On consistent reduction in discrete-event systems

In this paper we develop a general framework, called 'consistent reduction' for formalizing and solving a class of minimization/reduction problems in discrete-event systems. Given an arbitrary finite-state automaton and a binary relation on its state set, we propose a consistent reduction procedure that generates a reduced automaton, preserving certain special properties of the original automaton. The key concept of the consistent reduction procedure is the reduction cover; in each cell of this cover, any two states, as well as their future states reached by the same system trajectories, satisfy the binary relation. We demonstrate the developed general framework on a reduction problem in state estimation.