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110a957fc2e185a8429cb65cfa28fb0b.ppt

  • Количество слайдов: 130

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Reachability 8 Reachability 8

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Safe Invariants 10 Safe Invariants 10

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More Concretely 12 More Concretely 12

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State Space Exploration 14 State Space Exploration 14

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Refined Boolean Abstraction 16 Refined Boolean Abstraction 16

Refined Boolean Abstraction 17 Refined Boolean Abstraction 17

Invariant 18 Invariant 18

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Overview 20 Overview 20

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Safe Invariants 22 Safe Invariants 22

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45 Slide courtesy of Patrick Cousot 45 Slide courtesy of Patrick Cousot

46 Slide courtesy of Patrick Cousot 46 Slide courtesy of Patrick Cousot

47 Slide courtesy of Patrick Cousot 47 Slide courtesy of Patrick Cousot

48 Slide courtesy of Patrick Cousot 48 Slide courtesy of Patrick Cousot

Overview 49 Overview 49

Abstract Interpretation, So Far 50 Abstract Interpretation, So Far 50

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52 Diagram from Cousot, POPL 1977 52 Diagram from Cousot, POPL 1977

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Part I: Summary 61 Part I: Summary 61

Overview 62 Overview 62

Boolean Abstraction 63 Boolean Abstraction 63

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Part II: Overview 65 Part II: Overview 65

Predicate Abstraction 66 Predicate Abstraction 66

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Abstracting Assigns via WP 77 Abstracting Assigns via WP 77

WP Problem 78 WP Problem 78

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Abstracting Assignments 80 Abstracting Assignments 80

Assignment Example 81 Assignment Example 81

Assignment Example 82 Assignment Example 82

Abstracting Assumes 83 Abstracting Assumes 83

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Refined Boolean Abstraction 85 Refined Boolean Abstraction 85

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Part II: Overview 87 Part II: Overview 87

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Binary Decision Diagrams 93 Binary Decision Diagrams 93

Binary Decision Diagrams 94 Binary Decision Diagrams 94

Binary Decision Diagrams 95 Binary Decision Diagrams 95

Hash Consing + Variable Elimination 96 Hash Consing + Variable Elimination 96

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Part II: Overview 98 Part II: Overview 98

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Source Code 106 Source Code 106

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Part III: Comparison 108 Part III: Comparison 108

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Abstraction/Refinement 113 Abstraction/Refinement 113

Guarded Command Language 114 Guarded Command Language 114

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Safe Backward Invariants 117 Safe Backward Invariants 117

Predicate Abstraction 118 Predicate Abstraction 118

Free Lattice of DNF over {a, b} 119 Free Lattice of DNF over {a, b} 119

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FAIR 121 FAIR 121

Widening 122 Widening 122

Interval Widening, Revisited 123 Interval Widening, Revisited 123

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FAIR 125 FAIR 125

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Proof of Theorem 127 Proof of Theorem 127

Summary 128 Summary 128

What We Did 129 What We Did 129

Searching for Solutions 130 Searching for Solutions 130