Co-detectability of multi-agent discrete event systems

In this paper decentralized detectability is investigated. Our goal is to determine the current state of the system with a set of local agents. Each agent has a limited observation and does not share its observations with other agents. We say that a system is co-detectable if after some finite number of observations, at least one local agent can determine the current state of the system. Similar to the centralized case, we define four types of co-detectablities: strong co-detectablity, (weak) co-detectablity, strong periodic co-detectablity and (weak) periodic co-detectablity. In order to study decentralized detectabilities, we introduce and construct a co-observer to describe the state estimations of all the local agents. Co-observer can be used to check all four types of co-detectabilities. Furthermore, we introduce and construct a co-detector to check strong co-detectability and strong periodic co-detectability. Co-detector is nondeterministic and can be constructed in polynomial time and space.