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Journal of Software:2014.25(6):1133-1142

有界闭域上的线性赋值循环终止性分析
李轶,吴文渊,冯勇
(中国科学院 重庆绿色智能技术研究院 自动推理与认知重庆市重点实验室, 重庆 401120)
Termination Analysis of Loops with Linear Assignment over Closed and Bounded Domains
LI Yi,WU Wen-Yuan,FENG Yong
(Chongqing Key Laboratory of Automated Reasoning and Cognition, Automated Reasoning and Cognition Center, Chongqing Institute of Green and Intelligent Technology, The Chinese Academy of Sciences, Chongqing 401120, China)
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Received:September 03, 2012    Revised:February 04, 2013
> 中文摘要: 对有界闭域上的线性赋值循环程序终止性问题进行研究.利用Jordan 标准型技术将原循环程序的终止性问题约减为终止性等价的具有简单结构的循环程序的终止性问题.证明了当线性迭代映射满足一定条件时,该类循环程序不可终止的充分必要条件是:迭代映射在有界闭域上有不动点或周期轨.
Abstract:Termination of linear programs over closed and bounded domains is analyzed in this paper. The termination of this class of loops can be reduced to that of another class of loops by means of Jordan canonical forms. It has been shown that under some condition, this kind of loops do not terminate over the domains if and only if there exist fixed points or periodic orbits in the domains.
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基金项目:国家自然科学基金(61103110);重庆市科技攻关项目(cstc2012ggB40004) 国家自然科学基金(61103110);重庆市科技攻关项目(cstc2012ggB40004)
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李轶,吴文渊,冯勇.有界闭域上的线性赋值循环终止性分析.软件学报,2014,25(6):1133-1142

LI Yi,WU Wen-Yuan,FENG Yong.Termination Analysis of Loops with Linear Assignment over Closed and Bounded Domains.Journal of Software,2014,25(6):1133-1142