A nonhomogeneous system of linear recurrence equations can be recognized by an automaton A over a one-letter alphabet A = {z}. Conversely, the automaton A generates precisely this nonhomogeneous system of linear recurrence equations. We present the solutions of these systems and apply the z-transform to these solutions to obtain their series representation. Finally, we show some results that simplify the series representation of the z-transform of these solutions. We consider single systems as well as the composition of two systems.

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