1 Model Checking E. M. Clarke, O. Grumberg, D. A. Peled

2 Model Checking Models Temporal Logics Model Checking Kripke Structure Graph (SCC) Tableaux Automata Symbolic (BDD, Fixpoint) On the Fly Partial order reduction

3 Chapter 2: Modeling Systems Modeling Concurrent Systems –Kripke Structure (S,S 0,R,L) –First Order Representation (V,S 0,R) –Granularity of Transitions Concurrent Systems –Digital Circuits (Synchronous/Asynchronous) –Programs –Concurrent Programs

4 Chapter 3: Temporal Logics CTL* –Temporal Operators –Path Quantifier –Path and State Formulas CTL and LTL –CTL/ACTL –LTL Fairness –Fairness Constraints –Fair Kripke Structure (S,R,L,F) –Fair Semantics

5 Chapter 4: Model Checking CTL Model Checking (Labeling) –CheckEU –CheckEG –Fairness (CheckFairEG) LTL Model Checking by Tableau –PSPACE/NP-Hard –Tableau Construction (s,K) –Check Self-fulfilling SCC CTL* Model Checking –CTL and LTL Subformulas –Divide and Conquer

6 Chapter 5: Binary Decision Diagrams Representing Boolean Formulas/Functions –Ordered Binary Decision Trees –Ordered Binary Decision Diagrams –OBDD Operations Representing Kripke Structure –Boolean Representation of Variables –Relation = Characterization Function –Characterization Function = OBDD –(S,S 0,R,L) = OBDDs

7 Chapter 6: Symbolic MC Fixpoint Representation –Fixpoint –Fixpoint Computation –CTL Formulas Symbolic CTL Model Checking –Quantifier Boolean Formulas –CheckEX/CheckEU/CheckEG Fairness –Fixpoint Representation of Fair EGf –CheckFairEG/CheckFairEX/CheckFairEU

8 Chapter 6(2): Symbolic MC Counterexamples and Witnesses Relational Product Computation –RelProd –Partitioned Transition Relations Symbolic LTL Model Checking –Tableaux for LTL Formulas –Product of Kripke Structures and LTL Tableaux –Fairness Constraints for Until-Subformulas –Symbolic Model Checking

9 Chapter 7: MC for  -Calculus Propositional  -Calculus –Modified Kripke Structure (S,T,L) –Relational Variables and Environments –Alternation Depth Evaluating Fixpoint Formulas –Algorithms –OBDD Representation CTL to  -Calculus Complexity

10 Chapter 9: MC and Automata Automata –Finite Words –Infinite Words Buchi Automata –Nondeterministic Buchi Automata –Generalized Buchi Automata Checking Emptiness –Double DFS –Correctness

11 Chapter 9(2): MC and Automata LTL to Automata On the Fly Model Checking Checking Language Containment Symbolically

12 Chapter 10: Partial Order Reduction Concurrency in Asynchronous Systems –Depth First Search –ample(s) versus enabled(s) Independence and Invisibility –Independence –Invisibility –Invariant under Stuttering Partial Order Reduction for LTL_x –c0 – c4

13 Chapter 10(2): Partial Order Red. Calculating Ample Sets –c0, c2, c1 – Heuristic, c3 – c3’ –Heuristic –On the Fly Reduction –Correctness Partial Order Reduction in SPIN –MC in Practice

14 Chapter 8: MC in Practice SMV Model Checker –Modules –Synchronous and interleaved Composition –Nondeterministic Transitions –Transition Relations Model Checking Example –IEEE Futurebus+ Standard

15 归类 不同类型的模型 不同类型的时序逻辑 各种模型检测算法 ( 优化方法 ) 及算法正确性分析 模型检测工具和实例

16 模型 Kripke Structures Fair Kripke Structures Modified Kripke Structures First Order Representation Digital Circuits (Synchronous/Asynchronous) Programs and Concurrent Programs Buchi Automata Generalized Buchi Automata 模型之间的 关系 模型之间的 转换 不同模型的 特点

17 时序逻辑 CTL* CTL/ACTL LTL  -Calculus 逻辑的 语法语义 不同逻辑的 关系 不同逻辑的 特点

18 模型检测相关算法 (1) CTL Model Checking (Labeling) LTL Model Checking by Tableau CTL* Model Checking Symbolic CTL Model Checking Symbolic Fair CTL Model Checking Symbolic LTL Model Checking Model Checking for  -Calculus Checking Emptiness 算法 复杂性 算法的 基本原理 算法 正确性

19 模型检测相关算法 (2) Counterexamples and Witnesses Relational Product Computation LTL to Automata CTL to  -Calculus Concurrent Programs to First Order Rep.

20 模型检测相关算法 (3) On the Fly Model Checking Partial Order Reduction Heuristics for Ample Sets Checking Language Containment Symbolically

21 模型检测算法相关数据结构 OBDD 表示方法 化简和计算 方法

22 模型检测工具 SMV – IEEE Futurebus+ Standard SPIN – Leader Election

总体课程目标 掌握模型检测基础理论 – 不同类型的模型 – 不同类型的时序逻辑 – 各种模型检测算法及算法正确性分析 具备模型检测方法研究及应用的能力 – 能够较快阅读本专业方向的文献 – 能够针对特定问题设计模型检测算法 – 能够应用模型检测方法和工具对特定问题进行验证