Characterization of co-observable languages and formulas for their super/sublanguages
Characterization of co-observable languages and formulas for their super/sublanguages
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DOI：
10.1109/tac.2005.844724
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发表时间：
2005-04
影响因子：
6.8
通讯作者：
S. Takai;Ratnesh Kumar;T. Ushio
中科院分区：
文献类型：
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作者：
S. Takai;Ratnesh Kumar;T. Ushio
在离散事件系统的分散监督控制的背景下，我们提出了几种基于不动点的共同可观察语言的特征，包括C&P /spl或/ D&A共同可观察语言，C&P共同可观察语言和D&A共同可观察语言。我们还为每个类提供了计算父/子语言的公式。在共观察语言类在交/并下不闭合的情况下，我们给出了所给出的上/子语言公式的上界/下界。超级/子语言的计算以及它们的上界/下界的计算导致了其他类共同可观察语言的引入，即强C&P共同可观察语言、强D&A共同可观察语言、局部可观察语言和强局部可观察语言。给出了上述语言类的不动点特征，并研究了它们在交/并下的闭包性。我们还研究了不动算子是否保留前缀闭包、相对闭包（也称为L/sub m/(G)-闭包）和可控制性。
We present fixed-point based characterization of several classes of co-observable languages that are of interest in the context of decentralized supervisory control of discrete-event systems, including C&P /spl or/ D&A co-observable languages, C&P co-observable languages, and D&A co-observable languages. We also provide formulas for computing super/sublanguages for each of these classes. In cases where the class of co-observable languages is not closed under intersection/union, we provide upper/lower bound of the super/sublanguage formula we present. The computation of super/sublanguages and also computation of their upper/lower bounds has lead to the introduction of other classes of co-observable languages, namely, strongly C&P co-observable languages, strongly D&A co-observable languages, locally observable languages, and strongly locally observable languages. Fixed-point based characterization of all the above language classes is also given, and their closure under intersection/union is investigated. We also study whether the fixed-point operator preserves prefix closure, relative closure (also called L/sub m/(G)-closure), and controllability.