New results and connections between the cover problem, the compensator problem and realization theory: The scalar case

We investigate the cover problem and a certain compensator problem, which turn out to be equivalent. It is first shown that the (minimal) solutions of the cover problem are in bijective correspondence with the (minimal) partial realizations of an appropriately defined sequence. By elaborating on this result, we obtain a direct, polynomial solution of the compensator problem, which is given in terms of closed formulae.