Title: geometric quantifier elimination heuristics for automatically generating octagonal and max-plus invariants
Author: Kapur Deepak
; Zhang Zhihai
; Horbach Matthias
; Zhao Hengjun
; Lu Qi
; Nguyen ThanhVu
Keyword: Abstracting
Source: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Issued Date: 2013
Volume: 7788, Pages: 189-228 Indexed Type: EI
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
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. 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. Language: 英语
Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/15627
Appears in Collections: 软件所图书馆_期刊论文
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Recommended Citation:
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),2013-01-01,7788:189-228.
