Decentralized observability of discrete event systems with synchronizations

This paper deals with the problem of decentralized observability of discrete event systems. We consider a set of sites each capable of observing a subset of the total event set. When a synchronization occurs, each site transmits its own observation to a coordinator that decides if the word observed belongs to a reference language K or not. Two different properties are studied: uniform q-observability and q-sync observability. It is proved that both properties are decidable for regular languages. Finally, under the assumption that languages K and L are regular, and all the events are observable by at least one site, we propose a procedure to determine the instants at which synchronization should occur to detect the occurrence of any word not in K, as soon as it occurs. The advantage of the proposed approach is that most of the burdensome computations can be moved off-line.