| 多项式循环程序的秩函数探测 |
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| 引用本文： | 李轶,冯勇. 多项式循环程序的秩函数探测[J]. 软件学报, 2019, 30(11): 3243-3258 |
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| 作者姓名： | 李轶 冯勇 |
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| 作者单位： | 中国科学院 重庆绿色智能技术研究院, 重庆 401120,中国科学院 重庆绿色智能技术研究院, 重庆 401120 |
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| 基金项目： | 国家自然科学基金（61572024，61103110，11671377）；重庆市自然科学基金（cstc2019jcyj-msxmX0638） |
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| 摘 要： | 秩函数法是循环程序终止性分析的主流方法.针对一类多分支多项式循环程序，这类程序的秩函数计算问题被证明可归结为单形上正定多项式的探测问题，从而便于利用线性规划工具Simplex去计算这类程序的秩函数.不同于现有基于柱形代数分解的量词消去算法，该方法能够在可接受的时间内计算更为复杂的多项式秩函数.
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| 关 键 词： | 可信计算 多分支循环程序 终止性 秩函数 |
| 收稿时间： | 2017-09-01 |
| 修稿时间： | 2017-11-09 |
Detection of Ranking Functions of Polynomial Loop Programs |
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| LI Yi and FENG Yong. Detection of Ranking Functions of Polynomial Loop Programs[J]. Journal of Software, 2019, 30(11): 3243-3258 |
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| Authors: | LI Yi and FENG Yong |
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| Affiliation: | Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing 401120, China and Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing 401120, China |
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| Abstract: | Synthesizing ranking functions of loop programs is the dominant method for checking their termination. In this study, the synthesis of ranking functions of a class of loop program is reduced to the detection of positive polynomial on the standard simplex. This then enables the computation of the desired ranking functions by linear programming tool. Different from the existing methods based on cylindrical algebraic decomposition, the proposed method in the study can get more expressive polynomial ranking functions within an acceptable time. |
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| Keywords: | trusted computing multi-path loop program termination ranking function |
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