We consider the problem of linearizing a pseudo-Boolean function $f : \{0,1\}^n \to \mathbb{R}$ by means of $k$ Boolean functions. Such a linearization yields an integer linear programming formulation with only $k$ auxiliary variables. This motivates the definition of the linarization complexity of $f$ as the minimum such $k$. Our theoretical contributions are the proof that random polynomials almost surely have a high linearization complexity and characterizations of its value in case we do or do not restrict the set of admissible Boolean functions. The practical relevance is shown by devising and evaluating integer linear programming models of two such linearizations for the low auto-correlation binary sequences problem. Still, many problems around this new concept remain open.

翻译：我们考虑通过$k$个布尔函数线性化伪布尔函数$f : \{0,1\}^n \to \mathbb{R}$的问题。此类线性化可产生仅需$k个辅助变量的整数线性规划公式。这引出了$f$的线性化复杂度的定义，即满足条件的最小$k$值。我们的理论贡献包括：证明随机多项式几乎必然具有高线性化复杂度，以及在允许或限制布尔函数集合的情况下对其值的特征刻画。通过为低自相关二进制序列问题设计并评估两种此类线性化的整数线性规划模型，展示了该新概念的实际相关性。然而，围绕这一新概念的诸多问题仍有待解决。