Stability of deterministic finite state machines

We approach deterministic finite state machines from a systems point of view and we consider three notions of input/output stability: finite gain input/output stability, external stability and incremental input/output stability, as they apply to this class of systems. We propose linear programming based algorithms for verifying stability of a system, or lack thereof, in the finite gain input/output and the external sense. We show that for this class of systems, incremental input/output stability and external stability are equivalent notions, stronger than the notion of finite gain input/output stability.