geometric quantifier elimination heuristics for automatically generating octagonal and max-plus invariants

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	geometric quantifier elimination heuristics for automatically generating octagonal and max-plus invariants
	Kapur Deepak ; Zhang Zhihai ; Horbach Matthias ; Zhao Hengjun ; Lu Qi ; Nguyen ThanhVu
刊名	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
	2013
卷号	7788 页码:189-228
关键词	Abstracting
ISSN号	0302-9743
中文摘要	Geometric heuristics for the quantifier elimination approach presented by Kapur (2004) are investigated to automatically derive loop invariants expressing weakly relational numerical properties (such as l &le x &le h or l &le ±x ±y &le h) for imperative programs. Such properties have been successfully used to analyze commercial software consisting of hundreds of thousands of lines of code (using for example, the Astre´e tool based on abstract interpretation framework proposed by Cousot and his group). The main attraction of the proposed approach is its much lower complexity in contrast to the abstract interpretation approach (O(n ²) in contrast to O(n ⁴), where n is the number of variables) with the ability to still generate invariants of comparable strength. This approach has been generalized to consider disjunctive invariants of the similar form, expressed using maximum function (such as max (x + a,y + b,z + c,d) &le max (x + e,y + f,z + g,h)), thus enabling automatic generation of a subclass of disjunctive invariants for imperative programs as well. © Springer-Verlag Berlin Heidelberg 2013.
英文摘要	Geometric heuristics for the quantifier elimination approach presented by Kapur (2004) are investigated to automatically derive loop invariants expressing weakly relational numerical properties (such as l &le x &le h or l &le ±x ±y &le h) for imperative programs. Such properties have been successfully used to analyze commercial software consisting of hundreds of thousands of lines of code (using for example, the Astre´e tool based on abstract interpretation framework proposed by Cousot and his group). The main attraction of the proposed approach is its much lower complexity in contrast to the abstract interpretation approach (O(n ²) in contrast to O(n ⁴), where n is the number of variables) with the ability to still generate invariants of comparable strength. This approach has been generalized to consider disjunctive invariants of the similar form, expressed using maximum function (such as max (x + a,y + b,z + c,d) &le max (x + e,y + f,z + g,h)), thus enabling automatic generation of a subclass of disjunctive invariants for imperative programs as well. © Springer-Verlag Berlin Heidelberg 2013.
收录类别	EI
语种	英语
公开日期	2013-09-17
内容类型	期刊论文
源URL	[http://ir.iscas.ac.cn/handle/311060/15627]
专题	软件研究所_软件所图书馆_期刊论文
推荐引用方式 GB/T 7714	Kapur Deepak,Zhang Zhihai,Horbach Matthias,et al. geometric quantifier elimination heuristics for automatically generating octagonal and max-plus invariants[J]. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics),2013,7788:189-228.
APA	Kapur Deepak,Zhang Zhihai,Horbach Matthias,Zhao Hengjun,Lu Qi,&Nguyen ThanhVu.(2013).geometric quantifier elimination heuristics for automatically generating octagonal and max-plus invariants.Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics),7788,189-228.
MLA	Kapur Deepak,et al."geometric quantifier elimination heuristics for automatically generating octagonal and max-plus invariants".Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 7788(2013):189-228.