This paper has three objectives. The first objective is to provide a simpler proof concerning a
sufficient condition due to Ferfera under which bilinearity is preserved for cascade
interconnections. The next objective is to provide a specific counterexample to show that this
condition does not apply to the feedback connection. The final objective is to show that the
well-known correspondence between rational series and formal power series recognized by
weighted finite-state automata can be generalized to produce a correspondence between …