锚定LTL分离

Grgur Petric Maretic, M. Dashti, D. Basin
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引用次数: 2

摘要

Gabbay分离定理是线性时间逻辑的一个基本结果。我们证明,当且仅当从LTL到只有未来时间连接词的线性时间逻辑的转换是初等的,分离受限的LTL公式类(称为锚定LTL)是初等的。为了证明这一结果,我们定义了LTL的正则分离,并建立了锚定LTL公式的正则分离与识别这些公式的ω自动机之间的对应关系。锚定LTL公式的规范分离还有两个进一步的应用。首先,构造性地证明了任何LTL性质的安全闭包都是LTL性质,从而证明了LTL的分解定理:每一个LTL公式都等价于一个安全LTL公式和一个活跃LTL公式的合取。其次,我们描述了LTL的安全性、活跃性、绝对活跃性、稳定性和公平性。我们的描述是有效的:我们将决定LTL公式是否定义这些属性的问题简化为LTL的有效性问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Anchored LTL separation
Gabbay's separation theorem is a fundamental result for linear temporal logic (LTL). We show that separating a restricted class of LTL formulas, called anchored LTL, is elementary if and only if the translation from LTL to the linear temporal logic with only future temporal connectives is elementary. To prove this result, we define a canonical separation for LTL, and establish a correspondence between a canonical separation of anchored LTL formulas and the ω-automata that recognize these formulas. The canonical separation of anchored LTL formulas has two further applications. First, we constructively prove that the safety closure of any LTL property is an LTL property, thus proving the decomposition theorem for LTL: every LTL formula is equivalent to the conjunction of a safety LTL formula and a liveness LTL formula. Second, we characterize safety, liveness, absolute liveness, stable, and fairness properties in LTL. Our characterization is effective: We reduce the problem of deciding whether an LTL formula defines any of these properties to the validity problem for LTL.
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