On finite memory observability of a class of systems over finite alphabets with linear dynamics

In this paper, we consider systems over finite alphabets with linear internal dynamics and quantized output. We motivate the need for a new notion of observability for this class of systems, and we propose a new definition of finite memory observability. The observers are drawn from the class of deterministic finite state machines, with the objective of estimating the system state for the purpose of output prediction. We derive both necessary and sufficient conditions for the system to be finite memory observable, and we illustrate with examples.