Verifying weak and strong k-step opacity in discrete-event systems✩

Opacity is an important system-theoretic property expressing whether a system may reveal its secret to a passive observer (an intruder) who knows the structure of the system but has only limited observations of its behavior. Several notions of opacity have been discussed in the literature, including current-state opacity, k-step opacity, and infinite-step opacity. We investigate weak and strong kstep opacity, the notions that generalize both current-state opacity and infinite-step opacity, and ask whether the intruder is not able to decide, at any time instant, when respectively whether the system was in a secret state during the last k observable steps. We design a new algorithm verifying weak k-step opacity, the complexity of which is lower than the complexity of existing algorithms and does not depend on the parameter k, and show how to use it to verify strong k-step opacity by reducing strong k-step opacity to weak k-step opacity. The complexity of the resulting algorithm is again better than the complexity of existing algorithms and does not depend on the parameter k.& COPY; 2023 Elsevier Ltd. All rights reserved.

Automated summary

Opacity is an important property in system theory that determines whether a system can keep its secrets from passive observers with limited observations. This study focuses on weak and strong k-step opacity, proposing a new algorithm to verify weak k-step opacity, which has lower complexity and is not dependent on the parameter k. The algorithm can also be used to verify strong k-step opacity by reducing it to weak k-step opacity, achieving better complexity and independence from the parameter k.