  The expressive power of interval temporal logics (ITLs) makes them one of the
most natural choices in a number of application domains, ranging from the
specification and verification of complex reactive systems to automated
planning. However, for a long time, because of their high computational
complexity, they were considered not suitable for practical purposes. The
recent discovery of several computationally well-behaved ITLs has finally
changed the scenario.
  In this paper, we investigate the finite satisfiability and model checking
problems for the ITL D, that has a single modality for the sub-interval
relation, under the homogeneity assumption (that constrains a proposition
letter to hold over an interval if and only if it holds over all its points).
We first prove that the satisfiability problem for D, over finite linear
orders, is PSPACE-complete, and then we show that the same holds for its model
checking problem, over finite Kripke structures. In such a way, we enrich the
set of tractable interval temporal logics with a new meaningful representative.
