Adjacent initial states-based differential privacy for probabilistic labeled Petri nets

Privacy protection has received widespread attention from the community of discrete event systems to protect the sensitive information of users or organizations from being leaked. The existing privacy protection methods cannot protect the state information of probabilistic discrete event systems via repeated observations, which represents the information pertaining to system resource configurations. This work introduces differential privacy into the framework of probabilistic labeled Petri nets to solve the problems pertaining to the initial state protection. For two initial states that are adjacent under a specified measure, a state differential privacy verification method is proposed by determining whether the probability distributions of observations generated from adjacent initial states are similar. An external attacker is unlikely to infer the initial state via repeated observations if the system satisfies state differential privacy for certain adjacent initial states. For a probabilistic labeled Petri net, which does not satisfy state differential privacy, a supervisory control method is proposed for enforcement. A maximally permissive controller can be constructed based on the control specification proposed in this paper. Experimental studies show that the method proposed in the paper can effectively protect the privacy of given adjacent initial states.