离散事件系统不透明度概念的比较
Comparing the Notions of Opacity for Discrete-Event Systems
摘要：
不透明度是一种信息流特性，它表征了一个系统是否会向被动的观察者揭示它的秘密。在文献中已经引入了几个不透明度的概念。我们研究了基于语言的不透明度，当前状态不透明度，初始状态不透明度，初始和最终状态不透明度，K步不透明度和无限步不透明度的概念。比较这些概念是一个自然的问题，Wu和Lafortune对此进行了研究和总结，他们提供了当前状态不透明性、初始和最终状态不透明性和基于语言的不透明性之间的转换，对于前缀封闭的语言，还提供了基于语言的不透明性和初始状态不透明性之间的转换。我们扩展这些结果表明，所有讨论的概念的不透明度是相互转化。除了更深入地了解概念之间的差异外，变换还可以应用于复杂性结果。特别是，变换是可计算的多项式时间，并保持可观察的事件和确定性的数量，因此计算复杂性的验证的概念相吻合。我们提供了一个完整的和改进的复杂性图片所讨论的概念的不透明度的验证，并提高算法的复杂性，决定基于语言的不透明度，无限步不透明度，和K步不透明度。
英文摘要：
Opacity is an information flow property characterizing whether a system reveals its secret to a passive observer. Several notions of opacity have been introduced in the literature. We study the notions of language-based opacity, current-state opacity, initial-state opacity, initial-and-final-state opacity, K-step opacity, and infinite-step opacity. Comparing the notions is a natural question that has been investigated and summarized by Wu and Lafortune, who provided transformations among current-state opacity, initial-and-final-state opacity, and language-based opacity, and, for prefix-closed languages, also between language-based opacity and initial-state opacity. We extend these results by showing that all the discussed notions of opacity are transformable to each other. Besides a deeper insight into the differences among the notions, the transformations have applications in complexity results. In particular, the transformations are computable in polynomial time and preserve the number of observable events and determinism, and hence the computational complexities of the verification of the notions coincide. We provide a complete and improved complexity picture of the verification of the discussed notions of opacity, and improve the algorithmic complexity of deciding language-based opacity, infinite-step opacity, and K-step opacity.
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