Assessment of initial-state-opacity in live and bounded labeled Petri net systems via optimization techniques

Opacity is a property of discrete event systems (DES) that is related to the possibility of hiding a secret to external observers, the so called intruders. If the secret is the system initial state, then the related opacity problem is referred to as Initial State Opacity (ISO). This paper gives a necessary and sufficient condition to check ISO in DES modeled as bounded and live labeled Petri nets (PNs). The proposed approach relies on both the algebraic representation of labeled PNs dynamic, and on their structural representation in terms of minimal support T-invariants. The proposed necessary and sufficient condition enables ISO assessment by means of the solution of Integer Linear Programming problems, which can be efficiently solved nowadays by means of off-the-shelf optimization tools.