of finite model theory |
| title_sort | elements of finite model theory |
| topic | Endliche Modelltheorie - Lehrbuch Model theory Endliche Modelltheorie (DE-588)4615978-2 gnd Algorithmus (DE-588)4001183-5 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Endlicher Graph (DE-588)4283258-5 gnd Komplexität (DE-588)4135369-9 gnd |
| topic_facet | Endliche Modelltheorie - Lehrbuch Model theory Endliche Modelltheorie Algorithmus Finite-Elemente-Methode Endlicher Graph Komplexität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012846339&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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