Verification of $K$ -Step Opacity and Analysis of Its Complexity

Motivated by security and privacy considerations in a variety of applications of discrete event systems, we describe and analyze the computational complexity required for verifying the notion of K -step opacity for systems that are modeled as nondeterministic finite automata with partial observation on their transitions. Specifically, a system is K-step opaque if, at any specific point within the last K observations, the entrance of the system state to a given set of secret states remains opaque (uncertain) to an intruder who has complete knowledge of the system model and observes system activity through some natural projection map. We provide two methods for verifying K -step opacity using two different state estimator constructions, and analyze the computational complexity of both.