扩展复杂性的一般化，它捕获了$P$
A generalization of extension complexity that captures $P$
摘要：
本文给出了多面体$Q$扩张复杂性的一个推广。一方面，它是足够的一般性，使所有的问题在$P$可以制定为线性规划的多项式大小的扩展复杂性。另一方面，它仍然允许非多项式下界证明$NP$ -硬问题独立于是否$P=NP$。这种泛化称为$H$ -free扩展复杂度，允许在计算$Q$的扩展复杂度时排除一组有效的不等式$H$。给出了硬匹配问题（当$H$为奇集不等式时）和旅行商问题（当$H$为子图消去约束时）的无$H$扩张复杂性的结果.
英文摘要：
In this paper we propose a generalization of the extension complexity of a polyhedron $Q$. On the one hand it is general enough so that all problems in $P$ can be formulated as linear programs with polynomial size extension complexity. On the other hand it still allows non-polynomial lower bounds to be proved for $NP$-hard problems independently of whether or not $P=NP$. The generalization, called $H$-free extension complexity, allows for a set of valid inequalities $H$ to be excluded in computing the extension complexity of $Q$. We give results on the $H$-free extension complexity of hard matching problems (when $H$ are the odd set inequalities) and the traveling salesman problem (when $H$ are the subtour elimination constraints).
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