ISBN: 3-540-63982-9
TITLE: Automatic Verification of Sequential Infinite-State Processes
AUTHOR: Burkart, Olaf
TOC:

1. Introduction 1 
1.1 Sequential Processes 2 
1.2 Model Checking 3 
1.3 Equivalence Checking 5 
1.4 Organisation of This Book 6 
2. Background 9 
2.1 Introduction 9 
2.2 Fixpoint Theory 9 
2.2.1 Ordered Sets 9 
2.2.2 Fixpoint Theorems 12 
2.3 Relations and Rewrite Systems 13 
2.3.1 Relations 14 
2.3.2 Rewrite Systems 14 
2.4 Context-Free Languages 15 
2.5 Processes and Labelled Transition Graphs 17 
2.5.1 Behavioural Equivalences 20 
2.5.2 Normedness and Determinism 21 
2.6 Context-Free Processes 22 
2.6.1 Syntax and Semantics 23 
2.6.2 Normedness 28 
2.6.3 Self-bisimulations 30 
3. Pushdown Processes 33 
3.1 Introduction 33 
3.2 Syntax and Semantics 34 
3.3 Expressiveness 38 
3.4 PDPA Laws 40 
3.5 Pushdown Normal Form 43 
3.6 Parallel Composition 48 
3.6.1 Example 50 
3.7 Parallel Decomposition and 2-PDNF 51 
3.8 Related work 55 
3.8.1 Context-Free Graphs 56 
3.8.2 Prefix Transition Graphs 58 
3.8.3 Pushdown Transition Graphs 58 
3.8.4 Equational graphs 59 
3.8.5 MSOL Definable Hypergraphs 62 
3.8.6 BPA with the state operator 64 
4. Model Checking 67 
4.1 Introduction 67 
4.2 The Modal -Calculus 67 
4.2.1 Syntax 68 
4.2.2 Semantics 70 
4.2.3 Continuity 72 
4.2.4 Alternation Depth 73 
4.3 Assertion-Based Semantics 74 
4.3.1 A Motivating Example 75 
4.3.2 Definition of Assertion-Based Semantics 76 
4.3.3 Properties of Assertion-Based Semantics 77 
4.4 Verifying Behavioural Properties 96 
4.4.1 Hierarchical Equational -Formulas 96 
4.4.2 The Model Checking Algorithm 100 
4.4.3 A Working Example 110 
4.5 Expressiveness of the modal -calculus 111 
5. Equivalence Checking 115 
5.1 Introduction 115 
5.2 The Bisimulation Equivalence Problem 115 
5.3 Separability 116 
5.4 Deciding Bisimilarity of Normed BPA 124 
5.5 A Bound for Separability 130 
5.6 The Algorithm 137 
5.6.1 Bisimulation Bases 138 
5.6.2 The Computation of an Initial Base 140 
5.6.3 The Branching Algorithm 146 
5.6.4 Summary of the Decision Procedure 148 
6. Summary and Perspectives 151 
6.1 Summary of the Main Results 151 
6.2 Perspectives 152 
6.2.1 Model Checking 152 
6.2.2 Equivalence Checking 153 
6.2.3 Regularity of Context-Free Processes 154 
Index 161 
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