We present an alternative Double Description representation for the domain of NNC (not necessarily closed) polyhedra, together with the corresponding Chernikova-like conversion procedure. The representation uses no slack variable at all and provides a solution to a few technical issues caused by the encoding of an NNC polyhedron as a closed polyhedron in a higher dimension space. We then reconstruct the abstract domain of NNC polyhedra, providing all the operators needed to interface it with commonly available static analysis tools: while doing this, we highlight the efficiency gains enabled by the new representation and we show how the canonicity of the new representation allows for the specification of proper, semantic widening operators. A thorough experimental evaluation shows that our new abstract domain achieves significant efficiency improvements with respect to classical implementations for NNC polyhedra.

我们为NNC（不一定是封闭的）多面体域提供了一种替代的Double Description表示形式，以及相应的类似Chernikova的转换过程。该表示形式完全不使用松弛变量，并提供了解决一些技术问题的方法，这些问题是由NNC多面体编码为高维空间中的封闭多面体而引起的。然后，我们重构NNC多面体的抽象域，为将其与常用的静态分析工具进行交互提供所需的所有运算符：在此过程中，我们突出显示了新表示形式所带来的效率提高，并展示了新表示形式的规范性如何用于规范适当的语义扩展运算符。