时间逻辑中的渐近行为

E. Asarin, Michel Blockelet, Aldric Degorre, C. Dima, C. Mu
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引用次数: 5

摘要

我们研究了无界时间算子与有界时间算子的“逼近性”,当某些时间界趋于∞时。更具体地说,对于Alur等人的参数线性时间逻辑的片段PLTL - φ和PLTL - φ中的公式,我们提供了计算所有参数趋于∞时的极限熵的算法。因此,我们可以通过将有界算子的每次出现替换为其无界版本来确定两个片段中的一个公式的极限熵是否与它的无界变换的极限熵一致。该算法首先将PLTL的两个片段转化为两类离散时间定时自动机,并分析它们的强连接分量。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Asymptotic behaviour in temporal logic
We study the "approximability" of unbounded temporal operators with time-bounded operators, as soon as some time bounds tend to ∞. More specifically, for formulas in the fragments PLTL⋄ and PLTL◻ of the Parametric Linear Temporal Logic of Alur et al., we provide algorithms for computing the limit entropy as all parameters tend to ∞. As a consequence, we can decide the problem whether the limit entropy of a formula in one of the two fragments coincides with that of its time-unbounded transformation, obtained by replacing each occurrence of a time-bounded operator into its time-unbounded version. The algorithms proceed by translation of the two fragments of PLTL into two classes of discrete-time timed automata and analysis of their strongly-connected components.
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