State-event observers for labeled transition systems

In many discrete-event systems (DES) both state and event information are of importance to the systems designer. As a first step towards obtaining hierarchical models of systems, the behavior of DESs with unobservable transitions and state output maps is considered. Observers for deterministic DES are generalized to nondeterministic DES and characterized using the join semi-lattice of compatible partitions of a transition system. This characterization points to efficient algorithms for computing both strong and weak state-event observers as solutions to the relational coarsest partition problem. The strong and weak observation equivalences of Milner are shown to be special cases of our observers under the trivial (constant) state output map