  We introduce the notion of porous invariants for multipath (or
branching/nondeterministic) affine loops over the integers; these invariants
are not necessarily convex, and can in fact contain infinitely many 'holes'.
Nevertheless, we show that in many cases such invariants can be automatically
synthesised, and moreover can be used to settle (non-)reachability questions
for various interesting classes of affine loops and target sets.
