A finite CSP could be solved by an exhaustive generate-and-test algorithm. The assignment space, $D$, is the set of total assignments. The algorithm returns one model or all models.

The generate-and-test algorithm to find one model is as follows: check each total assignment in turn; if an assignment is found that satisfies all of the constraints, return that assignment. A generate-and-test algorithm to find all models is the same except, instead of returning the first model found, it saves all of the models found.

If each of the $n$ variable domains has size $d$, then $D$ has $d^n$ elements. If there are $e$ constraints, the total number of constraints tested is $O(e{d}^n)$. As $n$ becomes large, this very quickly becomes intractable, and so we must find alternative solution methods.