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中文摘要：
程序变量的值范围信息对于编译器优化、程序分析与验证等应用至关重要.抽象解释理论提供了一种通用框架为程序变量计算近似的但是可靠的值范围.然而该框架下已有的数值抽象域在表达非凸性质方面存在一定的局限性,影响了值范围分析的精度.文中基于抽象解释理论,提出一个新的数值抽象域——单变量区间线性不等式抽象域.其主要思想是使用单变量区间线性不等式约束作为域元素的约束表示方法.该抽象域的表达能力强于经典的区间抽象域,并允许表达某类非凸、非连通性质.同时,其域操作存在高效的实现算法.该抽象域具有很强的可扩展性,能够应用在实际大规模的程序分析中.
英文摘要：
interpretation provides a general framework to compute statically approximate but sound value ranges for program variables.However,most existing numerical abstract domains under the framework have limitations in expressing non-convex properties,which may lead to imprecision during the value range analysis.This paper proposes a new numerical abstract domain under the framework of abstract interpretation,namely an abstract domain of one-variable interval linear inequalities.The main idea is to use one-variable interval linear inequality constraints as the representation of domain elements.The new domain is more expressive than the classic interval abstract domain and allows expressing certain non-convex,unconnected properties.Moreover,its domain operations can be implemented via efficient algorithms.Thus,it has high scalability and can be applied in large-scale program analysis in practice.
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