Decentralized opacity of discrete event systems

In this paper, we investigate opacity of discrete event systems in a decentralized framework with several agents, each of them performing its observation of the system. We consider two cases, one without coordination among agents and one with coordination. Both cases are useful because many systems used today are distributed over a network, some with agents coordinating among themselves and some without. We introduce general definitions of decentralized opacity for both cases. The definitions are based on languages. Therefore, they are flexible and can include other properties of discrete event systems as special cases. In particular, we show that co-observability used in supervisory control is a special case of decentralized opacity. We illustrate the usefulness of decentralized opacity by applying it in solving an interesting security problem in computer systems.