Arc-Consistency (AC3) and one Challenges?

Question

In Applying Arc-Consistency (AC3) algorithms on one Constraint Satisfaction Problem, if domain of one variable be empty, what is the next step?

1) halt.

2) do backtrack.

3) start from another initial state.

4) it depends on that we are in which step.

Solution (4). I think (1) is true because it mean we cannot find any consistent assignment and halt. anyone can describe why (4) is true?

Answer 1

With the particular algorithm you're using, if the domain of a variable shrinks until it is empty, then it means that the constraint problem has no solutions. Therefore the algorithm should halt in the failure state.