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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
	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.; EI; 0; 189-228; 7788
语种	英语
出处	EI
出版者	lecture notes in computer science including subseries lecture notes in artificial intelligence and lecture notes in bioinformatics
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/327767]
专题	数学科学学院
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. 2013-01-01.

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