# Forward checking

Formally, let $LaTeX: N = (X, D, C)$ be a binary constraint network and $LaTeX: Y \subseteq X$ such that $LaTeX: |D(x_i)| = 1$ for all $LaTeX: x_i \in Y$. $LaTeX: N$ is forward checking consistent according to the instantiation $LaTeX: I$ on $LaTeX: Y$ iff $LaTeX: I$ is locally consistent and for all $LaTeX: x_i \in Y$, for all $LaTeX: x_j \in X \setminus Y$, for all $LaTeX: c(x_i, x_j) \in C$, $LaTeX: c(x_i, x_j)$ is arc consistent.