Non-termination Analysis of Linear Loop Programs with Conditionals

Zhongqin Bi, Meijing Shan, Bin Wu
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引用次数: 1

Abstract

Non-termination analysis of loop programs plays a central role in many applications, especially in the field of safety critical softwares. This paper presents a method to analyze non-termination of linear programs with conditionals. We transform the linear loop programs with conditionals into the nested linear loop programs, and then check whether the inner loop terminates or not by the positive eigenvalues and their corresponding eigenvectors. If one of the inner loop in the nested linear loop is non-terminating, then the linear loop is non-terminating. Otherwise, we need to use ranking function or finite differences of expressions over transition systems to analyze the termination of the outer loop.
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带条件的线性循环程序的非终止分析
循环程序的非终止分析在许多应用中起着核心作用,特别是在安全关键软件领域。本文给出了一种分析带条件的线性规划的非终止性的方法。我们将带条件的线性循环程序转化为嵌套的线性循环程序,然后通过正特征值及其对应的特征向量来检验内循环是否终止。如果嵌套线性循环中的一个内循环是非终止的,则该线性循环是非终止的。否则,我们需要使用排序函数或转换系统上表达式的有限差分来分析外循环的终止。
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