# Arc consistency

A consistency property in constraint programming used as a basis for inference. A variable $LaTeX: x$ is arc-consistent with another variable $LaTeX: y$ if for every value in the domain of $LaTeX: x$ there exists a value in the domain of $LaTeX: y$ such that the binary constraint $LaTeX: C(x,y)$ is satisfied. A binary constraint $LaTeX: C(x,y)$ is arc-consistent if both of its variables are arc-consistent with respect to each other.