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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 | |
| Source | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
 |
| ISSN | 0302-9743 |
| Volume | 7788Pages:189-228 |
| English Abstract | 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.; 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. |
| Indexed Type | EI |
| Keyword | Abstracting |
| Department | (1) Department of Computer Science University of New Mexico Albuquerque NM United States; (2) School of Mathematical Sciences Peking University Beijing China; (3) Institute of Software Chinese Academy of Sciences Beijing China |
| Language | 英语 |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/15627 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation 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. |
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