In this paper, we deal with the ultimately-periodic finite interval temporal logic model checking problem. The problem has been shown to be in PTIME for full Halpern and Shoham's interval temporal logic (HS for short) over finite models, as well as for the HS fragment featuring a modality for Allen relation meets and metric constraints over non-sparse ultimately-periodic (finite) models, that is, over ultimately-periodic models whose representation is polynomial in their size. Here, we generalize the latter result to the case of sparse ultimately-periodic models.
