自從2011年被提出以後，性質導向可達性演算法已經被公認為目前最佳的模型檢查引擎。然而目前還有許多案例為性質導向可達性演算法無法解決，因此改良性質導向可達性演算法一直都是個重要的問題。在這篇論文中，我們將性質導向可達性演算法與麥克米倫內插法結合使其可以跳過遞迴封鎖方塊階段所花費的巨量時間藉此改善效能。實驗結果顯示我們方法之效能在世界硬體模型檢查比賽中可以解決比性質導向可達性演算法與麥克米倫內插法更多的案例。

Property directed reachability / IC3 (PDR) has been recognized to be the most powerful model checking engine since it was proposed in 2011. However, there are still a lot of benchmarks which cannot be solved by PDR. The demand of improving PDR is quite urgent. In this thesis, we proposed a method combining PDR with McMillan''s interpolant to help PDR skip the huge runtime during recursive blocking cube phase to improve the performance. The experimental result shows that our method can solve more cases than the original PDR and McMillan''s interpolation-based model checker on HWMCC''s benchmarks.

誌謝 i
中文摘要 ii
Abstract iii
Contents iv
List of Figures vi
List of Tables vii
1 Introduction 1
1.1 Related Works 2
1.2 Contributions of the Thesis 3
1.3 Organizations of the Thesis 3
2 Preliminaries 4
2.1 Propositional Satisfiability 4
2.2 Finite State Transition System 4
2.3 Model Checking Problem 5
2.4 Bounded Model Checking 6
2.5 Interpolation Based Model Checking 8
2.6 Property Directed Reachability 12
3 PDR with Interpolant Refinement 15
3.1 Motivation 15
3.2 Implementation 19
3.2.1 Blocking Phase 21
3.2.2 Refining Phase 23
3.2.3 Propagating Phase 24
3.3 Correctness 26
4 Case Study 27
4.1 Strenght and Weakness 27
4.2 Cases We Gain 28
4.3 Cases We Lose 32
5 Experimental Results 33
6 Conclusion and Future Work 42
Reference 43

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