The verification of codiagnosability in the case of dynamic observations

We consider the verification of the properties of diagnosability and codiagnosability in discrete event systems where observations are dynamic. Instead of having a fixed set of observable events, it is assumed that the observability properties of an event are state-dependent: an event occurrence at a state will be observable to a diagnosing agent if that agent activates in time the sensor corresponding to the event or receives a communication about the occurrence of the event. In this context, the known polynomial-complexity tests based on verifier automata for the properties of diagnosability and codiagnosability with fixed observable event set(s) are no longer directly applicable. We develop a new testing procedure that can handle state-based dynamic observations and remains of polynomial complexity in the state space of the system. This new testing procedure employs a covering of the state space of the system based on cluster automata, which enhances its computational efficiency. Based on cluster automata, a new type of verifier automaton is built, called the C-VERIFIER. Our use of cluster automata and C-VERIFIERS also yields computational savings in the special case of fixed observable event sets.