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arXiv 0705.4604cs.LO
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基于一元差分逻辑的时态验证

Temporal Runtime Verification using Monadic Difference Logic

Henrik Reif Andersen, Kaare J. Kristoffersen

摘要:

在本文中,我们提出了一个算法进行运行时验证的有界时序逻辑超过定时运行。该算法由三个要素组成。首先,将待验证的有界时态公式转化为差分不等式上的一元一阶逻辑,我们称之为一元差分逻辑。其次,在定时运行的每一步,通过计算与该步的状态和时间的商来修改一元差分公式。第三,通过一元差分逻辑的判定过程来检验所得到的公式是重言式还是不可满足的。基于数据结构差分决策图,我们进一步给出了一元差分逻辑的简单决策过程。该算法是完备的,在一个非常强的意义上的一个子类的时间公式的特点是均匀monadic和它是近似的其他公式。近似值来自于这样一个事实,即并非所有不可满足或重言式公式都能在运行时验证的尽可能早的时间被识别。与现有的方法相反,所提出的算法不工作的语法重写,但采用有效的决策结构,使它们适用于在实际应用中,例如商业软件。

英文摘要:

In this paper we present an algorithm for performing runtime verification of a bounded temporal logic over timed runs. The algorithm consists of three elements. First, the bounded temporal formula to be verified is translated into a monadic first-order logic over difference inequalities, which we call monadic difference logic. Second, at each step of the timed run, the monadic difference formula is modified by computing a quotient with the state and time of that step. Third, the resulting formula is checked for being a tautology or being unsatisfiable by a decision procedure for monadic difference logic. We further provide a simple decision procedure for monadic difference logic based on the data structure Difference Decision Diagrams. The algorithm is complete in a very strong sense on a subclass of temporal formulae characterized as homogeneously monadic and it is approximate on other formulae. The approximation comes from the fact that not all unsatisfiable or tautological formulae are recognised at the earliest possible time of the runtime verification. Contrary to existing approaches, the presented algorithms do not work by syntactic rewriting but employ efficient decision structures which make them applicable in real applications within for instance business software.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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