Abstract
Opacity is a property asking whether a system may reveal its secret to a passive observer who knows the structure of the system but has only limited observations of its behavior. Several notions of opacity have been studied. Similarities among the opacity notions have been investigated via transformations, which have many potential applications. We investigate K-step opacity (K-SO), a notion that generalizes both current-state opacity and infinite-step opacity, and asks whether the intruder cannot decide, at any instant, whether or when the system was in a secret state during the last K observable steps. We provide new polynomial-time transformations among K-SO and other opacity notions. Our results lead, among others, to the general solution of an open problem concerning the computational complexity of the verification of K-SO.
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