有界闭域上的线性赋值循环终止性分析*

摘要

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.%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。