Undecidable problems of decentralized observation and control

We introduce a notion of decentralized observability for discrete-event systems, which we call joint observability. We prove that checking joint observability of a regular language w.r.t. one observer is decidable, whereas for two (or more) observers the problem becomes undecidable. Based on this result, we show that a related decentralized control problem is also undecidable. We finally provide an extensive study relating our work to existing work in the literature