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.

翻译：我们引入了多途径(或分支/非确定性)同系物环绕多途径(或分支/非确定性)的多孔变量概念;这些异系物不一定是二次曲线,事实上可以包含无限多的“洞 ” 。 然而,我们表明,在许多情况下,这种异系物可以自动合成,此外,还可以用于解决(不可接触的)不同种类有趣的同系物环和目标集的问题。