  Zonotopes are becoming an increasingly popular set representation for formal
verification techniques. This is mainly due to their efficient representation
and their favorable computational complexity of important operations in
high-dimensional spaces. In particular, zonotopes are closed under Minkowski
addition and linear maps, which can be very efficiently implemented.
Unfortunately, zonotopes are not closed under Minkowski difference for
dimensions greater than two. However, we present an algorithm that efficiently
computes a halfspace representation of the Minkowski difference of two
zonotopes. In addition, we present an efficient algorithm that computes an
approximation of the Minkowski difference in generator representation. The
efficiency of the proposed solution is demonstrated by numerical experiments.
These experiments show a reduced computation time in comparison to that when
first the halfspace representation of zonotopes is obtained and the Minkowski
difference is performed subsequently.
