Verifying Weak and Strong k-Step Opacity in Discrete-Event Systems

TL;DR

This paper introduces more efficient algorithms for verifying weak and strong k-step opacity in discrete-event systems, improving computational complexity and independence from the parameter k.

Contribution

It presents new algorithms for verifying weak and strong k-step opacity with lower complexity and no dependence on k, and reduces strong to weak k-step opacity verification.

Findings

New algorithm for weak k-step opacity with lower complexity.

Verification of strong k-step opacity via reduction to weak k-step opacity.

Algorithms' complexity is independent of the parameter k.

Abstract

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 k-step 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 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.