  In this paper, we study the finite satisfiability problem for the logic BE
under the homogeneity assumption. BE is the cornerstone of Halpern and Shoham's
interval temporal logic, and features modal operators corresponding to the
prefix (a.k.a. "Begins") and suffix (a.k.a. "Ends") relations on intervals. In
terms of complexity, BE lies in between the "Chop logic C", whose
satisfiability problem is known to be non-elementary, and the PSPACE-complete
interval logic D of the sub-interval (a.k.a. "During") relation. BE was shown
to be EXPSPACE-hard, and the only known satisfiability procedure is primitive
recursive, but not elementary. Our contribution consists of tightening the
complexity bounds of the satisfiability problem for BE, by proving it to be
EXPSPACE-complete. We do so by devising an equi-satisfiable normal form with
boundedly many nested modalities. The normalization technique resembles Scott's
quantifier elimination, but it turns out to be much more involved due to the
limitations enforced by the homogeneity assumption.
