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DOI:
Journal of Software:2008.19(1):39-47

变量极小不可满足在模型检测中的应用
陈振宇,陶志红,KLEINEBüNINGHans,王立福
(东南大学 计算机科学与工程学院,江苏 南京 210096;北京大学 软件与微电子学院,北京 100871;Department of Computer Science, University of Paderborn, Paderborn 33095, Germany)
Applying Variable Minimal Unsatisfiability in Model Checking
CHEN Zhen-Yu,TAO Zhi-Hong,KLEINE BüNING Hans,WANG Li-Fu
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Received:May 25, 2006    Revised:November 03, 2006
> 中文摘要: 提出一个结合变量抽象和有界模型检测(BMC)的验证框架,用于证明反例不存在或输出存在反例.引入变量极小不可满足(VMU)的数学概念来驱动抽象精化的验证过程.一个VMU公式F的变量集合是保证其不可满足性的一个极小集合.严格证明了VMU驱动的精化满足抽象精化框架中的两个理想性质:有效性和极小性.虽然VMU的判定问题和极小不可满足(MU)一样难,即DP完全的,该案例研究表明,在变量抽象精化过程中,VMU比MU更为有效.
Abstract:This paper presents a framework combining variable abstraction with bounded model checking, in order to prove the counterexamples' absence or establish the counterexamples' existence. A mathematical definition of variable minimal unsatisfiability (VMU) is introduced to drive this abstraction refinement process. The set of variables of VMU formula is a minimal one guaranteeing its unsatisfiability. Furthermore, the authors prove that VMU-driven refinement is valid and minimal by mathematical reasoning. Although the determining problem of VMU is as hard as the well-known problem called minimal unsatisfiability (MU), i.e. DP-complete, the case study has shown that VMU could be more effective than MU in variable abstraction refinement process.
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基金项目:Supported by the National Natural Science Foundation of China under Grant Nos.60425206, 60773104, 60403016, 60633010 (国家自然科学基金); in Part by the Jiangsu Planned Projects for Postdoctoral Research Funds of China under Grant No.0701003B (江苏省博士后科研资助计划) Supported by the National Natural Science Foundation of China under Grant Nos.60425206, 60773104, 60403016, 60633010 (国家自然科学基金); in Part by the Jiangsu Planned Projects for Postdoctoral Research Funds of China under Grant No.0701003B (江苏省博士后科研资助计划)
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陈振宇,陶志红,KLEINE BüNING Hans,王立福.变量极小不可满足在模型检测中的应用.软件学报,2008,19(1):39-47

CHEN Zhen-Yu,TAO Zhi-Hong,KLEINE BüNING Hans,WANG Li-Fu.Applying Variable Minimal Unsatisfiability in Model Checking.Journal of Software,2008,19(1):39-47