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：考虑通过$k$个布尔函数对伪布尔函数$f : \{0,1\}^n \to \mathbb{R}$进行线性化的问题。此类线性化可得到仅含$k个辅助变量的整数线性规划形式，从而自然引出将$f的线性化复杂度定义为该最小值$k$。我们的理论贡献在于：证明了随机多项式几乎必然具有高线性化复杂度，并刻画了在限制或不限制可容许布尔函数集合时该复杂度的取值。实际意义体现在：针对低自相关二元序列问题，设计并评估了两种此类线性化的整数线性规划模型。然而，这一新概念仍存在许多未解决问题。