  We consider a class of systems over finite alphabets, namely discrete-time
systems with linear dynamics and a finite input alphabet. We formulate a notion
of finite uniform bisimulation, and motivate and propose a notion of regular
finite uniform bisimulation. We derive sufficient conditions for the existence
of finite uniform bisimulations, and propose and analyze algorithms to compute
finite uniform bisimulations when the sufficient conditions are satisfied. We
investigate the necessary conditions, and conclude with a set of illustrative
examples.
