Immediate observability of discrete event systems with application to user-interface design

A human interacting with a hybrid system is often presented, through information displays, with a simplified representation of the underlying system. This interface should not overwhelm the human with unnecessary information, and thus usually contains only a subset of information about the true system model, yet, if properly designed, represents an abstraction of the true system which the human is able to use to safely interact with the system [M. Heymann and A. Degani, 2002]. For cases in which the human interacts with all or part of the system from a remote location, and communication has a high cost, the need for a simple abstraction, which reduces the amount of information that must be transmitted, is of the utmost importance. The user should be able to immediately determine the actual state of the system, based on the information displayed through the interface. In this paper, we derive conditions for immediate observability in which the current state of the system can be unambiguously reconstructed from the output associated with the current state and the last or next event. Then, we show how to construct a discrete event system output function, which makes a system immediately observable, and apply this to a reduced state machine, which represents an interface.