  We define and study a new abstract domain which is a fine-grained combination
of zonotopes with polyhedric domains such as the interval, octagon, linear
templates or polyhedron domain. While abstract transfer functions are still
rather inexpensive and accurate even for interpreting non-linear computations,
we are able to also interpret tests (i.e. intersections) efficiently. This
fixes a known drawback of zonotopic methods, as used for reachability analysis
for hybrid sys- tems as well as for invariant generation in abstract
interpretation: intersection of zonotopes are not always zonotopes, and there
is not even a best zonotopic over-approximation of the intersection. We
describe some examples and an im- plementation of our method in the APRON
library, and discuss some further in- teresting combinations of zonotopes with
non-linear or non-convex domains such as quadratic templates and maxplus
polyhedra.
