Transformations between opacity for discrete-event systems

Opacity is an important property in information-flow security. It characterizes whether the secret behavior of a system is ambiguous to a potentially malicious intruder who knows the structure of the system. Several notions of standard opacity have been introduced in the literature, including current-state opacity, initial-state opacity,
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-step opacity, infinite-step opacity, etc. Subsequently, strong versions of these opacity have been proposed to improve the confidentiality of the system. To better understand the differences between opacity of different notions, the transformations have always been concerned. Since the existing transformations are only between several standard opacity, it would be of interest to consider the transformations between strong current-state opacity and standard infinite-step opacity. We make some changes based on the original system to construct a new system that can implement the transformations between strong current-state opacity and standard infinite-step opacity. The necessary and sufficient conditions for holding the transformations between them are also provided. Finally, several examples are given to illustrate the feasibility of these transformations.