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Abstract Opacity is an important system property that is particularly relevant in the context of system security and privacy. A system is considered opaque if the predefined secret behavior of the system is not leaked to an external intruder. In this work, the opacity property is studied in the framework of labeled Petri nets (LPNs). The secret in an LPN system is characterized by a subset of reachable markings. Firstly, an opacity basis reachability graph (OBRG) containing opacity information of the system is developed to denote a system’s reachability set without computing all reachable states. Then the observer of the OBRG is computed, based on which a necessary and sufficient condition is derived to verify the opacity of the LPN system. Finally, given an LPN that does not satisfy the opacity, a maximally permissive supervisor is introduced to guarantee that the controlled system is opaque.
Xie et al. (2024) studied this question.