GRAPH STRUCTRE AND MONADIC SECOND-ORDER LOGIC A LANGUAGE-THEORETIC APPROACHPDF电子书下载

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

4 Equational 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 fiinite 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 Defiinitions 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 satisfiiability 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 tree-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

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