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GRAPH STRUCTRE AND MONADIC SECOND-ORDER LOGIC A LANGUAGE-THEORETIC APPROACH2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

GRAPH STRUCTRE AND MONADIC SECOND-ORDER LOGIC A LANGUAGE-THEORETIC APPROACH
  • BRUNO COURCELLE JOOST ENGELFRIET 著
  • 出版社： CAMBRIDGE UNIVERSITY PRESS
  • ISBN：0521898331
  • 出版时间：2012
  • 标注页数：728页
  • 文件大小：258MB
  • 文件页数：741页
  • 主题词：

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图书目录

Introduction1

1 Overview16

1.1 Context-free grammars17

1.2 Inductive sets of properties and recognizability28

1.3 Monadic second-order logic40

1.4 Two graph algebras46

1.5 Fixed-parameter tractability53

1.6 Decidability of monadic second-order logic56

1.7 Graph transductions58

1.8 Monadic second-order logic with edge set quantifications68

1.9 Relational structures74

1.10 References78

2 Graph algebras and widths of graphs80

2.1 Algebras and terms81

2.2 Graphs87

2.3 The HR algebra of graphs with sources99

2.4 Tree-decompositions121

2.5 The VR algebra of simple graphs with ports144

2.6 Many-sorted graph algebras176

2.7 References185

3 Equational and recognizable sets in many-sorted algebras188

3.1 The equational sets of an algebra189

3.2 Transformations of equation systems206

3.3 Intermezzo on automata221

3.4 The recognizable sets of an algebra227

3.5 References259

4 Equational and recognizable sets of graphs260

4.1 HR-equational sets of graphs261

4.2 HR-recognizable sets of graphs281

4.3 VR-equational sets of simple graphs292

4.4 VR-recognizable sets of simple graphs305

4.5 HR- and VR-equational and recognizable sets312

4.6 References313

5 Monadic second-order logic315

5.1 Relational structures and logical languages315

5.2 Graph properties expressible in monadic second-order logic331

5.3 Monadic second-order logic and recognizability358

5.4 Decidable monadic second-order theories408

5.5 Logical characterization of recognizability409

5.6 Equivalences of logical formulas416

5.7 References425

6 Algorithmic applications427

6.1 Fixed-parameter tractable algorithms for model-checking428

6.2 Decomposition and parsing algorithms433

6.3 Monadic second-order formulas compiled into fiinite automata439

6.4 Other monadic second-order problems solved with automata493

6.5 References503

7 Monadic second-order transductions505

7.1 Defiinitions and basic properties506

7.2 The Equationality Theorem for the VR algebra534

7.3 Graph transductions using incidence graphs555

7.4 The Equationality Theorem for the HR algebra559

7.5 Decidability of monadic second-order satisfiiability problems566

7.6 Questions about logical characterizations of recognizability574

7.7 References576

8 Transductions of terms and words578

8.1 Terminology580

8.2 Tree-walking transducers585

8.3 The basic characterization591

8.4 From jumping to walking593

8.5 From global to local tests595

8.6 Multi bottom-up tree-to-word transducers604

8.7 Attribute grammars and macro tree transducers610

8.8 Nondeterminism613

8.9 VR-equational sets of terms and words614

8.10 References618

9 Relational structures621

9.1 Two types of ternary relational structures related to ordered sets622

9.2 Relational structures of bounded tree-width629

9.3 Terms denoting relational structures636

9.4 Sparse relational structures651

9.5 References685

Conclusion and open problems686

References691

Index of notation711

Index721

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