Model checking is one of the most powerful and widespread
tools for system verification with applications in many areas
of computer science and artificial intelligence. The large majority
of model checkers deal with properties expressed in
point-based temporal logics, such as LTL and CTL. However,
there exist relevant properties of systems which are inherently
interval-based. Model checking algorithms for interval
temporal logics (ITLs) have recently been proposed to check
interval properties of computations. As the model checking
problem for full Halpern and Shoham’s ITL (HS for short)
turns out to be decidable, but computationally heavy, research
has focused on its well-behaved fragments. In this paper, we
provide an almost final picture of the computational complexity
of model checking for HS fragments with modalities for
(a subset of) Allen’s relations meets, met by, starts, and ends
