Symbolic Verification of Current-State Opacity of Discrete Event Systems Using Petri Nets

Given a discrete event system, it is said to be opaque if an intruder who can partially observe system behavior cannot infer that the system is necessarily in a predefined secret. A discrete event system is current-state opaque if an intruder is never able to verify whether the current state of the system is within the secret states. This article addresses the verification of current-state opacity of a discrete event system modeled with Petri nets, where the secret is defined as a set of states. The existing methods cannot deal with large-sized systems due to the curse of dimensionality. Multi-valued decision diagrams (MDDs) are widely accepted as an efficient and compact data structure for representing the extremely large reachability sets of Petri nets. We show that MDDs can be used in Petri nets with partial observable transitions and propose an approach for the verification of current-state opacity for bounded Petri nets. It is shown by experimental studies that the symbolic approach is practically more efficient than traditional techniques such as basis reachability graphs (BRGs).