Graph structure and monadic second order logic: a language-theoretic approach
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2012
|
| Edition: | 1. publ. |
| Series: | Encyclopedia of mathematics and its applications
138 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [691] - 710 |
| Physical Description: | XIV, 728 Seiten Diagramme |
| ISBN: | 9780521898331 0521898331 |
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MARC
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| 246 | 1 | |a Graph structure and monadic second-order logic | |
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| 300 | |a XIV, 728 Seiten |b Diagramme | ||
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Record in the Search Index
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|---|---|
| adam_text |
Contents
Foreword by
Maurice Nivat
page
xi
Introduction
1
1
Overview
16
1.1
Context-free grammars
17
1.2
Inductive sets of properties and recognizability
28
1.3
Monadic second-order logic
40
1.4
Two graph algebras
46
1.5
Fixed-parameter tractability
53
1.6
Decidability of monadic second-order logic
56
1.7
Graph transductions
58
1.8
Monadic second-order logic with edge set quantifications
68
1.9
Relational structures
74
1.10
References
78
2
Graph algebras and widths of graphs
80
2.1
Algebras and terms
81
2.2
Graphs
87
2.3
The HR algebra of graphs with sources
99
2.4
Tree-decompositions
121
2.5
The VR algebra of simple graphs with ports
144
2.6
Many-sorted graph algebras
176
2.7
References
185
3
Equational and recognizable sets in many-sorted algebras
188
3.1
The equational sets of an algebra
189
3.2
Transformations of equation systems
206
3.3
Intermezzo on automata
221
3.4
The recognizable sets of an algebra
227
3.5
References
259
viii Contents
4
Equationai and recognizable sets of graphs
260
4.1
HR-equational sets of graphs
261
4.2
HR-recognizable sets of graphs
281
4.3
VR-equational sets of simple graphs
292
4.4
VR-recognizable sets of simple graphs
305
4.5
HR- and VR-equational and recognizable sets
312
4.6
References
313
5
Monadic second-order logic
315
5.1
Relational structures and logical languages
315
5.2
Graph properties expressible in monadic
second-order logic
331
5.3
Monadic second-order logic and recognizability
358
5.4
Decidable monadic second-order theories
408
5.5
Logical characterization of recognizability
409
5.6
Equivalences of logical formulas
416
5.7
References
425
6
Algorithmic applications
427
6.1
Fixed-parameter tractable algorithms for model-checking
428
6.2
Decomposition and parsing algorithms
433
6.3
Monadic second-order formulas compiled into finite automata
439
6.4
Other monadic second-order problems solved with automata
493
6.5
References
503
7
Monadic second-order transductions
505
7.1
Definitions and basic properties
506
7.2
The Equationality Theorem for the VR algebra
534
7.3
Graph transductions using incidence graphs
555
7.4
The Equationality Theorem for the HR algebra
559
7.5
Decidability of monadic second-order satisfiability problems
566
7.6
Questions about logical characterizations of recognizability
574
7.7
References
576
8
Transductions of terms and words
578
8.1
Terminology
580
8.2
Tree-walking transducers
585
8.3
The basic characterization
591
8.4
From jumping to walking
593
8.5
From global to local tests
595
8.6
Multi
bottom-up
îree-to-word
transducers
604
8.7
Attribute grammars and macro tree transducers
610
8.8
Nondeterminism
613
8.9
VR-equational sets of terms and words
614
8.10
References
618
Contents ix
9 Relational
structures
621
9.1
Two types of ternary relational structures related
to ordered sets
622
9.2
Relational structures of bounded tree-width
629
9.3
Terms denoting relational structures
636
9.4
Sparse relational structures
651
9.5
References
685
Conclusion and open problems
686
References
691
Index of notation
711
Index
721 |
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| discipline | Mathematik |
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| isbn | 9780521898331 0521898331 |
| language | English |
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| physical | XIV, 728 Seiten Diagramme |
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| publishDateSearch | 2012 |
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| publisher | Cambridge Univ. Press |
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| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Courcelle, Bruno Verfasser (DE-588)1025653947 aut Graph structure and monadic second order logic a language-theoretic approach Bruno Courcelle ; Joost Engelfriet Graph structure and monadic second-order logic 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2012 XIV, 728 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 138 Literaturverz. S. [691] - 710 Graphentheorie (DE-588)4113782-6 gnd rswk-swf Endliche Modelltheorie (DE-588)4615978-2 gnd rswk-swf Graph theory. Finite model theory. Graphentheorie (DE-588)4113782-6 s Endliche Modelltheorie (DE-588)4615978-2 s DE-604 Engelfriet, Joost Verfasser (DE-588)1025656245 aut Encyclopedia of mathematics and its applications 138 (DE-604)BV000903719 138 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025290117&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Courcelle, Bruno Engelfriet, Joost Graph structure and monadic second order logic a language-theoretic approach Encyclopedia of mathematics and its applications Graphentheorie (DE-588)4113782-6 gnd Endliche Modelltheorie (DE-588)4615978-2 gnd |
| subject_GND | (DE-588)4113782-6 (DE-588)4615978-2 |
| title | Graph structure and monadic second order logic a language-theoretic approach |
| title_alt | Graph structure and monadic second-order logic |
| title_auth | Graph structure and monadic second order logic a language-theoretic approach |
| title_exact_search | Graph structure and monadic second order logic a language-theoretic approach |
| title_full | Graph structure and monadic second order logic a language-theoretic approach Bruno Courcelle ; Joost Engelfriet |
| title_fullStr | Graph structure and monadic second order logic a language-theoretic approach Bruno Courcelle ; Joost Engelfriet |
| title_full_unstemmed | Graph structure and monadic second order logic a language-theoretic approach Bruno Courcelle ; Joost Engelfriet |
| title_short | Graph structure and monadic second order logic |
| title_sort | graph structure and monadic second order logic a language theoretic approach |
| title_sub | a language-theoretic approach |
| topic | Graphentheorie (DE-588)4113782-6 gnd Endliche Modelltheorie (DE-588)4615978-2 gnd |
| topic_facet | Graphentheorie Endliche Modelltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025290117&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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