Pseudo-Boolean functions

Let f: \mathbb{B}^{n} \to \mathbb{R}. Then f can be written as

\[f(\mathbf{x}) = \sum_{\omega \subseteq [n]} c_{\omega} \prod_{j \in \omega} x_{j}\]

where $c_{\omega} \in \mathbb{R}$ and $x_{j} \in \{ 0, 1 \}$ for all $j \in [n] = \{ 1, \dots, n \}$.