On ranking functions for single-path linear-constraint loops

被引:0
|
作者
Yi Li
Wenyuan Wu
Yong Feng
机构
[1] Chongqing Institute of Green and Intelligent Technology,
[2] Chinese Academy of Sciences,undefined
来源
International Journal on Software Tools for Technology Transfer | 2020年 / 22卷
关键词
Software reliability; Program termination; Linear ranking functions; Farkas’ lemma;
D O I
暂无
中图分类号
学科分类号
摘要
Program termination is a fundamental research topic in program analysis. In this paper, we present a new complete polynomial-time method for the existence problem of linear ranking functions for single-path loops described by a conjunction of linear constraints, when variables range over the reals (or rationals). Unlike existing methods, our method does not depend on Farkas’ Lemma and provides us with counterexamples to existence of linear ranking functions, when no linear ranking function exists. In addition, we extend our results established over the rationals to the setting of the integers. This deduces an alternative approach to deciding whether or not a given SLC loop has a linear ranking function over the integers. Finally, we prove that the termination of bounded single-path linear-constraint loops is decidable over the reals (or rationals).
引用
收藏
页码:655 / 666
页数:11
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