多项式循环程序的秩函数探测  

Detection of Ranking Functions of Polynomial Loop Programs

作　　者：李轶[1] 冯勇[1] LI Yi;FENG Yong(Chongqing Institute of Green and Intelligent Technology,Chinese Academy of Sciences,Chongqing 401120,China)

机构地区：[1]中国科学院重庆绿色智能技术研究院

出　　处：《软件学报》2019年第11期3243-3258,共16页Journal of Software

基　　金：国家自然科学基金(61572024,61103110,11671377);重庆市自然科学基金(cstc2019jcyj-msxm X0638)~~

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.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.

关 键 词：可信计算 多分支循环程序 终止性 秩函数 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]