On two-way observer and its application to the verification of infinite-step and K-step opacity

We investigate the verification of the properties of infinite-step opacity and K-step opacity for partially-observed discrete event systems. A system is said to be infinite-step opaque (respectively, K-step opaque) if the intruder can never determine for sure that the system was in a secret state for any instant within infinite steps (respectively, K steps) prior to that particular instant. We derive a new separation principle for state estimates which characterizes the information dependence in this opacity verification problem. A new information structure called the two-way observer is proposed. Based on the two-way observer, we provide new algorithms for the verification of infinite-step opacity and the verification of K-step opacity, respectively. We show that the proposed verification algorithms have lower computational complexity than the known algorithms in the literature.